diff --git "a/20211029_101219/answers-students.wa" "b/20211029_101219/answers-students.wa"
new file mode 100644--- /dev/null
+++ "b/20211029_101219/answers-students.wa"
@@ -0,0 +1,12015 @@
+
+// both bulbs a and c still have a closed path
+// Bulbs A and C are still in closed paths
+
+1 both :
+2 bulbs :
+3 a :
+4 and :
+5 c :
+6 still :
+7 have :
+8 a :
+9 closed :
+10 path :
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+
+
+2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 and the positive terminal are connected.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// positive battery is seperated by a gap from terminal 2
+// Terminal 2 and the positive terminal are separated by the gap
+
+1 positive :
+2 battery :
+3 is :
+4 seperated :
+5 by :
+6 a :
+7 gap :
+8 from :
+9 terminal :
+10 2 :
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+5 6 7 <==> 9 10 11 // EQUI // 5 //
+8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// There is no difference between the two terminals.
+// The terminals are in the same state.
+
+1 There :
+2 is :
+3 no :
+4 difference :
+5 between :
+6 the :
+7 two :
+8 terminals. :
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+2 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the switch has to be contained in the same path as the bulb and the battery
+// The switch and the bulb have to be in the same path
+
+1 the :
+2 switch :
+3 has :
+4 to :
+5 be :
+6 contained :
+7 in :
+8 the :
+9 same :
+10 path :
+11 as :
+12 the :
+13 bulb :
+14 and :
+15 the :
+16 battery :
+
+
+1 The :
+2 switch :
+3 and :
+4 the :
+5 bulb :
+6 have :
+7 to :
+8 be :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 // EQUI // 5 //
+11 <==> 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// there is a gap in terminal 1
+// Terminals 1 and 2 are in the same electrical state
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 terminal :
+7 1 :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 in :
+7 the :
+8 same :
+9 electrical :
+10 state :
+
+
+5 6 7 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// The battery uses the chemical reation to create voltage
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 The :
+2 battery :
+3 uses :
+4 the :
+5 chemical :
+6 reation :
+7 to :
+8 create :
+9 voltage :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 <==> 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+9 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// a batter uses a chemical reaction to create voltage
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 a :
+2 batter :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 create :
+9 voltage :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+4 5 6 <==> 4 5 6 // EQUI // 5 //
+9 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the battery alone is in a closed path
+// The battery is contained in a path which does not contain any other components
+
+1 the :
+2 battery :
+3 alone :
+4 is :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 which :
+9 does :
+10 not :
+11 contain :
+12 any :
+13 other :
+14 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Because there is a gap in the circuit.
+// there is a gap in the circuit
+
+1 Because :
+2 there :
+3 is :
+4 a :
+5 gap :
+6 in :
+7 the :
+8 circuit. :
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 the :
+7 circuit :
+
+
+2 <==> 1 // EQUI // 5 //
+4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and B are not within the same path as bulb C.
+// Bulb C is in a separate path
+
+1 Bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 not :
+7 within :
+8 the :
+9 same :
+10 path :
+11 as :
+12 bulb :
+13 C. :
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+5 6 <==> 3 // EQUI // 5 //
+11 <==> 4 5 6 7 // EQUI // 5 //
+12 13 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// because there was two negative connections
+// Terminals 1 and 2 are connected
+
+1 because :
+2 there :
+3 was :
+4 two :
+5 negative :
+6 connections :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 connected :
+
+
+2 <==> 5 6 // EQUI // 5 //
+4 5 6 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// bulb a is on a closed path with the battery
+// there is a path containing A and a different path containing B and C
+
+1 bulb :
+2 a :
+3 is :
+4 on :
+5 a :
+6 closed :
+7 path :
+8 with :
+9 the :
+10 battery :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A :
+7 and :
+8 a :
+9 different :
+10 path :
+11 containing :
+12 B :
+13 and :
+14 C :
+
+
+1 2 <==> 6 // EQUI // 5 //
+4 5 6 7 <==> 3 4 // EQUI // 5 //
+8 9 10 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// the other terminals are connected to the positive terminal.
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 the :
+2 other :
+3 terminals :
+4 are :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 terminal. :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 <==> 1 2 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 // EQUI // 5 //
+6 7 8 9 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The bulb takes away the path.
+// there is an open path
+
+1 The :
+2 bulb :
+3 takes :
+4 away :
+5 the :
+6 path. :
+
+
+1 there :
+2 is :
+3 an :
+4 open :
+5 path :
+
+
+5 6 <==> 1 // EQUI // 5 //
+
+
+
+
+
+// There is no gap between the positive terminal and terminal 4
+// Terminal 4 and the positive terminal are not separated by the gap
+
+1 There :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 positive :
+8 terminal :
+9 and :
+10 terminal :
+11 4 :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+1 <==> 10 11 12 // EQUI // 5 //
+5 6 7 8 9 10 11 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulb a created a gap
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 Bulb :
+2 a :
+3 created :
+4 a :
+5 gap :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 2 <==> 2 3 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to the positive terminal of the battery
+// Terminal 6 and the positive terminal are connected
+
+1 terminal :
+2 6 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 terminal :
+9 of :
+10 the :
+11 battery :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the bulb is in a closed circuit
+// the battery is in an open path
+
+1 the :
+2 bulb :
+3 is :
+4 in :
+5 a :
+6 closed :
+7 circuit :
+
+
+1 the :
+2 battery :
+3 is :
+4 in :
+5 an :
+6 open :
+7 path :
+
+
+3 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// The circuit is not closed around the battery.
+// The battery in 2 is not in a closed path
+
+1 The :
+2 circuit :
+3 is :
+4 not :
+5 closed :
+6 around :
+7 the :
+8 battery. :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+3 4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the bulb is not contained in a closed path.
+// The battery is contained in a path which does not contain any other components
+
+1 the :
+2 bulb :
+3 is :
+4 not :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path. :
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 which :
+9 does :
+10 not :
+11 contain :
+12 any :
+13 other :
+14 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+6 7 8 9 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// There is a gap in the circuit.
+// there is a gap in a circuit
+
+1 There :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 the :
+7 circuit. :
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 a :
+7 circuit :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulb B and bulb C are still on closed paths with the battery.
+// bulbs A and B are still in closed paths with the battery
+
+1 Bulb :
+2 B :
+3 and :
+4 bulb :
+5 C :
+6 are :
+7 still :
+8 on :
+9 closed :
+10 paths :
+11 with :
+12 the :
+13 battery. :
+
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Bulb A has a closed pathway
+// Bulb A was still contained in the same closed path with the battery.
+
+1 Bulb :
+2 A :
+3 has :
+4 a :
+5 closed :
+6 pathway :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 6 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// bulbs a and c are not in the same closed path as bulb b
+// Bulb B is in a separate path
+
+1 bulbs :
+2 a :
+3 and :
+4 c :
+5 are :
+6 not :
+7 in :
+8 the :
+9 same :
+10 closed :
+11 path :
+12 as :
+13 bulb :
+14 b :
+
+
+1 Bulb :
+2 B :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+5 6 <==> 3 // EQUI // 5 //
+7 8 9 10 11 <==> 4 5 6 7 // EQUI // 5 //
+12 <==> 3 // EQUI // 5 //
+13 14 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Only one terminal is involved in the circuit.
+// The battery in 2 is not in a closed path
+
+1 Only :
+2 one :
+3 terminal :
+4 is :
+5 involved :
+6 in :
+7 the :
+8 circuit. :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+4 5 <==> 7 8 9 10 // EQUI // 5 //
+6 7 8 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// there was closed paths between the battery
+// Bulb A was still contained in the same closed path with the battery.
+
+1 there :
+2 was :
+3 closed :
+4 paths :
+5 between :
+6 the :
+7 battery :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+2 <==> 5 // EQUI // 5 //
+3 4 <==> 6 7 8 9 10 // EQUI // 5 //
+5 6 7 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// the gap separates the positive battery terminal from terminal 2
+// Terminal 2 and the positive terminal are separated by the gap
+
+1 the :
+2 gap :
+3 separates :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 from :
+9 terminal :
+10 2 :
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 9 10 11 // EQUI // 5 //
+3 <==> 7 8 // EQUI // 5 //
+4 5 6 7 8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulb a, bulb b, and bulb c are contained in differentclosed paths.
+// A and C are in different paths with the battery
+
+1 bulb :
+2 a, :
+3 bulb :
+4 b, :
+5 and :
+6 bulb :
+7 c :
+8 are :
+9 contained :
+10 in :
+11 differentclosed :
+12 paths. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 // EQUI // 5 //
+8 9 <==> 4 // EQUI // 5 //
+10 11 12 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// If any bulb is out, it affects the whole system and everything is blocked from the battery.
+// each bulb is in its own path
+
+1 If :
+2 any :
+3 bulb :
+4 is :
+5 out, :
+6 it :
+7 affects :
+8 the :
+9 whole :
+10 system :
+11 and :
+12 everything :
+13 is :
+14 blocked :
+15 from :
+16 the :
+17 battery. :
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+6 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// it is not in the same path.
+// Bulb A is still in a closed path with the battery
+
+1 it :
+2 is :
+3 not :
+4 in :
+5 the :
+6 same :
+7 path. :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// There will be a gap in the path
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 There :
+2 will :
+3 be :
+4 a :
+5 gap :
+6 in :
+7 the :
+8 path :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+2 3 <==> 1 // EQUI // 5 //
+4 5 6 7 8 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Bulb B and C are still contained in a path with the battery
+// bulbs B and C are still in closed paths with the battery
+
+1 Bulb :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 contained :
+8 in :
+9 a :
+10 path :
+11 with :
+12 the :
+13 battery :
+
+
+1 bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulbs a and c are still contained in a closed path with the battery.
+// Bulbs A and C are still in closed paths with the battery
+
+1 bulbs :
+2 a :
+3 and :
+4 c :
+5 are :
+6 still :
+7 contained :
+8 in :
+9 a :
+10 closed :
+11 path :
+12 with :
+13 the :
+14 battery. :
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Terminal one is not connected to the positive battery terminal
+// Terminal 1 and the positive terminal are not connected
+
+1 Terminal :
+2 one :
+3 is :
+4 not :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 battery :
+10 terminal :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulb A and switch Z are in a closed path
+// Bulb A is still contained in a closed path with the battery and switch Z.
+
+1 bulb :
+2 A :
+3 and :
+4 switch :
+5 Z :
+6 are :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 Z. :
+
+
+1 2 3 4 5 <==> 1 2 // EQUI // 5 //
+6 <==> 4 // EQUI // 5 //
+7 8 9 10 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Terminal 5 is connected to the postitive battery terminal
+// Terminal 5 and the positive terminal are connected
+
+1 Terminal :
+2 5 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 postitive :
+8 battery :
+9 terminal :
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Terminal 6 is connected to the positive battery terminal
+// Terminal 6 and the positive terminal are connected
+
+1 Terminal :
+2 6 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 battery :
+9 terminal :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the red x means that the circuit is not safe.
+// there is a short circuit
+
+1 the :
+2 red :
+3 x :
+4 means :
+5 that :
+6 the :
+7 circuit :
+8 is :
+9 not :
+10 safe. :
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+6 7 <==> 1 // EQUI // 5 //
+
+
+
+
+
+// both bulbs B and C are in the same path as bulb A
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 both :
+2 bulbs :
+3 B :
+4 and :
+5 C :
+6 are :
+7 in :
+8 the :
+9 same :
+10 path :
+11 as :
+12 bulb :
+13 A :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+2 3 4 5 <==> 6 7 8 9 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+7 8 9 10 <==> 11 12 13 14 // EQUI // 5 //
+11 <==> 1 // EQUI // 5 //
+12 13 <==> 2 3 // EQUI // 5 //
+
+
+
+
+
+// if the electrical state is non-zero you can find the gap in the circuit
+// A non-zero voltage means that there is a gap
+
+1 if :
+2 the :
+3 electrical :
+4 state :
+5 is :
+6 non-zero :
+7 you :
+8 can :
+9 find :
+10 the :
+11 gap :
+12 in :
+13 the :
+14 circuit :
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 there :
+7 is :
+8 a :
+9 gap :
+
+
+6 <==> 1 2 3 // EQUI // 5 //
+10 11 <==> 8 9 // EQUI // 5 //
+
+
+
+
+
+// The battery is contained in a closed circuit and there is nothing in its pathway
+// The battery is contained in a closed path which does not contain any other components
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 circuit :
+9 and :
+10 there :
+11 is :
+12 nothing :
+13 in :
+14 its :
+15 pathway :
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 which :
+10 does :
+11 not :
+12 contain :
+13 any :
+14 other :
+15 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+9 <==> 9 // EQUI // 5 //
+10 <==> 13 14 15 // EQUI // 5 //
+12 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// A terminal is not connected to the positive battery terminal.
+// Terminals 1 and 4 are connected
+
+1 A :
+2 terminal :
+3 is :
+4 not :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 battery :
+10 terminal. :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+6 7 8 9 10 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// there is a gap in the circuit
+// Terminals 1 and 4 are connected
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 the :
+7 circuit :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+2 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal is not seperated by a gap from terminal 5
+// Terminal 5 and the positive terminal are not separated by the gap
+
+1 the :
+2 positive :
+3 terminal :
+4 is :
+5 not :
+6 seperated :
+7 by :
+8 a :
+9 gap :
+10 from :
+11 terminal :
+12 5 :
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 6 <==> 7 8 9 // EQUI // 5 //
+7 8 9 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// You can find where there is a gap
+// Measuring voltage indicates whether two terminals are separated by a gap.
+
+1 You :
+2 can :
+3 find :
+4 where :
+5 there :
+6 is :
+7 a :
+8 gap :
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 whether :
+5 two :
+6 terminals :
+7 are :
+8 separated :
+9 by :
+10 a :
+11 gap. :
+
+
+7 8 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// has to do something with a gap
+// Terminal 2 and the positive terminal are separated by the gap
+
+1 has :
+2 to :
+3 do :
+4 something :
+5 with :
+6 a :
+7 gap :
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+5 6 7 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Because the positive circuit has a voltage of 1.5 volts.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 Because :
+2 the :
+3 positive :
+4 circuit :
+5 has :
+6 a :
+7 voltage :
+8 of :
+9 1.5 :
+10 volts. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+2 3 4 <==> 1 2 3 4 5 6 // EQUI // 5 //
+6 7 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// There is a chemical reaction.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 There :
+2 is :
+3 a :
+4 chemical :
+5 reaction. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+3 4 5 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// when the switch is the in a closed path with the bulb
+// When the switch and the bulb are contained in the same path
+
+1 when :
+2 the :
+3 switch :
+4 is :
+5 the :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 bulb :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+6 7 8 9 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulb b and c are in a closed path
+// B and C are in the same path
+
+1 bulb :
+2 b :
+3 and :
+4 c :
+5 are :
+6 in :
+7 a :
+8 closed :
+9 path :
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 <==> 4 // EQUI // 5 //
+6 7 8 9 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// There is a difference in electrical states.
+// the terminals are not connected
+
+1 There :
+2 is :
+3 a :
+4 difference :
+5 in :
+6 electrical :
+7 states. :
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+5 6 7 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// the bulb will not light
+// there is no gap between the terminals
+
+1 the :
+2 bulb :
+3 will :
+4 not :
+5 light :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+3 4 5 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// bulb a and c are contained on the same path with the battery
+// A and C are not in the same path with the battery
+
+1 bulb :
+2 a :
+3 and :
+4 c :
+5 are :
+6 contained :
+7 on :
+8 the :
+9 same :
+10 path :
+11 with :
+12 the :
+13 battery :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 5 // EQUI // 5 //
+7 8 9 10 <==> 6 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The path does not close
+// the battery is in an open path
+
+1 The :
+2 path :
+3 does :
+4 not :
+5 close :
+
+
+1 the :
+2 battery :
+3 is :
+4 in :
+5 an :
+6 open :
+7 path :
+
+
+1 2 3 4 5 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// The difference between the electrical states is 1.5 volts
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 The :
+2 difference :
+3 between :
+4 the :
+5 electrical :
+6 states :
+7 is :
+8 1.5 :
+9 volts :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// there is still a closed path
+// If bulb A burns out, bulbs B and C are still in a closed path
+
+1 there :
+2 is :
+3 still :
+4 a :
+5 closed :
+6 path :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 bulbs :
+7 B :
+8 and :
+9 C :
+10 are :
+11 still :
+12 in :
+13 a :
+14 closed :
+15 path :
+
+
+2 <==> 10 // EQUI // 5 //
+3 <==> 11 // EQUI // 5 //
+4 5 6 <==> 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// a gap causes a lost connection
+// A non-zero voltage means that the terminals are not connected.
+
+1 a :
+2 gap :
+3 causes :
+4 a :
+5 lost :
+6 connection :
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 the :
+7 terminals :
+8 are :
+9 not :
+10 connected. :
+
+
+3 <==> 4 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal and terminal 6 are connected
+// Terminal 6 and the positive terminal are connected
+
+1 the :
+2 positive :
+3 terminal :
+4 and :
+5 terminal :
+6 6 :
+7 are :
+8 connected :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal is connected to terminal 6
+// Terminal 6 and the positive terminal are connected
+
+1 the :
+2 positive :
+3 terminal :
+4 is :
+5 connected :
+6 to :
+7 terminal :
+8 6 :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Because there is no gap at terminal 1
+// terminal 1 is connected to the negative battery terminal
+
+1 Because :
+2 there :
+3 is :
+4 no :
+5 gap :
+6 at :
+7 terminal :
+8 1 :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 <==> 3 4 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is conncted to the positive terminal
+// Terminal 6 and the positive terminal are connected
+
+1 terminal :
+2 6 :
+3 is :
+4 conncted :
+5 to :
+6 the :
+7 positive :
+8 terminal :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// When the switch is in the same papth as the bulb.
+// When the switch and the bulb are contained in the same path
+
+1 When :
+2 the :
+3 switch :
+4 is :
+5 in :
+6 the :
+7 same :
+8 papth :
+9 as :
+10 the :
+11 bulb. :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and C are in separate paths.
+// A and C are in different paths
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 in :
+7 separate :
+8 paths. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 <==> 4 // EQUI // 5 //
+6 7 8 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb a and bulb b are still in a closed path with the battery.
+// bulbs A and B are still in closed paths with the battery
+
+1 bulb :
+2 a :
+3 and :
+4 bulb :
+5 b :
+6 are :
+7 still :
+8 in :
+9 a :
+10 closed :
+11 path :
+12 with :
+13 the :
+14 battery. :
+
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The positive battery terminal was not separted by a gap from terminal 6
+// Terminal 6 and the positive terminal are not separated by the gap
+
+1 The :
+2 positive :
+3 battery :
+4 terminal :
+5 was :
+6 not :
+7 separted :
+8 by :
+9 a :
+10 gap :
+11 from :
+12 terminal :
+13 6 :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+5 6 7 <==> 7 8 9 // EQUI // 5 //
+8 9 10 <==> 10 11 12 // EQUI // 5 //
+11 12 13 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// A GAP WIL BE CREATED
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 A :
+2 GAP :
+3 WIL :
+4 BE :
+5 CREATED :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 2 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb a and c are contained in different paths with the battery
+// A and C are in different paths with the battery
+
+1 bulb :
+2 a :
+3 and :
+4 c :
+5 are :
+6 contained :
+7 in :
+8 different :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+7 8 9 <==> 5 6 7 // EQUI // 5 //
+10 11 12 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// The positive terminal is connected to terminal 4.
+// Terminal 4 and the positive terminal are connected
+
+1 The :
+2 positive :
+3 terminal :
+4 is :
+5 connected :
+6 to :
+7 terminal :
+8 4. :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// not contained inthe same path
+// If C burns out, then A and B are still in a closed path.
+
+1 not :
+2 contained :
+3 inthe :
+4 same :
+5 path :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+3 4 5 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb c does not create a gap in the path for bulb b and a
+// If C is damaged, A and B are still in a closed path
+
+1 bulb :
+2 c :
+3 does :
+4 not :
+5 create :
+6 a :
+7 gap :
+8 in :
+9 the :
+10 path :
+11 for :
+12 bulb :
+13 b :
+14 and :
+15 a :
+
+
+1 If :
+2 C :
+3 is :
+4 damaged, :
+5 A :
+6 and :
+7 B :
+8 are :
+9 still :
+10 in :
+11 a :
+12 closed :
+13 path :
+
+
+1 2 <==> 2 // EQUI // 5 //
+6 7 8 9 10 <==> 10 11 12 13 // EQUI // 5 //
+11 12 13 14 15 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// becuase the other terminals are connected to the positive battery terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 becuase :
+2 the :
+3 other :
+4 terminals :
+5 are :
+6 connected :
+7 to :
+8 the :
+9 positive :
+10 battery :
+11 terminal :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 <==> 6 7 // EQUI // 5 //
+7 8 9 10 11 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because terminal one and the positive battery terminal are on a closed path
+// terminal 1 is connected to the negative battery terminal
+
+1 because :
+2 terminal :
+3 one :
+4 and :
+5 the :
+6 positive :
+7 battery :
+8 terminal :
+9 are :
+10 on :
+11 a :
+12 closed :
+13 path :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+2 3 4 5 6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Battery will always have voltage.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 Battery :
+2 will :
+3 always :
+4 have :
+5 voltage. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the terminals are not connected
+// Terminal 1 and the positive terminal are not connected
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal is connected to terminal 6
+// Terminal 6 and the positive terminal are connected
+
+1 the :
+2 positive :
+3 battery :
+4 terminal :
+5 is :
+6 connected :
+7 to :
+8 terminal :
+9 6 :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+5 6 <==> 7 8 // EQUI // 5 //
+7 8 9 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulb a was on a closed path
+// Bulb A is still contained in a closed path with the battery.
+
+1 bulb :
+2 a :
+3 was :
+4 on :
+5 a :
+6 closed :
+7 path :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 5 // EQUI // 5 //
+4 5 6 7 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Because terminal 4 is connected to the negative terminal
+// Terminal 4 and the positive battery terminal are in the same electrical state
+
+1 Because :
+2 terminal :
+3 4 :
+4 is :
+5 connected :
+6 to :
+7 the :
+8 negative :
+9 terminal :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 are :
+9 in :
+10 the :
+11 same :
+12 electrical :
+13 state :
+
+
+2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb c is in its own pathway
+// Bulb C is in a separate path
+
+1 bulb :
+2 c :
+3 is :
+4 in :
+5 its :
+6 own :
+7 pathway :
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// the voltage is nearest the burnt out bulb
+// Measuring voltage indicates the place where the electrical state changes due to a damaged bulb.
+
+1 the :
+2 voltage :
+3 is :
+4 nearest :
+5 the :
+6 burnt :
+7 out :
+8 bulb :
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 damaged :
+15 bulb. :
+
+
+1 2 <==> 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 8 <==> 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// You needed both a battery and a blub with the same path, and the path must be closed
+// there is a closed path containing both the bulb and a battery
+
+1 You :
+2 needed :
+3 both :
+4 a :
+5 battery :
+6 and :
+7 a :
+8 blub :
+9 with :
+10 the :
+11 same :
+12 path, :
+13 and :
+14 the :
+15 path :
+16 must :
+17 be :
+18 closed :
+
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path :
+6 containing :
+7 both :
+8 the :
+9 bulb :
+10 and :
+11 a :
+12 battery :
+
+
+4 5 6 7 8 <==> 8 9 10 11 12 // EQUI // 5 //
+9 10 11 12 <==> 7 // EQUI // 5 //
+13 <==> 6 // EQUI // 5 //
+14 15 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Because the battery runs in a closed circuit.
+// there is an incomplete circuit
+
+1 Because :
+2 the :
+3 battery :
+4 runs :
+5 in :
+6 a :
+7 closed :
+8 circuit. :
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+1 <==> 2 // EQUI // 5 //
+5 6 7 8 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// If bulb B is damaged, then the circut is no longer closed.
+// there is no closed path
+
+1 If :
+2 bulb :
+3 B :
+4 is :
+5 damaged, :
+6 then :
+7 the :
+8 circut :
+9 is :
+10 no :
+11 longer :
+12 closed. :
+
+
+1 there :
+2 is :
+3 no :
+4 closed :
+5 path :
+
+
+9 <==> 2 // EQUI // 5 //
+12 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// terminal 1, terminal 2, and terminal 3 are connected o the negative battery
+// Terminals 1, 2 and 3 are connected to the negative battery terminal
+
+1 terminal :
+2 1, :
+3 terminal :
+4 2, :
+5 and :
+6 terminal :
+7 3 :
+8 are :
+9 connected :
+10 o :
+11 the :
+12 negative :
+13 battery :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 // EQUI // 5 //
+8 9 <==> 6 7 // EQUI // 5 //
+10 11 12 13 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// "Because it didn""t cause a gap."
+// each bulb is in its own path
+
+1 "Because :
+2 it :
+3 didn""t :
+4 cause :
+5 a :
+6 gap." :
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+2 <==> 4 5 6 7 // EQUI // 5 //
+5 6 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// because there is a gap between terminal 1 and terminal 6.
+// There is a gap between terminals 1 and 6
+
+1 because :
+2 there :
+3 is :
+4 a :
+5 gap :
+6 between :
+7 terminal :
+8 1 :
+9 and :
+10 terminal :
+11 6. :
+
+
+1 There :
+2 is :
+3 a :
+4 gap :
+5 between :
+6 terminals :
+7 1 :
+8 and :
+9 6 :
+
+
+2 <==> 1 // EQUI // 5 //
+3 <==> 2 // EQUI // 5 //
+4 5 <==> 3 4 // EQUI // 5 //
+6 7 8 9 10 11 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because bulbs b and c are on a closed path with the battery
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+1 because :
+2 bulbs :
+3 b :
+4 and :
+5 c :
+6 are :
+7 on :
+8 a :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery :
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 <==> 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 13 // EQUI // 5 //
+11 12 13 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// The switch determines whether the path is open or closed.
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 The :
+2 switch :
+3 determines :
+4 whether :
+5 the :
+6 path :
+7 is :
+8 open :
+9 or :
+10 closed. :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 12 13 // EQUI // 5 //
+3 <==> 14 // EQUI // 5 //
+5 6 <==> 8 9 10 11 // EQUI // 5 //
+7 <==> 7 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal is separated by a gap from terminal 4
+// Terminal 4 and the positive battery terminal are in the same electrical state
+
+1 the :
+2 positive :
+3 battery :
+4 terminal :
+5 is :
+6 separated :
+7 by :
+8 a :
+9 gap :
+10 from :
+11 terminal :
+12 4 :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 are :
+9 in :
+10 the :
+11 same :
+12 electrical :
+13 state :
+
+
+1 2 3 4 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// an incomplete circuit would not effect the the electrical state between the terminals.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 an :
+2 incomplete :
+3 circuit :
+4 would :
+5 not :
+6 effect :
+7 the :
+8 the :
+9 electrical :
+10 state :
+11 between :
+12 the :
+13 terminals. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 3 <==> 1 2 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 // EQUI // 5 //
+11 12 13 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// terminals 4, 5, and 6 are connected to the positive battery terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 terminals :
+2 4, :
+3 5, :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 7 <==> 6 7 // EQUI // 5 //
+8 9 10 11 12 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// The path it was on
+// there is a path containing both Z and C
+
+1 The :
+2 path :
+3 it :
+4 was :
+5 on :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+4 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// If the bulb is on the same closed path
+// The damaged bulb and the other bulb must be contained in the same path
+
+1 If :
+2 the :
+3 bulb :
+4 is :
+5 on :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+5 6 7 8 9 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb a was still contained in a closed path with the battery.
+// Bulb A was still contained in the same closed path with the battery.
+
+1 bulb :
+2 a :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery. :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 7 8 9 <==> 6 7 8 9 10 // EQUI // 5 //
+10 11 12 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// If one bulb is removed, the others stop working
+// A and C are in the same closed path
+
+1 If :
+2 one :
+3 bulb :
+4 is :
+5 removed, :
+6 the :
+7 others :
+8 stop :
+9 working :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+2 3 <==> 1 2 3 // EQUI // 5 //
+8 <==> 4 // EQUI // 5 //
+
+
+
+
+
+// because all the terminals are connected to other terminals, an open switch disrupts that.
+// the open switch creates a gap
+
+1 because :
+2 all :
+3 the :
+4 terminals :
+5 are :
+6 connected :
+7 to :
+8 other :
+9 terminals, :
+10 an :
+11 open :
+12 switch :
+13 disrupts :
+14 that. :
+
+
+1 the :
+2 open :
+3 switch :
+4 creates :
+5 a :
+6 gap :
+
+
+10 11 12 <==> 1 2 3 // EQUI // 5 //
+
+
+
+
+
+// There is a gap between the two bulb terminals
+// the terminals are separated by a gap
+
+1 There :
+2 is :
+3 a :
+4 gap :
+5 between :
+6 the :
+7 two :
+8 bulb :
+9 terminals :
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+2 3 4 <==> 3 4 5 6 7 // EQUI // 5 //
+5 6 7 8 9 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// a short circuit has occured
+// there is a short circuit
+
+1 a :
+2 short :
+3 circuit :
+4 has :
+5 occured :
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 2 3 <==> 3 4 5 // EQUI // 5 //
+4 5 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// there will be a gap at bulb b, thus affecting the rest of the circuit
+// bulb B creates a gap
+
+1 there :
+2 will :
+3 be :
+4 a :
+5 gap :
+6 at :
+7 bulb :
+8 b, :
+9 thus :
+10 affecting :
+11 the :
+12 rest :
+13 of :
+14 the :
+15 circuit :
+
+
+1 bulb :
+2 B :
+3 creates :
+4 a :
+5 gap :
+
+
+1 <==> 3 // EQUI // 5 //
+4 5 <==> 4 5 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// terminal 3 and the positie terminal are not connected.
+// Terminal 3 and the positive terminal are not connected
+
+1 terminal :
+2 3 :
+3 and :
+4 the :
+5 positie :
+6 terminal :
+7 are :
+8 not :
+9 connected. :
+
+
+1 Terminal :
+2 3 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 9 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// The positive battery terminal was not seperated by a gap from terminal 4.
+// Terminal 4 and the positive terminal are not separated by the gap
+
+1 The :
+2 positive :
+3 battery :
+4 terminal :
+5 was :
+6 not :
+7 seperated :
+8 by :
+9 a :
+10 gap :
+11 from :
+12 terminal :
+13 4. :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+5 6 7 <==> 7 8 9 // EQUI // 5 //
+8 9 10 <==> 10 11 12 // EQUI // 5 //
+11 12 13 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is connected to the negative terminal.
+// terminal 1 is connected to the negative battery terminal
+
+1 Terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 terminal. :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// A terminal is not connected to the positive battery terminal.
+// Terminals 1 and 2 are connected
+
+1 A :
+2 terminal :
+3 is :
+4 not :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 battery :
+10 terminal. :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal and terminal 2 are seperated by a gap
+// Terminal 2 and the positive terminal are separated by the gap
+
+1 the :
+2 positive :
+3 terminal :
+4 and :
+5 terminal :
+6 2 :
+7 are :
+8 seperated :
+9 by :
+10 a :
+11 gap :
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+9 10 11 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// there is not gap between the terminals
+// terminal 1 is connected to the negative battery terminal
+
+1 there :
+2 is :
+3 not :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+5 6 7 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// there is a gap between teh positive battery terminal and terminal 4.
+// Terminal 4 and the positive battery terminal are in the same electrical state
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 between :
+6 teh :
+7 positive :
+8 battery :
+9 terminal :
+10 and :
+11 terminal :
+12 4. :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 battery :
+7 terminal :
+8 are :
+9 in :
+10 the :
+11 same :
+12 electrical :
+13 state :
+
+
+5 6 7 8 9 10 11 12 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// The positive battery was not connected to terminal one.
+// Terminal 1 and the positive terminal are not connected
+
+1 The :
+2 positive :
+3 battery :
+4 was :
+5 not :
+6 connected :
+7 to :
+8 terminal :
+9 one. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+4 5 6 <==> 7 8 9 // EQUI // 5 //
+7 8 9 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and B will still be contained in a closed path to the battery.
+// bulbs A and B are still in closed paths with the battery
+
+1 Bulbs :
+2 A :
+3 and :
+4 B :
+5 will :
+6 still :
+7 be :
+8 contained :
+9 in :
+10 a :
+11 closed :
+12 path :
+13 to :
+14 the :
+15 battery. :
+
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 8 <==> 5 // EQUI // 5 //
+9 10 11 12 <==> 7 8 9 // EQUI // 5 //
+13 14 15 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the two components are seperated.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 the :
+2 two :
+3 components :
+4 are :
+5 seperated. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// because terminal 1 is directly connected to terminal 4
+// Terminals 1 and 4 are connected
+
+1 because :
+2 terminal :
+3 1 :
+4 is :
+5 directly :
+6 connected :
+7 to :
+8 terminal :
+9 4 :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+6 <==> 5 6 // EQUI // 5 //
+7 8 9 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal and terminal 4 are connected
+// Terminal 4 and the positive terminal are connected
+
+1 the :
+2 positive :
+3 battery :
+4 terminal :
+5 and :
+6 terminal :
+7 4 :
+8 are :
+9 connected :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 6 // EQUI // 5 //
+8 9 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 and terminal 2 are on the same side.
+// Terminals 1 and 2 are connected
+
+1 Terminal :
+2 1 :
+3 and :
+4 terminal :
+5 2 :
+6 are :
+7 on :
+8 the :
+9 same :
+10 side. :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 connected :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 7 8 9 10 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// not connected to positive battery
+// Terminal 2 and the positive terminal are not connected
+
+1 not :
+2 connected :
+3 to :
+4 positive :
+5 battery :
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 7 8 9 // EQUI // 5 //
+3 4 5 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// The battery uses a chemical reaction to maintain the voltage,
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 The :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 the :
+10 voltage, :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 <==> 4 5 6 // EQUI // 5 //
+7 8 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Because the bulb does not have a closed path.
+// The bulb is not in the closed path containing the battery
+
+1 Because :
+2 the :
+3 bulb :
+4 does :
+5 not :
+6 have :
+7 a :
+8 closed :
+9 path. :
+
+
+1 The :
+2 bulb :
+3 is :
+4 not :
+5 in :
+6 the :
+7 closed :
+8 path :
+9 containing :
+10 the :
+11 battery :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 3 4 // EQUI // 5 //
+7 8 9 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// there is a difference in electrical states
+// the terminals are separated by a gap
+
+1 there :
+2 is :
+3 a :
+4 difference :
+5 in :
+6 electrical :
+7 states :
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+3 4 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to postive terminal of the battery
+// Terminal 6 and the positive terminal are connected
+
+1 terminal :
+2 is :
+3 connected :
+4 to :
+5 postive :
+6 terminal :
+7 of :
+8 the :
+9 battery :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 <==> 1 2 3 4 5 6 // EQUI // 5 //
+2 3 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is seperated from the positive terminal
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 Terminal :
+2 1 :
+3 is :
+4 seperated :
+5 from :
+6 the :
+7 positive :
+8 terminal :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Battery is not contained i a closed path.
+// The battery in 4 is not in a closed path
+
+1 Battery :
+2 is :
+3 not :
+4 contained :
+5 i :
+6 a :
+7 closed :
+8 path. :
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 <==> 1 2 // EQUI // 5 //
+2 3 4 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 was connected to the positive battery terminal
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 terminal :
+2 1 :
+3 was :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 battery :
+9 terminal :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// There are 2 paths in this diagram
+// there is a path containing A and a different path containing B and C
+
+1 There :
+2 are :
+3 2 :
+4 paths :
+5 in :
+6 this :
+7 diagram :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A :
+7 and :
+8 a :
+9 different :
+10 path :
+11 containing :
+12 B :
+13 and :
+14 C :
+
+
+1 <==> 1 // EQUI // 5 //
+
+
+
+
+
+// Because the switch was connected to the closed circuit
+// there is no path containing both switch Y and bulb A
+
+1 Because :
+2 the :
+3 switch :
+4 was :
+5 connected :
+6 to :
+7 the :
+8 closed :
+9 circuit :
+
+
+1 there :
+2 is :
+3 no :
+4 path :
+5 containing :
+6 both :
+7 switch :
+8 Y :
+9 and :
+10 bulb :
+11 A :
+
+
+2 3 <==> 7 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// damaged bulb creates a gap.
+// a damaged bulb creates a gap
+
+1 damaged :
+2 bulb :
+3 creates :
+4 a :
+5 gap. :
+
+
+1 a :
+2 damaged :
+3 bulb :
+4 creates :
+5 a :
+6 gap :
+
+
+1 2 <==> 1 2 3 // EQUI // 5 //
+3 <==> 4 // EQUI // 5 //
+4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// that the battery connection does not work
+// there is a short circuit
+
+1 that :
+2 the :
+3 battery :
+4 connection :
+5 does :
+6 not :
+7 work :
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+1 <==> 2 // EQUI // 5 //
+2 3 4 5 6 7 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// because the terminals are not connected
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 because :
+2 the :
+3 terminals :
+4 are :
+5 not :
+6 connected :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+2 3 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Terminal 5 is connected to teh positive battery terminal
+// Terminal 5 and the positive terminal are connected
+
+1 Terminal :
+2 5 :
+3 is :
+4 connected :
+5 to :
+6 teh :
+7 positive :
+8 battery :
+9 terminal :
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 was connected to the positive terminal
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 terminal :
+2 1 :
+3 was :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 terminal :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// there is a gap between terminal one and two and the positive battery terminal
+// Terminals 1 and 2 are in the same electrical state
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 between :
+6 terminal :
+7 one :
+8 and :
+9 two :
+10 and :
+11 the :
+12 positive :
+13 battery :
+14 terminal :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 in :
+7 the :
+8 same :
+9 electrical :
+10 state :
+
+
+5 6 7 8 9 10 11 12 13 14 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c are contained on the same path with the battery
+// B and C are in the same path with the battery
+
+1 bulbs :
+2 b :
+3 and :
+4 c :
+5 are :
+6 contained :
+7 on :
+8 the :
+9 same :
+10 path :
+11 with :
+12 the :
+13 battery :
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// because there is no closed path to the battery
+// the path is not closed
+
+1 because :
+2 there :
+3 is :
+4 no :
+5 closed :
+6 path :
+7 to :
+8 the :
+9 battery :
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+3 4 5 6 <==> 1 2 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 is not connected to the positive battery terminal
+// Terminal 1 and the positive terminal are not connected
+
+1 terminal :
+2 1 :
+3 is :
+4 not :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 battery :
+10 terminal :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the battery is not in a closed bath alone
+// The battery in 2 is not in a closed path
+
+1 the :
+2 battery :
+3 is :
+4 not :
+5 in :
+6 a :
+7 closed :
+8 bath :
+9 alone :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// terminal 5 is connected to postive terminal of the battery
+// Terminal 5 and the positive terminal are connected
+
+1 terminal :
+2 5 :
+3 is :
+4 connected :
+5 to :
+6 postive :
+7 terminal :
+8 of :
+9 the :
+10 battery :
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// if x and z are closed then it will create a closed path
+// there is a path containing A, C, Z and X
+
+1 if :
+2 x :
+3 and :
+4 z :
+5 are :
+6 closed :
+7 then :
+8 it :
+9 will :
+10 create :
+11 a :
+12 closed :
+13 path :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A, :
+7 C, :
+8 Z :
+9 and :
+10 X :
+
+
+2 3 4 <==> 6 7 8 9 10 // EQUI // 5 //
+8 <==> 2 // EQUI // 5 //
+11 12 13 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// positive terminal is serperated from terminal 2
+// Terminal 2 and the positive terminal are separated by the gap
+
+1 positive :
+2 terminal :
+3 is :
+4 serperated :
+5 from :
+6 terminal :
+7 2 :
+
+
+1 Terminal :
+2 2 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// the battery is not closed the bulb is.
+// The battery in 2 is not in a closed path
+
+1 the :
+2 battery :
+3 is :
+4 not :
+5 closed :
+6 the :
+7 bulb :
+8 is. :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// there is not a gap in the connection
+// the terminals are not separated by a gap
+
+1 there :
+2 is :
+3 not :
+4 a :
+5 gap :
+6 in :
+7 the :
+8 connection :
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 separated :
+6 by :
+7 a :
+8 gap :
+
+
+2 3 <==> 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// if a bulb is in a closed circuit with a battery and a switch the switch will affect the bulb.
+// When the switch and the bulb are contained in the same path
+
+1 if :
+2 a :
+3 bulb :
+4 is :
+5 in :
+6 a :
+7 closed :
+8 circuit :
+9 with :
+10 a :
+11 battery :
+12 and :
+13 a :
+14 switch :
+15 the :
+16 switch :
+17 will :
+18 affect :
+19 the :
+20 bulb. :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+19 20 <==> 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c were contained in a closed path with the battery.
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+1 bulbs :
+2 b :
+3 and :
+4 c :
+5 were :
+6 contained :
+7 in :
+8 a :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 <==> 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 13 // EQUI // 5 //
+11 12 13 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// Because neither components are in closed paths.
+// Circuit 4 has no closed paths
+
+1 Because :
+2 neither :
+3 components :
+4 are :
+5 in :
+6 closed :
+7 paths. :
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+5 6 7 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// you can see where the gap is
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+1 you :
+2 can :
+3 see :
+4 where :
+5 the :
+6 gap :
+7 is :
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+3 <==> 3 // EQUI // 5 //
+5 6 <==> 13 14 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+
+
+
+
+
+// if there is a gap in the circuit there the bulb will not light up.
+// A non-zero voltage means that the terminals are not connected.
+
+1 if :
+2 there :
+3 is :
+4 a :
+5 gap :
+6 in :
+7 the :
+8 circuit :
+9 there :
+10 the :
+11 bulb :
+12 will :
+13 not :
+14 light :
+15 up. :
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 the :
+7 terminals :
+8 are :
+9 not :
+10 connected. :
+
+
+2 <==> 1 2 3 // EQUI // 5 //
+6 7 8 <==> 6 7 // EQUI // 5 //
+9 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and Bulb B and the battery are in a closed path.
+// If C burns out, then A and B are still in a closed path with the battery.
+
+1 Bulb :
+2 A :
+3 and :
+4 Bulb :
+5 B :
+6 and :
+7 the :
+8 battery :
+9 are :
+10 in :
+11 a :
+12 closed :
+13 path. :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery. :
+
+
+9 <==> 9 10 // EQUI // 5 //
+10 11 12 13 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// That there is a gap
+// there is no gap between the terminals
+
+1 That :
+2 there :
+3 is :
+4 a :
+5 gap :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+4 5 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// if the switch and bulb are contained in the same path, the switch will affect the bulb.
+// When the switch and the bulb are contained in the same path
+
+1 if :
+2 the :
+3 switch :
+4 and :
+5 bulb :
+6 are :
+7 contained :
+8 in :
+9 the :
+10 same :
+11 path, :
+12 the :
+13 switch :
+14 will :
+15 affect :
+16 the :
+17 bulb. :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 <==> 2 3 4 5 6 // EQUI // 5 //
+6 7 <==> 7 8 // EQUI // 5 //
+8 9 10 11 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Voltage is the difference between a positive and negative end on a battery.
+// terminal 1 is connected to the negative battery terminal
+
+1 Voltage :
+2 is :
+3 the :
+4 difference :
+5 between :
+6 a :
+7 positive :
+8 and :
+9 negative :
+10 end :
+11 on :
+12 a :
+13 battery. :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+5 6 7 8 9 10 11 12 13 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the path passes the energy through the switch
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 the :
+2 path :
+3 passes :
+4 the :
+5 energy :
+6 through :
+7 the :
+8 switch :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 8 9 10 11 // EQUI // 5 //
+6 7 8 <==> 12 13 // EQUI // 5 //
+
+
+
+
+
+// that the bulb terminal and battery terminal are on the same side of a disconnected circut
+// The terminals are in the same state.
+
+1 that :
+2 the :
+3 bulb :
+4 terminal :
+5 and :
+6 battery :
+7 terminal :
+8 are :
+9 on :
+10 the :
+11 same :
+12 side :
+13 of :
+14 a :
+15 disconnected :
+16 circut :
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+2 3 4 5 6 7 <==> 1 2 // EQUI // 5 //
+8 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// Because the battery is not in a closed path.
+// The battery in 4 is not in a closed path
+
+1 Because :
+2 the :
+3 battery :
+4 is :
+5 not :
+6 in :
+7 a :
+8 closed :
+9 path. :
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 9 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// switch x is in the closed path with bulb a
+// Bulb A is still contained in a closed path with the battery and switch X.
+
+1 switch :
+2 x :
+3 is :
+4 in :
+5 the :
+6 closed :
+7 path :
+8 with :
+9 bulb :
+10 a :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 X. :
+
+
+1 2 <==> 10 11 12 13 14 15 // EQUI // 5 //
+4 5 6 7 <==> 6 7 8 9 // EQUI // 5 //
+8 9 10 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// There was a closed circuit
+// Bulb A is still contained in a closed path with the battery.
+
+1 There :
+2 was :
+3 a :
+4 closed :
+5 circuit :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery. :
+
+
+1 <==> 10 11 12 // EQUI // 5 //
+3 4 5 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// "because switch z is in bulb c""s closed path"
+// there is a path containing both Z and C
+
+1 "because :
+2 switch :
+3 z :
+4 is :
+5 in :
+6 bulb :
+7 c""s :
+8 closed :
+9 path" :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+2 3 <==> 7 8 9 // EQUI // 5 //
+4 <==> 5 // EQUI // 5 //
+8 9 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Bulb A was still in a closed path
+// Bulb A is still contained in a closed path with the battery and switch X.
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 X. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Because there is a gap due to a damaged bulb.
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+1 Because :
+2 there :
+3 is :
+4 a :
+5 gap :
+6 due :
+7 to :
+8 a :
+9 damaged :
+10 bulb. :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+4 5 <==> 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// Bulb A was still in a closed path with the battery
+// Bulb A was still contained in the same closed path with the battery.
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+9 10 11 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// The battery and light bulb are not contained in a close path
+// The battery in 4 is not in a closed path
+
+1 The :
+2 battery :
+3 and :
+4 light :
+5 bulb :
+6 are :
+7 not :
+8 contained :
+9 in :
+10 a :
+11 close :
+12 path :
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 3 4 5 <==> 1 2 // EQUI // 5 //
+6 7 8 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// and the circut is closed
+// A and C are in the same closed path
+
+1 and :
+2 the :
+3 circut :
+4 is :
+5 closed :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 <==> 4 // EQUI // 5 //
+4 5 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// "becuase bulb C is on it""s own pathway."
+// Bulb C is in a separate path
+
+1 "becuase :
+2 bulb :
+3 C :
+4 is :
+5 on :
+6 it""s :
+7 own :
+8 pathway." :
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// if bulb A burns out then bulbs B and C will no longer be in a closed path.
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 if :
+2 bulb :
+3 A :
+4 burns :
+5 out :
+6 then :
+7 bulbs :
+8 B :
+9 and :
+10 C :
+11 will :
+12 no :
+13 longer :
+14 be :
+15 in :
+16 a :
+17 closed :
+18 path. :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 // EQUI // 5 //
+4 5 <==> 4 5 // EQUI // 5 //
+7 8 9 10 <==> 6 7 8 9 // EQUI // 5 //
+15 16 17 18 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is not connected to the positive terminal.
+// Terminal 1 and the positive terminal are not connected
+
+1 Terminal :
+2 1 :
+3 is :
+4 not :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 terminal. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 5 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because the battery is not in a closed circuit
+// The battery in 2 is not in a closed path
+
+1 because :
+2 the :
+3 battery :
+4 is :
+5 not :
+6 in :
+7 a :
+8 closed :
+9 circuit :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 5 <==> 5 6 // EQUI // 5 //
+6 7 8 9 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// the terminal it is connected to is not working
+// there is no gap between the terminals
+
+1 the :
+2 terminal :
+3 it :
+4 is :
+5 connected :
+6 to :
+7 is :
+8 not :
+9 working :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 2 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// There must be a closed path and a battery.
+// there is a closed path containing both the bulb and a battery
+
+1 There :
+2 must :
+3 be :
+4 a :
+5 closed :
+6 path :
+7 and :
+8 a :
+9 battery. :
+
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path :
+6 containing :
+7 both :
+8 the :
+9 bulb :
+10 and :
+11 a :
+12 battery :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 // EQUI // 5 //
+4 5 6 7 8 9 <==> 3 4 5 6 7 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to terminal 6
+// Terminals 1 and 6 are not connected
+
+1 terminal :
+2 is :
+3 connected :
+4 to :
+5 terminal :
+6 6 :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+
+
+4 5 6 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// because bulb a is in a closed circuit with the battery and switch x
+// Bulb A is still contained in a closed path with the battery and switch X.
+
+1 because :
+2 bulb :
+3 a :
+4 is :
+5 in :
+6 a :
+7 closed :
+8 circuit :
+9 with :
+10 the :
+11 battery :
+12 and :
+13 switch :
+14 x :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 X. :
+
+
+1 <==> 4 // EQUI // 5 //
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 // EQUI // 5 //
+9 10 11 12 13 14 <==> 10 11 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// If the path is not closed, the switch will not affect the bbulb
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 If :
+2 the :
+3 path :
+4 is :
+5 not :
+6 closed, :
+7 the :
+8 switch :
+9 will :
+10 not :
+11 affect :
+12 the :
+13 bbulb :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 8 9 10 11 // EQUI // 5 //
+7 8 <==> 14 // EQUI // 5 //
+
+
+
+
+
+// bulb b and c are on a closed path to the battery
+// If bulb A burns out, bulbs B and C are still in a closed path
+
+1 bulb :
+2 b :
+3 and :
+4 c :
+5 are :
+6 on :
+7 a :
+8 closed :
+9 path :
+10 to :
+11 the :
+12 battery :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 bulbs :
+7 B :
+8 and :
+9 C :
+10 are :
+11 still :
+12 in :
+13 a :
+14 closed :
+15 path :
+
+
+1 2 3 4 <==> 6 7 8 9 // EQUI // 5 //
+5 <==> 10 // EQUI // 5 //
+6 7 8 9 <==> 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// since a a gap does not affect the voltage of a battery
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+1 since :
+2 a :
+3 a :
+4 gap :
+5 does :
+6 not :
+7 affect :
+8 the :
+9 voltage :
+10 of :
+11 a :
+12 battery :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+2 3 4 <==> 13 14 15 // EQUI // 5 //
+8 9 10 11 12 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Because there is a light bulb
+// The battery in 2 is not in a closed path
+
+1 Because :
+2 there :
+3 is :
+4 a :
+5 light :
+6 bulb :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+3 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the bulb will be burned out because the terminals
+// The damaged bulb and the other bulb must be contained in the same path
+
+1 the :
+2 bulb :
+3 will :
+4 be :
+5 burned :
+6 out :
+7 because :
+8 the :
+9 terminals :
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+1 2 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+7 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// Because the positive batter terminal and terminal 6 were connected.
+// Terminal 6 and the positive terminal are connected
+
+1 Because :
+2 the :
+3 positive :
+4 batter :
+5 terminal :
+6 and :
+7 terminal :
+8 6 :
+9 were :
+10 connected. :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+2 3 4 5 6 7 8 <==> 1 2 3 4 5 6 // EQUI // 5 //
+9 10 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// because the the circuit is complete.
+// the path is not closed
+
+1 because :
+2 the :
+3 the :
+4 circuit :
+5 is :
+6 complete. :
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+2 3 4 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Bulbs B and C will still be on closed paths with the battery
+// bulbs B and C are still in closed paths with the battery
+
+1 Bulbs :
+2 B :
+3 and :
+4 C :
+5 will :
+6 still :
+7 be :
+8 on :
+9 closed :
+10 paths :
+11 with :
+12 the :
+13 battery :
+
+
+1 bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+11 12 13 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the bulb is contained in an closed circuit
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 the :
+2 bulb :
+3 is :
+4 contained :
+5 in :
+6 an :
+7 closed :
+8 circuit :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// THE ARE ON THE SAME PATH
+// A and C are in the same path
+
+1 THE :
+2 ARE :
+3 ON :
+4 THE :
+5 SAME :
+6 PATH :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+
+
+1 <==> 1 2 3 // EQUI // 5 //
+2 <==> 4 // EQUI // 5 //
+3 4 5 6 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// Bulb a and switch Y are not in the same path.
+// Switch Y and bulb A are not in the same closed path
+
+1 Bulb :
+2 a :
+3 and :
+4 switch :
+5 Y :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 path. :
+
+
+1 Switch :
+2 Y :
+3 and :
+4 bulb :
+5 A :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 closed :
+12 path :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 7 <==> 6 7 // EQUI // 5 //
+8 9 10 11 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// A chemical reaction inside the battery makes the electrical states of the positive and negative terminals different at all times.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 A :
+2 chemical :
+3 reaction :
+4 inside :
+5 the :
+6 battery :
+7 makes :
+8 the :
+9 electrical :
+10 states :
+11 of :
+12 the :
+13 positive :
+14 and :
+15 negative :
+16 terminals :
+17 different :
+18 at :
+19 all :
+20 times. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 3 <==> 4 5 6 // EQUI // 5 //
+4 5 6 <==> 1 2 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+11 12 13 14 15 16 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// becasue the terminals 4,5, and 6 are connected to the positive terminal of the battery
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 becasue :
+2 the :
+3 terminals :
+4 4,5, :
+5 and :
+6 6 :
+7 are :
+8 connected :
+9 to :
+10 the :
+11 positive :
+12 terminal :
+13 of :
+14 the :
+15 battery :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+2 3 4 5 6 <==> 1 2 3 4 5 // EQUI // 5 //
+7 8 <==> 6 7 // EQUI // 5 //
+9 10 11 12 13 14 15 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// switch Y does not effect bulb A
+// Switch Y and bulb A are not in the same closed path
+
+1 switch :
+2 Y :
+3 does :
+4 not :
+5 effect :
+6 bulb :
+7 A :
+
+
+1 Switch :
+2 Y :
+3 and :
+4 bulb :
+5 A :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 closed :
+12 path :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// bulb c creates a gap
+// If C burns out, then A and B are still in a closed path with the battery.
+
+1 bulb :
+2 c :
+3 creates :
+4 a :
+5 gap :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery. :
+
+
+1 2 <==> 2 // EQUI // 5 //
+3 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Bulb C and the battery are not contained in a closed pathway
+// Bulb C was no longer in a closed path with the battery
+
+1 Bulb :
+2 C :
+3 and :
+4 the :
+5 battery :
+6 are :
+7 not :
+8 contained :
+9 in :
+10 a :
+11 closed :
+12 pathway :
+
+
+1 Bulb :
+2 C :
+3 was :
+4 no :
+5 longer :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 // EQUI // 5 //
+9 10 11 12 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// the two terminals will both be 0
+// The terminals are in the same state.
+
+1 the :
+2 two :
+3 terminals :
+4 will :
+5 both :
+6 be :
+7 0 :
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+1 2 3 <==> 1 2 // EQUI // 5 //
+5 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// bulb b is not in the same path with bulbs a and c.
+// Bulb B is in a separate path
+
+1 bulb :
+2 b :
+3 is :
+4 not :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 bulbs :
+11 a :
+12 and :
+13 c. :
+
+
+1 Bulb :
+2 B :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 // EQUI // 5 //
+
+
+
+
+
+// The electrical state is interferred with.
+// A non-zero voltage means that the terminals are not connected.
+
+1 The :
+2 electrical :
+3 state :
+4 is :
+5 interferred :
+6 with. :
+
+
+1 A :
+2 non-zero :
+3 voltage :
+4 means :
+5 that :
+6 the :
+7 terminals :
+8 are :
+9 not :
+10 connected. :
+
+
+1 2 3 <==> 1 2 3 // EQUI // 5 //
+
+
+
+
+
+// Because the battery and the bulb are not in a closed path.
+// The battery in 4 is not in a closed path
+
+1 Because :
+2 the :
+3 battery :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 not :
+9 in :
+10 a :
+11 closed :
+12 path. :
+
+
+1 The :
+2 battery :
+3 in :
+4 4 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+2 3 4 5 6 <==> 1 2 // EQUI // 5 //
+7 8 <==> 5 6 // EQUI // 5 //
+9 10 11 12 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// "because by measuring voltage, you find the gap where there""s a difference in electrical states."
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+1 "because :
+2 by :
+3 measuring :
+4 voltage, :
+5 you :
+6 find :
+7 the :
+8 gap :
+9 where :
+10 there""s :
+11 a :
+12 difference :
+13 in :
+14 electrical :
+15 states." :
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+2 3 <==> 1 // EQUI // 5 //
+4 <==> 2 // EQUI // 5 //
+7 8 <==> 11 12 13 14 // EQUI // 5 //
+9 <==> 4 5 // EQUI // 5 //
+10 11 12 <==> 6 // EQUI // 5 //
+13 14 15 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// again, bulbs a and b will be contained on a closed path
+// If C burns out, then A and B are still in a closed path.
+
+1 again, :
+2 bulbs :
+3 a :
+4 and :
+5 b :
+6 will :
+7 be :
+8 contained :
+9 on :
+10 a :
+11 closed :
+12 path :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+2 3 4 5 <==> 6 7 8 // EQUI // 5 //
+6 7 8 <==> 5 // EQUI // 5 //
+9 10 11 12 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c are contiained in the the same path with the battery.
+// A and C are not in the same path with the battery
+
+1 bulbs :
+2 b :
+3 and :
+4 c :
+5 are :
+6 contiained :
+7 in :
+8 the :
+9 the :
+10 same :
+11 path :
+12 with :
+13 the :
+14 battery. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// There is a gap in the path.
+// Terminals 1 and 2 are in the same electrical state
+
+1 There :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 the :
+7 path. :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 2 :
+5 are :
+6 in :
+7 the :
+8 same :
+9 electrical :
+10 state :
+
+
+1 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// bulb a is in a closed path with a battery
+// Bulb A is still in a closed path with the battery
+
+1 bulb :
+2 a :
+3 is :
+4 in :
+5 a :
+6 closed :
+7 path :
+8 with :
+9 a :
+10 battery :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb C affect each other.
+// A and C are in the same closed path
+
+1 Bulb :
+2 A :
+3 and :
+4 bulb :
+5 C :
+6 affect :
+7 each :
+8 other. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+
+
+
+
+
+// switch z is contained in a closed path
+// there is a path containing both Z and C
+
+1 switch :
+2 z :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 2 <==> 7 8 9 // EQUI // 5 //
+3 4 <==> 1 // EQUI // 5 //
+5 6 7 8 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// the bulb terminal and the negative battery terminal are separated by a gap
+// there is no gap between the terminals
+
+1 the :
+2 bulb :
+3 terminal :
+4 and :
+5 the :
+6 negative :
+7 battery :
+8 terminal :
+9 are :
+10 separated :
+11 by :
+12 a :
+13 gap :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 2 3 4 5 6 7 8 <==> 5 6 7 // EQUI // 5 //
+11 12 13 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and C are still in a closed path with the battery.
+// Bulbs A and C are still contained in closed paths with the battery
+
+1 Bulb :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 a :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 contained :
+8 in :
+9 closed :
+10 paths :
+11 with :
+12 the :
+13 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+5 <==> 5 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 8 9 10 <==> 8 9 10 // EQUI // 5 //
+11 12 13 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// if switch and bulb are contained in the same closed path
+// When the switch and the bulb are contained in the same path
+
+1 if :
+2 switch :
+3 and :
+4 bulb :
+5 are :
+6 contained :
+7 in :
+8 the :
+9 same :
+10 closed :
+11 path :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 <==> 2 3 4 5 6 // EQUI // 5 //
+5 6 <==> 7 8 // EQUI // 5 //
+7 8 9 10 11 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// there is a gap between the positive battery connection and the bulb terminal.
+// there is no gap between the terminals
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 between :
+6 the :
+7 positive :
+8 battery :
+9 connection :
+10 and :
+11 the :
+12 bulb :
+13 terminal. :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 <==> 1 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 9 10 11 12 13 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulb A is not on the same path that Bulb B and bulb C are.
+// there is a path containing A and a different path containing B and C
+
+1 Bulb :
+2 A :
+3 is :
+4 not :
+5 on :
+6 the :
+7 same :
+8 path :
+9 that :
+10 Bulb :
+11 B :
+12 and :
+13 bulb :
+14 C :
+15 are. :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A :
+7 and :
+8 a :
+9 different :
+10 path :
+11 containing :
+12 B :
+13 and :
+14 C :
+
+
+1 2 <==> 6 // EQUI // 5 //
+5 6 7 8 <==> 1 // EQUI // 5 //
+10 11 12 13 14 <==> 12 13 14 // EQUI // 5 //
+15 <==> 7 // EQUI // 5 //
+
+
+
+
+
+// it runs on a different current
+// If C burns out, then A and B are still in a closed path with the battery.
+
+1 it :
+2 runs :
+3 on :
+4 a :
+5 different :
+6 current :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery. :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 11 12 13 14 // EQUI // 5 //
+3 4 5 6 <==> 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to the difference
+// Terminal 6 and the positive terminal are connected
+
+1 terminal :
+2 6 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 difference :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the batteries terminals are not connected
+// Circuit 4 has no closed paths
+
+1 the :
+2 batteries :
+3 terminals :
+4 are :
+5 not :
+6 connected :
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+1 2 3 <==> 1 2 // EQUI // 5 //
+4 5 6 <==> 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because if there is a voltage that means there is a gap
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+1 because :
+2 if :
+3 there :
+4 is :
+5 a :
+6 voltage :
+7 that :
+8 means :
+9 there :
+10 is :
+11 a :
+12 gap :
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+3 <==> 7 8 9 // EQUI // 5 //
+5 6 <==> 2 // EQUI // 5 //
+9 <==> 11 12 // EQUI // 5 //
+11 12 <==> 13 14 // EQUI // 5 //
+
+
+
+
+
+// Find where there are different electrical states
+// Measuring voltage indicates the place where the electrical state changes due to a gap.
+
+1 Find :
+2 where :
+3 there :
+4 are :
+5 different :
+6 electrical :
+7 states :
+
+
+1 Measuring :
+2 voltage :
+3 indicates :
+4 the :
+5 place :
+6 where :
+7 the :
+8 electrical :
+9 state :
+10 changes :
+11 due :
+12 to :
+13 a :
+14 gap. :
+
+
+2 <==> 3 // EQUI // 5 //
+3 <==> 6 // EQUI // 5 //
+5 6 7 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// circuit 2 is connected to the battery
+// there is no closed path containing the battery
+
+1 circuit :
+2 2 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 battery :
+
+
+1 there :
+2 is :
+3 no :
+4 closed :
+5 path :
+6 containing :
+7 the :
+8 battery :
+
+
+5 6 7 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the gap in the circuit causes the circuit to be an open circuit
+// there is a gap in a circuit
+
+1 the :
+2 gap :
+3 in :
+4 the :
+5 circuit :
+6 causes :
+7 the :
+8 circuit :
+9 to :
+10 be :
+11 an :
+12 open :
+13 circuit :
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 a :
+7 circuit :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+3 4 5 <==> 1 // EQUI // 5 //
+6 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// there is a gap in the circuit
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 the :
+7 circuit :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+3 4 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the path has to be closed for the bulb to light up
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 the :
+2 path :
+3 has :
+4 to :
+5 be :
+6 closed :
+7 for :
+8 the :
+9 bulb :
+10 to :
+11 light :
+12 up :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 8 9 10 11 // EQUI // 5 //
+7 8 9 <==> 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// There is no gap so there is no difference in voltage
+// there is no gap between the terminals
+
+1 There :
+2 is :
+3 no :
+4 gap :
+5 so :
+6 there :
+7 is :
+8 no :
+9 difference :
+10 in :
+11 voltage :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+1 <==> 1 // EQUI // 5 //
+2 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// Voltage is the difference between a positive and negative end on the battery.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 Voltage :
+2 is :
+3 the :
+4 difference :
+5 between :
+6 a :
+7 positive :
+8 and :
+9 negative :
+10 end :
+11 on :
+12 the :
+13 battery. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+3 4 <==> 9 10 11 // EQUI // 5 //
+5 6 7 8 9 10 11 12 13 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulb had a short circuit
+// there is a complete circuit
+
+1 bulb :
+2 had :
+3 a :
+4 short :
+5 circuit :
+
+
+1 there :
+2 is :
+3 a :
+4 complete :
+5 circuit :
+
+
+3 4 5 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb C are in a closed path with the battery.
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+1 Bulb :
+2 A :
+3 and :
+4 bulb :
+5 C :
+6 are :
+7 in :
+8 a :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+6 <==> 6 7 8 // EQUI // 5 //
+7 8 9 10 <==> 9 10 11 12 13 // EQUI // 5 //
+11 12 13 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// Terminals 4, 5, and 6 are only connected to the positive battery terminal.
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 Terminals :
+2 4, :
+3 5, :
+4 and :
+5 6 :
+6 are :
+7 only :
+8 connected :
+9 to :
+10 the :
+11 positive :
+12 battery :
+13 terminal. :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 // EQUI // 5 //
+8 <==> 6 7 // EQUI // 5 //
+9 10 11 12 13 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the positive battery terminal
+// the terminals are not connected
+
+1 a :
+2 terminal :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 battery :
+9 terminal :
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// because the terminals are in the same state
+// terminal 1 is connected to the negative battery terminal
+
+1 because :
+2 the :
+3 terminals :
+4 are :
+5 in :
+6 the :
+7 same :
+8 state :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// "because switch y isn""t included in bulb A""s closed path"
+// Switch Y and bulb A are not in the same closed path
+
+1 "because :
+2 switch :
+3 y :
+4 isn""t :
+5 included :
+6 in :
+7 bulb :
+8 A""s :
+9 closed :
+10 path" :
+
+
+1 Switch :
+2 Y :
+3 and :
+4 bulb :
+5 A :
+6 are :
+7 not :
+8 in :
+9 the :
+10 same :
+11 closed :
+12 path :
+
+
+2 3 <==> 1 2 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 // EQUI // 5 //
+9 10 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the negative battery terminal is seperated by a gap from terminal 6
+// terminal 6 is separated by a gap from the negative battery terminal
+
+1 the :
+2 negative :
+3 battery :
+4 terminal :
+5 is :
+6 seperated :
+7 by :
+8 a :
+9 gap :
+10 from :
+11 terminal :
+12 6 :
+
+
+1 terminal :
+2 6 :
+3 is :
+4 separated :
+5 by :
+6 a :
+7 gap :
+8 from :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 <==> 8 9 10 11 12 // EQUI // 5 //
+7 8 9 <==> 5 6 7 // EQUI // 5 //
+10 11 12 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// that the bulb terminal is only connected to one of the battery terminals
+// there is no gap between the terminals
+
+1 that :
+2 the :
+3 bulb :
+4 terminal :
+5 is :
+6 only :
+7 connected :
+8 to :
+9 one :
+10 of :
+11 the :
+12 battery :
+13 terminals :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+5 <==> 1 // EQUI // 5 //
+8 9 10 11 12 13 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// there was a negavtive gap
+// terminal 4 is separated by a gap from the negative battery terminal
+
+1 there :
+2 was :
+3 a :
+4 negavtive :
+5 gap :
+
+
+1 terminal :
+2 4 :
+3 is :
+4 separated :
+5 by :
+6 a :
+7 gap :
+8 from :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+3 4 5 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to postive end of battery
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 terminal :
+2 is :
+3 connected :
+4 to :
+5 postive :
+6 end :
+7 of :
+8 battery :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+2 3 <==> 6 7 // EQUI // 5 //
+4 5 6 7 8 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 is connected to the 1.5 volt battery.
+// terminal 1 is connected to the negative battery terminal
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 1.5 :
+8 volt :
+9 battery. :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// The path must be closed
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 The :
+2 path :
+3 must :
+4 be :
+5 closed :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Bulbs B and C are contained on the same path with the battery.
+// B and C are in the same path with the battery
+
+1 Bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 contained :
+7 on :
+8 the :
+9 same :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the positive terminal of the battery
+// Terminal 6 and the positive terminal are connected
+
+1 a :
+2 terminal :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 terminal :
+9 of :
+10 the :
+11 battery :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// because a and b are in series and a and c are in parallel
+// If C burns out, then A and B are still in a closed path.
+
+1 because :
+2 a :
+3 and :
+4 b :
+5 are :
+6 in :
+7 series :
+8 and :
+9 a :
+10 and :
+11 c :
+12 are :
+13 in :
+14 parallel :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+2 3 4 <==> 6 7 8 // EQUI // 5 //
+9 10 11 <==> 2 // EQUI // 5 //
+12 <==> 9 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the positive terminal of the battery
+// Terminal 5 and the positive terminal are connected
+
+1 a :
+2 terminal :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 positive :
+8 terminal :
+9 of :
+10 the :
+11 battery :
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 <==> 1 2 3 4 5 6 // EQUI // 5 //
+3 4 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the bulb is not contained in the path
+// The bulb is not in the closed path containing the battery
+
+1 the :
+2 bulb :
+3 is :
+4 not :
+5 contained :
+6 in :
+7 the :
+8 path :
+
+
+1 The :
+2 bulb :
+3 is :
+4 not :
+5 in :
+6 the :
+7 closed :
+8 path :
+9 containing :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// because positive charge is before gap
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 because :
+2 positive :
+3 charge :
+4 is :
+5 before :
+6 gap :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+6 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Because it is not on the same path
+// If bulb A burns out, bulbs B and C are still in a closed path
+
+1 Because :
+2 it :
+3 is :
+4 not :
+5 on :
+6 the :
+7 same :
+8 path :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 bulbs :
+7 B :
+8 and :
+9 C :
+10 are :
+11 still :
+12 in :
+13 a :
+14 closed :
+15 path :
+
+
+1 <==> 11 // EQUI // 5 //
+5 6 7 8 <==> 12 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// Seperate paths connected to the battery
+// If bulb A burns out, B and C are no longer in a closed path with the battery
+
+1 Seperate :
+2 paths :
+3 connected :
+4 to :
+5 the :
+6 battery :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 B :
+7 and :
+8 C :
+9 are :
+10 no :
+11 longer :
+12 in :
+13 a :
+14 closed :
+15 path :
+16 with :
+17 the :
+18 battery :
+
+
+3 <==> 12 13 14 15 // EQUI // 5 //
+4 5 6 <==> 16 17 18 // EQUI // 5 //
+
+
+
+
+
+// A red X means the battery is in a short circuit.
+// there is a short circuit
+
+1 A :
+2 red :
+3 X :
+4 means :
+5 the :
+6 battery :
+7 is :
+8 in :
+9 a :
+10 short :
+11 circuit. :
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+4 <==> 2 // EQUI // 5 //
+8 9 10 11 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// The battery is not closed in a closed path.
+// Circuit 4 has no closed paths
+
+1 The :
+2 battery :
+3 is :
+4 not :
+5 closed :
+6 in :
+7 a :
+8 closed :
+9 path. :
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 5 <==> 3 // EQUI // 5 //
+6 7 8 9 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// terminal is connected to the battery
+// Terminals 1, 2 and 3 are connected to the negative battery terminal
+
+1 terminal :
+2 is :
+3 connected :
+4 to :
+5 the :
+6 battery :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 negative :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+2 3 <==> 6 7 // EQUI // 5 //
+4 5 6 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and Bulb C are not contained in the same closed path
+// A and C are not in the same path
+
+1 Bulb :
+2 A :
+3 and :
+4 Bulb :
+5 C :
+6 are :
+7 not :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 8 <==> 4 5 // EQUI // 5 //
+9 10 11 12 13 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulbs A and C are not on the same closed path.
+// A and C are not in the same path
+
+1 bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 not :
+7 on :
+8 the :
+9 same :
+10 closed :
+11 path. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+
+
+1 2 3 4 <==> 1 2 3 // EQUI // 5 //
+5 6 <==> 4 5 // EQUI // 5 //
+7 8 9 10 11 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulb, battery, and switch are in closed path
+// When the switch and the bulb are contained in the same path
+
+1 bulb, :
+2 battery, :
+3 and :
+4 switch :
+5 are :
+6 in :
+7 closed :
+8 path :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 2 3 4 <==> 2 3 4 5 6 // EQUI // 5 //
+5 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the paths of the circuit are no longer complete
+// there is an incomplete circuit
+
+1 the :
+2 paths :
+3 of :
+4 the :
+5 circuit :
+6 are :
+7 no :
+8 longer :
+9 complete :
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+1 2 3 4 5 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// there is no closed path in circuit 4.
+// Circuit 4 has no closed paths
+
+1 there :
+2 is :
+3 no :
+4 closed :
+5 path :
+6 in :
+7 circuit :
+8 4. :
+
+
+1 Circuit :
+2 4 :
+3 has :
+4 no :
+5 closed :
+6 paths :
+
+
+2 <==> 3 // EQUI // 5 //
+3 4 5 <==> 4 5 6 // EQUI // 5 //
+6 7 8 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// The battery keeps a chemical reaction reaction.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 The :
+2 battery :
+3 keeps :
+4 a :
+5 chemical :
+6 reaction :
+7 reaction. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 7 8 // EQUI // 5 //
+4 5 6 7 <==> 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// There is always a difference in voltage between two battery terminals.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 There :
+2 is :
+3 always :
+4 a :
+5 difference :
+6 in :
+7 voltage :
+8 between :
+9 two :
+10 battery :
+11 terminals. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+4 5 6 7 <==> 9 10 11 // EQUI // 5 //
+8 9 10 11 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// terminal 1is connected to terminal 4
+// Terminals 1 and 4 are connected
+
+1 terminal :
+2 1is :
+3 connected :
+4 to :
+5 terminal :
+6 4 :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+3 <==> 5 6 // EQUI // 5 //
+4 5 6 <==> 1 2 3 4 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and B will still be in a contained path.
+// If C burns out, then A and B are still in a closed path.
+
+1 Bulb :
+2 A :
+3 and :
+4 B :
+5 will :
+6 still :
+7 be :
+8 in :
+9 a :
+10 contained :
+11 path. :
+
+
+1 If :
+2 C :
+3 burns :
+4 out, :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path. :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+7 <==> 9 // EQUI // 5 //
+8 9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// bulb a is in a closed circuit with the battery without the y switch.
+// Bulb A is still in a closed path with the battery
+
+1 bulb :
+2 a :
+3 is :
+4 in :
+5 a :
+6 closed :
+7 circuit :
+8 with :
+9 the :
+10 battery :
+11 without :
+12 the :
+13 y :
+14 switch. :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// different paths with the battery
+// B and C are in the same path with the battery
+
+1 different :
+2 paths :
+3 with :
+4 the :
+5 battery :
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 5 6 7 8 // EQUI // 5 //
+3 4 5 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// "The electrical state at the terminal matches the battery""s electrical state"
+// terminal 1 is connected to the negative battery terminal
+
+1 "The :
+2 electrical :
+3 state :
+4 at :
+5 the :
+6 terminal :
+7 matches :
+8 the :
+9 battery""s :
+10 electrical :
+11 state" :
+
+
+1 terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+4 5 6 <==> 1 2 // EQUI // 5 //
+7 <==> 3 4 // EQUI // 5 //
+8 9 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// Circuit 2 is not a short circuit because the battery is not in a closed path with itself.
+// The battery in 2 is not in a closed path
+
+1 Circuit :
+2 2 :
+3 is :
+4 not :
+5 a :
+6 short :
+7 circuit :
+8 because :
+9 the :
+10 battery :
+11 is :
+12 not :
+13 in :
+14 a :
+15 closed :
+16 path :
+17 with :
+18 itself. :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+11 12 <==> 5 6 // EQUI // 5 //
+13 14 15 16 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// Bulb A is on a closed circut path
+// Bulb A was still contained in the same closed path with the battery.
+
+1 Bulb :
+2 A :
+3 is :
+4 on :
+5 a :
+6 closed :
+7 circut :
+8 path :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 5 6 7 8 <==> 6 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// Bulb B and bulb C are contained in different paths with the battery
+// B and C are in the same path with the battery
+
+1 Bulb :
+2 B :
+3 and :
+4 bulb :
+5 C :
+6 are :
+7 contained :
+8 in :
+9 different :
+10 paths :
+11 with :
+12 the :
+13 battery :
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+8 9 10 <==> 4 // EQUI // 5 //
+11 12 13 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the battery always has a voltage because there is a positive terminal and there is a negative terminal.
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 the :
+2 battery :
+3 always :
+4 has :
+5 a :
+6 voltage :
+7 because :
+8 there :
+9 is :
+10 a :
+11 positive :
+12 terminal :
+13 and :
+14 there :
+15 is :
+16 a :
+17 negative :
+18 terminal. :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+8 <==> 7 8 // EQUI // 5 //
+14 <==> 9 10 11 // EQUI // 5 //
+16 17 18 <==> 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// gap between 3 and positive battery
+// Terminal 3 and the positive terminal are separated by the gap
+
+1 gap :
+2 between :
+3 3 :
+4 and :
+5 positive :
+6 battery :
+
+
+1 Terminal :
+2 3 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 <==> 9 10 11 // EQUI // 5 //
+2 3 4 5 6 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because bulbs A and C are contained in different paths with the battery
+// A and C are in different paths with the battery
+
+1 because :
+2 bulbs :
+3 A :
+4 and :
+5 C :
+6 are :
+7 contained :
+8 in :
+9 different :
+10 paths :
+11 with :
+12 the :
+13 battery :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+8 9 10 <==> 5 6 7 // EQUI // 5 //
+11 12 13 <==> 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// because of the gap at bulb b
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+1 because :
+2 of :
+3 the :
+4 gap :
+5 at :
+6 bulb :
+7 b :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 2 3 4 <==> 13 14 15 // EQUI // 5 //
+
+
+
+
+
+// because bulb c was in an open path
+// Bulb C was not in a closed path
+
+1 because :
+2 bulb :
+3 c :
+4 was :
+5 in :
+6 an :
+7 open :
+8 path :
+
+
+1 Bulb :
+2 C :
+3 was :
+4 not :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// It is not a closed path.
+// the path is not closed
+
+1 It :
+2 is :
+3 not :
+4 a :
+5 closed :
+6 path. :
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+3 <==> 3 4 // EQUI // 5 //
+4 5 6 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// because switch y is not conatined in the closed path of bulb a and the battery.
+// Bulb A is still in a closed path with the battery
+
+1 because :
+2 switch :
+3 y :
+4 is :
+5 not :
+6 conatined :
+7 in :
+8 the :
+9 closed :
+10 path :
+11 of :
+12 bulb :
+13 a :
+14 and :
+15 the :
+16 battery. :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 <==> 4 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 // EQUI // 5 //
+11 12 13 14 15 16 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// A terminal is not connected to the negative battery terminal.
+// Terminals 1 and 6 are not connected
+
+1 A :
+2 terminal :
+3 is :
+4 not :
+5 connected :
+6 to :
+7 the :
+8 negative :
+9 battery :
+10 terminal. :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 5 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb B and C both still are on a closed path with the battery
+// bulbs B and C are still in closed paths with the battery
+
+1 bulb :
+2 B :
+3 and :
+4 C :
+5 both :
+6 still :
+7 are :
+8 on :
+9 a :
+10 closed :
+11 path :
+12 with :
+13 the :
+14 battery :
+
+
+1 bulbs :
+2 B :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+12 13 14 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// terminal 1 and terminal 6 are seperated by a gap
+// Terminals 1 and 6 are separated by the gap
+
+1 terminal :
+2 1 :
+3 and :
+4 terminal :
+5 6 :
+6 are :
+7 seperated :
+8 by :
+9 a :
+10 gap :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 separated :
+7 by :
+8 the :
+9 gap :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 7 <==> 5 6 // EQUI // 5 //
+8 9 10 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// because the battery is in a closed path.
+// the battery is contained in a closed path in which there is no bulb
+
+1 because :
+2 the :
+3 battery :
+4 is :
+5 in :
+6 a :
+7 closed :
+8 path. :
+
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 in :
+10 which :
+11 there :
+12 is :
+13 no :
+14 bulb :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 4 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// complete path including a battery and a bulb
+// there is a closed path containing both the bulb and a battery
+
+1 complete :
+2 path :
+3 including :
+4 a :
+5 battery :
+6 and :
+7 a :
+8 bulb :
+
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path :
+6 containing :
+7 both :
+8 the :
+9 bulb :
+10 and :
+11 a :
+12 battery :
+
+
+1 2 <==> 3 4 5 // EQUI // 5 //
+3 <==> 6 // EQUI // 5 //
+4 5 6 7 8 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c creat a gap in the path
+// Bulb B is in a separate path
+
+1 bulbs :
+2 b :
+3 and :
+4 c :
+5 creat :
+6 a :
+7 gap :
+8 in :
+9 the :
+10 path :
+
+
+1 Bulb :
+2 B :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+1 2 3 4 <==> 1 2 // EQUI // 5 //
+5 <==> 3 // EQUI // 5 //
+8 9 10 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal and terminal 5 are connected
+// Terminal 5 and the positive terminal are connected
+
+1 the :
+2 positive :
+3 battery :
+4 terminal :
+5 and :
+6 terminal :
+7 5 :
+8 are :
+9 connected :
+
+
+1 Terminal :
+2 5 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 connected :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 6 // EQUI // 5 //
+8 9 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// the the bulb terminal disconnected from the battery terminal
+// the terminals are not connected
+
+1 the :
+2 the :
+3 bulb :
+4 terminal :
+5 disconnected :
+6 from :
+7 the :
+8 battery :
+9 terminal :
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+6 7 8 9 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the battery is contained in the circuit and the light bulb is not
+// the battery is contained in a path in which there is no bulb
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 the :
+7 circuit :
+8 and :
+9 the :
+10 light :
+11 bulb :
+12 is :
+13 not :
+
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 in :
+9 which :
+10 there :
+11 is :
+12 no :
+13 bulb :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+9 10 11 <==> 12 13 // EQUI // 5 //
+12 13 <==> 11 // EQUI // 5 //
+
+
+
+
+
+// because the two ends of the battery do not connect to one another
+// the battery is in an open path
+
+1 because :
+2 the :
+3 two :
+4 ends :
+5 of :
+6 the :
+7 battery :
+8 do :
+9 not :
+10 connect :
+11 to :
+12 one :
+13 another :
+
+
+1 the :
+2 battery :
+3 is :
+4 in :
+5 an :
+6 open :
+7 path :
+
+
+5 6 7 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// When a switch is open the circuit is no longer complete
+// there is an incomplete circuit
+
+1 When :
+2 a :
+3 switch :
+4 is :
+5 open :
+6 the :
+7 circuit :
+8 is :
+9 no :
+10 longer :
+11 complete :
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+4 <==> 2 // EQUI // 5 //
+5 <==> 1 // EQUI // 5 //
+
+
+
+
+
+// if both bulbs are contained within a closed path
+// The damaged bulb and the other bulb must be contained in the same path
+
+1 if :
+2 both :
+3 bulbs :
+4 are :
+5 contained :
+6 within :
+7 a :
+8 closed :
+9 path :
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+4 5 <==> 8 9 10 // EQUI // 5 //
+6 7 8 9 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// The bulb is in a closed circuit and the battery exists in that circuit
+// The battery in 2 is not in a closed path
+
+1 The :
+2 bulb :
+3 is :
+4 in :
+5 a :
+6 closed :
+7 circuit :
+8 and :
+9 the :
+10 battery :
+11 exists :
+12 in :
+13 that :
+14 circuit :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+11 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// the closed path is connected to the light bulb
+// Bulb A was still contained in the same closed path with the battery.
+
+1 the :
+2 closed :
+3 path :
+4 is :
+5 connected :
+6 to :
+7 the :
+8 light :
+9 bulb :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 3 <==> 6 7 8 9 10 // EQUI // 5 //
+6 7 8 9 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// the electrical states between the terminals is the same, resulting in 0
+// The terminals are in the same state.
+
+1 the :
+2 electrical :
+3 states :
+4 between :
+5 the :
+6 terminals :
+7 is :
+8 the :
+9 same, :
+10 resulting :
+11 in :
+12 0 :
+
+
+1 The :
+2 terminals :
+3 are :
+4 in :
+5 the :
+6 same :
+7 state. :
+
+
+4 5 6 <==> 1 2 // EQUI // 5 //
+7 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb b and bulb c are contained within a closed path
+// B and C are in the same path with the battery
+
+1 bulb :
+2 b :
+3 and :
+4 bulb :
+5 c :
+6 are :
+7 contained :
+8 within :
+9 a :
+10 closed :
+11 path :
+
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 10 11 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// circuit 5 is in a closed path.
+// the battery is contained in a closed path in which there is no bulb
+
+1 circuit :
+2 5 :
+3 is :
+4 in :
+5 a :
+6 closed :
+7 path. :
+
+
+1 the :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 in :
+10 which :
+11 there :
+12 is :
+13 no :
+14 bulb :
+
+
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to terminal 1
+// Terminals 1 and 6 are separated by the gap
+
+1 terminal :
+2 6 :
+3 is :
+4 connected :
+5 to :
+6 terminal :
+7 1 :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 separated :
+7 by :
+8 the :
+9 gap :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// If bulb B is damaged there is a gap in the circuit
+// there is a gap in a circuit
+
+1 If :
+2 bulb :
+3 B :
+4 is :
+5 damaged :
+6 there :
+7 is :
+8 a :
+9 gap :
+10 in :
+11 the :
+12 circuit :
+
+
+1 there :
+2 is :
+3 a :
+4 gap :
+5 in :
+6 a :
+7 circuit :
+
+
+8 9 <==> 3 4 // EQUI // 5 //
+10 11 12 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb a is in a complete circuit with the battery when switch z is closed.
+// Bulb A is still contained in a closed path with the battery and switch Z.
+
+1 bulb :
+2 a :
+3 is :
+4 in :
+5 a :
+6 complete :
+7 circuit :
+8 with :
+9 the :
+10 battery :
+11 when :
+12 switch :
+13 z :
+14 is :
+15 closed. :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 Z. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+12 13 <==> 10 11 12 13 14 15 // EQUI // 5 //
+14 15 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// bulb a is on a closed path with the battery
+// Bulb A is still in a closed path with the battery
+
+1 bulb :
+2 a :
+3 is :
+4 on :
+5 a :
+6 closed :
+7 path :
+8 with :
+9 the :
+10 battery :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 <==> 3 // EQUI // 5 //
+4 5 6 7 <==> 5 6 7 8 // EQUI // 5 //
+8 9 10 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// because those terminals are connected to the positive terminal of the battery.
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 because :
+2 those :
+3 terminals :
+4 are :
+5 connected :
+6 to :
+7 the :
+8 positive :
+9 terminal :
+10 of :
+11 the :
+12 battery. :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+2 3 <==> 1 2 3 4 5 // EQUI // 5 //
+4 5 <==> 6 7 // EQUI // 5 //
+6 7 8 9 10 11 12 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Not contained in a closed path
+// Bulb C was not in a closed path
+
+1 Not :
+2 contained :
+3 in :
+4 a :
+5 closed :
+6 path :
+
+
+1 Bulb :
+2 C :
+3 was :
+4 not :
+5 in :
+6 a :
+7 closed :
+8 path :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+3 4 5 6 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal connected to positive charge
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 terminal :
+2 connected :
+3 to :
+4 positive :
+5 charge :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 <==> 1 2 3 4 5 // EQUI // 5 //
+2 <==> 6 7 // EQUI // 5 //
+3 4 5 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because voltage measures the difference between two points
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 because :
+2 voltage :
+3 measures :
+4 the :
+5 difference :
+6 between :
+7 two :
+8 points :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 5 6 7 8 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Bulbs a and c are in separate paths.
+// A, B and C are in different paths
+
+1 Bulbs :
+2 a :
+3 and :
+4 c :
+5 are :
+6 in :
+7 separate :
+8 paths. :
+
+
+1 A, :
+2 B :
+3 and :
+4 C :
+5 are :
+6 in :
+7 different :
+8 paths :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+6 7 8 <==> 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// terminal 6 is connected to postive terminal of battery
+// Terminals 1 and 6 are not connected
+
+1 terminal :
+2 6 :
+3 is :
+4 connected :
+5 to :
+6 postive :
+7 terminal :
+8 of :
+9 battery :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to the negative battery terminal
+// the terminals are not connected
+
+1 a :
+2 terminal :
+3 is :
+4 connected :
+5 to :
+6 the :
+7 negative :
+8 battery :
+9 terminal :
+
+
+1 the :
+2 terminals :
+3 are :
+4 not :
+5 connected :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Switch Z is in the same path as bulb A
+// Bulb A is still contained in a closed path with the battery and switch Z.
+
+1 Switch :
+2 Z :
+3 is :
+4 in :
+5 the :
+6 same :
+7 path :
+8 as :
+9 bulb :
+10 A :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 contained :
+6 in :
+7 a :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+13 and :
+14 switch :
+15 Z. :
+
+
+1 2 <==> 10 11 12 13 14 15 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// there will be a gap
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 there :
+2 will :
+3 be :
+4 a :
+5 gap :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+2 3 <==> 1 // EQUI // 5 //
+4 5 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// because each bulb has its own complete path
+// each bulb is in its own path
+
+1 because :
+2 each :
+3 bulb :
+4 has :
+5 its :
+6 own :
+7 complete :
+8 path :
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+1 <==> 3 // EQUI // 5 //
+2 3 <==> 1 2 // EQUI // 5 //
+5 6 7 8 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c have separate paths within the closed circuit
+// If bulb A burns out, B and C are no longer in a closed path with the battery
+
+1 bulbs :
+2 b :
+3 and :
+4 c :
+5 have :
+6 separate :
+7 paths :
+8 within :
+9 the :
+10 closed :
+11 circuit :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 B :
+7 and :
+8 C :
+9 are :
+10 no :
+11 longer :
+12 in :
+13 a :
+14 closed :
+15 path :
+16 with :
+17 the :
+18 battery :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+
+
+
+
+
+// A terminal is connected to a bulb.
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+1 A :
+2 terminal :
+3 is :
+4 connected :
+5 to :
+6 a :
+7 bulb. :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 <==> 6 7 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal has no gaps from terminal 4
+// Terminal 4 and the positive terminal are not separated by the gap
+
+1 the :
+2 positive :
+3 battery :
+4 terminal :
+5 has :
+6 no :
+7 gaps :
+8 from :
+9 terminal :
+10 4 :
+
+
+1 Terminal :
+2 4 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+5 6 7 <==> 7 8 9 10 11 12 // EQUI // 5 //
+8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// when a switch and bulb are whithin a closed path
+// When the switch and the bulb are contained in the same path
+
+1 when :
+2 a :
+3 switch :
+4 and :
+5 bulb :
+6 are :
+7 whithin :
+8 a :
+9 closed :
+10 path :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 <==> 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because the path is short
+// the path is not closed
+
+1 because :
+2 the :
+3 path :
+4 is :
+5 short :
+
+
+1 the :
+2 path :
+3 is :
+4 not :
+5 closed :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Bulb A will no longer be completing the circuts.
+// If bulb A burns out, neither B nor C is in a closed path
+
+1 Bulb :
+2 A :
+3 will :
+4 no :
+5 longer :
+6 be :
+7 completing :
+8 the :
+9 circuts. :
+
+
+1 If :
+2 bulb :
+3 A :
+4 burns :
+5 out, :
+6 neither :
+7 B :
+8 nor :
+9 C :
+10 is :
+11 in :
+12 a :
+13 closed :
+14 path :
+
+
+1 2 <==> 2 3 // EQUI // 5 //
+4 5 <==> 4 5 // EQUI // 5 //
+6 7 <==> 11 12 13 14 // EQUI // 5 //
+
+
+
+
+
+// Bulb C will create a gap in the path
+// each bulb is in its own path
+
+1 Bulb :
+2 C :
+3 will :
+4 create :
+5 a :
+6 gap :
+7 in :
+8 the :
+9 path :
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+7 8 9 <==> 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb a was contained on a closed path with the battery
+// Bulb A was still contained in the same closed path with the battery.
+
+1 bulb :
+2 a :
+3 was :
+4 contained :
+5 on :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+1 Bulb :
+2 A :
+3 was :
+4 still :
+5 contained :
+6 in :
+7 the :
+8 same :
+9 closed :
+10 path :
+11 with :
+12 the :
+13 battery. :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 5 // EQUI // 5 //
+5 6 7 8 <==> 6 7 8 9 10 // EQUI // 5 //
+9 10 11 <==> 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// Terminal 1 is connected to terminl 4.
+// Terminals 1 and 4 are connected
+
+1 Terminal :
+2 1 :
+3 is :
+4 connected :
+5 to :
+6 terminl :
+7 4. :
+
+
+1 Terminals :
+2 1 :
+3 and :
+4 4 :
+5 are :
+6 connected :
+
+
+1 2 <==> 1 2 3 4 // EQUI // 5 //
+3 4 <==> 5 6 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and B are not on the same path as Bulb C.
+// Bulb C is in a separate path
+
+1 Bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 not :
+7 on :
+8 the :
+9 same :
+10 path :
+11 as :
+12 Bulb :
+13 C. :
+
+
+1 Bulb :
+2 C :
+3 is :
+4 in :
+5 a :
+6 separate :
+7 path :
+
+
+5 6 <==> 3 // EQUI // 5 //
+11 <==> 4 5 6 7 // EQUI // 5 //
+12 13 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Each circuit must have a connection.
+// there is a complete circuit
+
+1 Each :
+2 circuit :
+3 must :
+4 have :
+5 a :
+6 connection. :
+
+
+1 there :
+2 is :
+3 a :
+4 complete :
+5 circuit :
+
+
+1 2 <==> 3 4 5 // EQUI // 5 //
+3 4 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// A switch contained in a closed path with a bulb and a battery will affect the bulb.
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 A :
+2 switch :
+3 contained :
+4 in :
+5 a :
+6 closed :
+7 path :
+8 with :
+9 a :
+10 bulb :
+11 and :
+12 a :
+13 battery :
+14 will :
+15 affect :
+16 the :
+17 bulb. :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 2 <==> 2 3 4 5 6 // EQUI // 5 //
+4 5 6 7 <==> 8 9 10 11 // EQUI // 5 //
+14 15 <==> 14 // EQUI // 5 //
+16 17 <==> 15 16 // EQUI // 5 //
+
+
+
+
+
+// Voltage is the difference between a positive and negative terminal on the battery.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 Voltage :
+2 is :
+3 the :
+4 difference :
+5 between :
+6 a :
+7 positive :
+8 and :
+9 negative :
+10 terminal :
+11 on :
+12 the :
+13 battery. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+3 4 <==> 9 10 11 // EQUI // 5 //
+5 6 7 8 9 10 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulbs b and c were in a closed paty with the battery.
+// Bulb B and Bulb C were still contained in the same closed path with the battery.
+
+1 bulbs :
+2 b :
+3 and :
+4 c :
+5 were :
+6 in :
+7 a :
+8 closed :
+9 paty :
+10 with :
+11 the :
+12 battery. :
+
+
+1 Bulb :
+2 B :
+3 and :
+4 Bulb :
+5 C :
+6 were :
+7 still :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 closed :
+13 path :
+14 with :
+15 the :
+16 battery. :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 <==> 6 // EQUI // 5 //
+10 11 12 <==> 14 15 16 // EQUI // 5 //
+
+
+
+
+
+// can complete the path by having z be closed
+// there is a path containing A, C, Z and X
+
+1 can :
+2 complete :
+3 the :
+4 path :
+5 by :
+6 having :
+7 z :
+8 be :
+9 closed :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A, :
+7 C, :
+8 Z :
+9 and :
+10 X :
+
+
+1 <==> 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+7 <==> 6 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// A switch will affect a bulb it the bulb and the switch are in the path as the battery
+// When the switch and the bulb are contained in the same path
+
+1 A :
+2 switch :
+3 will :
+4 affect :
+5 a :
+6 bulb :
+7 it :
+8 the :
+9 bulb :
+10 and :
+11 the :
+12 switch :
+13 are :
+14 in :
+15 the :
+16 path :
+17 as :
+18 the :
+19 battery :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 2 <==> 2 3 4 5 6 // EQUI // 5 //
+13 <==> 7 8 // EQUI // 5 //
+14 15 16 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the positive battery terminal is not connected
+// There is no gap between terminal 6 and the positive terminal
+
+1 the :
+2 positive :
+3 battery :
+4 terminal :
+5 is :
+6 not :
+7 connected :
+
+
+1 There :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 terminal :
+7 6 :
+8 and :
+9 the :
+10 positive :
+11 terminal :
+
+
+1 2 3 4 <==> 5 6 7 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb C are still on a closed path that contains the battery.
+// Bulbs A and C are still in closed paths with the battery
+
+1 Bulb :
+2 A :
+3 and :
+4 bulb :
+5 C :
+6 are :
+7 still :
+8 on :
+9 a :
+10 closed :
+11 path :
+12 that :
+13 contains :
+14 the :
+15 battery. :
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+10 with :
+11 the :
+12 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 4 // EQUI // 5 //
+6 <==> 5 // EQUI // 5 //
+7 <==> 6 // EQUI // 5 //
+8 9 10 11 <==> 7 8 9 // EQUI // 5 //
+13 14 15 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Bulbs A and C will still be on their own completed circuts.
+// Bulbs A and C are in a closed path
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 will :
+6 still :
+7 be :
+8 on :
+9 their :
+10 own :
+11 completed :
+12 circuts. :
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 in :
+7 a :
+8 closed :
+9 path :
+
+
+1 2 3 4 <==> 1 2 3 4 // EQUI // 5 //
+7 <==> 5 // EQUI // 5 //
+
+
+
+
+
+// The damaged bulb B has left a gap in the path so the charge can not reach it
+// Terminals 1, 2 and 3 are separated from the positive battery terminal by a gap
+
+1 The :
+2 damaged :
+3 bulb :
+4 B :
+5 has :
+6 left :
+7 a :
+8 gap :
+9 in :
+10 the :
+11 path :
+12 so :
+13 the :
+14 charge :
+15 can :
+16 not :
+17 reach :
+18 it :
+
+
+1 Terminals :
+2 1, :
+3 2 :
+4 and :
+5 3 :
+6 are :
+7 separated :
+8 from :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+13 by :
+14 a :
+15 gap :
+
+
+7 8 <==> 13 14 15 // EQUI // 5 //
+13 14 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// the terminal is separated from the battery terminal
+// the terminals are separated by a gap
+
+1 the :
+2 terminal :
+3 is :
+4 separated :
+5 from :
+6 the :
+7 battery :
+8 terminal :
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// a terminal is connected to another terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 a :
+2 terminal :
+3 is :
+4 connected :
+5 to :
+6 another :
+7 terminal :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+3 4 <==> 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulb A is connected to switch Z
+// There is no path containing both switch Y and bulb A
+
+1 bulb :
+2 A :
+3 is :
+4 connected :
+5 to :
+6 switch :
+7 Z :
+
+
+1 There :
+2 is :
+3 no :
+4 path :
+5 containing :
+6 both :
+7 switch :
+8 Y :
+9 and :
+10 bulb :
+11 A :
+
+
+1 2 <==> 7 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// there is a closed path, with switch z, that contains bulb a and the battery
+// there is a path containing A, C, Z and the battery
+
+1 there :
+2 is :
+3 a :
+4 closed :
+5 path, :
+6 with :
+7 switch :
+8 z, :
+9 that :
+10 contains :
+11 bulb :
+12 a :
+13 and :
+14 the :
+15 battery :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 A, :
+7 C, :
+8 Z :
+9 and :
+10 the :
+11 battery :
+
+
+1 <==> 1 // EQUI // 5 //
+6 7 8 <==> 5 // EQUI // 5 //
+11 12 13 14 15 <==> 6 7 8 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// Terminal 4, terminal 5, and terminal 6 are connected to the positive terminal
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 Terminal :
+2 4, :
+3 terminal :
+4 5, :
+5 and :
+6 terminal :
+7 6 :
+8 are :
+9 connected :
+10 to :
+11 the :
+12 positive :
+13 terminal :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 5 6 7 <==> 1 2 3 4 5 // EQUI // 5 //
+8 9 <==> 6 7 // EQUI // 5 //
+10 11 12 13 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// Circuit 2 is not a short circuit because the battery is not connected to itself.
+// The battery in 2 is not in a closed path
+
+1 Circuit :
+2 2 :
+3 is :
+4 not :
+5 a :
+6 short :
+7 circuit :
+8 because :
+9 the :
+10 battery :
+11 is :
+12 not :
+13 connected :
+14 to :
+15 itself. :
+
+
+1 The :
+2 battery :
+3 in :
+4 2 :
+5 is :
+6 not :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 7 8 9 10 // EQUI // 5 //
+8 <==> 5 6 // EQUI // 5 //
+9 10 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Because terminal 1 is seperated from the positive battery terminal.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 Because :
+2 terminal :
+3 1 :
+4 is :
+5 seperated :
+6 from :
+7 the :
+8 positive :
+9 battery :
+10 terminal. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulb a and bulb c are contained in different paths with the bttery.
+// A and C are in different paths with the battery
+
+1 bulb :
+2 a :
+3 and :
+4 bulb :
+5 c :
+6 are :
+7 contained :
+8 in :
+9 different :
+10 paths :
+11 with :
+12 the :
+13 bttery. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+8 with :
+9 the :
+10 battery :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+6 7 <==> 4 // EQUI // 5 //
+8 9 10 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// because bulb a is in a closed path with the battery.
+// Bulb A is still in a closed path with the battery
+
+1 because :
+2 bulb :
+3 a :
+4 is :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery. :
+
+
+1 Bulb :
+2 A :
+3 is :
+4 still :
+5 in :
+6 a :
+7 closed :
+8 path :
+9 with :
+10 the :
+11 battery :
+
+
+2 3 <==> 1 2 // EQUI // 5 //
+4 <==> 3 // EQUI // 5 //
+5 6 7 8 <==> 5 6 7 8 // EQUI // 5 //
+9 10 11 <==> 9 10 11 // EQUI // 5 //
+
+
+
+
+
+// the positive terminal is connected to the bulb
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 the :
+2 positive :
+3 terminal :
+4 is :
+5 connected :
+6 to :
+7 the :
+8 bulb :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because bulb a is in a closed path, and bulb c is in a closed path.
+// Bulbs A and C are still in closed paths
+
+1 because :
+2 bulb :
+3 a :
+4 is :
+5 in :
+6 a :
+7 closed :
+8 path, :
+9 and :
+10 bulb :
+11 c :
+12 is :
+13 in :
+14 a :
+15 closed :
+16 path. :
+
+
+1 Bulbs :
+2 A :
+3 and :
+4 C :
+5 are :
+6 still :
+7 in :
+8 closed :
+9 paths :
+
+
+2 3 <==> 1 2 3 4 // EQUI // 5 //
+4 5 6 7 8 <==> 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// The positive terminal has 1.5 V
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 The :
+2 positive :
+3 terminal :
+4 has :
+5 1.5 :
+6 V :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// because of the chemical in the battery
+// A battery uses a chemical reaction to maintain different electrical states at the terminals
+
+1 because :
+2 of :
+3 the :
+4 chemical :
+5 in :
+6 the :
+7 battery :
+
+
+1 A :
+2 battery :
+3 uses :
+4 a :
+5 chemical :
+6 reaction :
+7 to :
+8 maintain :
+9 different :
+10 electrical :
+11 states :
+12 at :
+13 the :
+14 terminals :
+
+
+1 2 3 4 <==> 4 5 6 // EQUI // 5 //
+5 6 7 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// Both components need to be in closed paths.
+// the bulb and the battery are in a closed path
+
+1 Both :
+2 components :
+3 need :
+4 to :
+5 be :
+6 in :
+7 closed :
+8 paths. :
+
+
+1 the :
+2 bulb :
+3 and :
+4 the :
+5 battery :
+6 are :
+7 in :
+8 a :
+9 closed :
+10 path :
+
+
+1 2 <==> 1 2 3 4 5 // EQUI // 5 //
+3 4 5 <==> 6 // EQUI // 5 //
+6 7 8 <==> 7 8 9 10 // EQUI // 5 //
+
+
+
+
+
+// bulb a and bulb c are wired in parallel
+// A and C are in different paths
+
+1 bulb :
+2 a :
+3 and :
+4 bulb :
+5 c :
+6 are :
+7 wired :
+8 in :
+9 parallel :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 different :
+7 paths :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+8 9 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// Bulb terminals 3 and 4
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 Bulb :
+2 terminals :
+3 3 :
+4 and :
+5 4 :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+1 2 3 4 5 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// the other bulb will not light.
+// The damaged bulb and the other bulb must be contained in the same path
+
+1 the :
+2 other :
+3 bulb :
+4 will :
+5 not :
+6 light. :
+
+
+1 The :
+2 damaged :
+3 bulb :
+4 and :
+5 the :
+6 other :
+7 bulb :
+8 must :
+9 be :
+10 contained :
+11 in :
+12 the :
+13 same :
+14 path :
+
+
+1 2 3 <==> 1 2 3 4 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// because there was a gap in the terminals
+// there is no path containing both switch Y and bulb A
+
+1 because :
+2 there :
+3 was :
+4 a :
+5 gap :
+6 in :
+7 the :
+8 terminals :
+
+
+1 there :
+2 is :
+3 no :
+4 path :
+5 containing :
+6 both :
+7 switch :
+8 Y :
+9 and :
+10 bulb :
+11 A :
+
+
+6 7 8 <==> 6 // EQUI // 5 //
+
+
+
+
+
+// if the switch is open in a path with the battery and bulb.
+// When the switch and the bulb are contained in the same path
+
+1 if :
+2 the :
+3 switch :
+4 is :
+5 open :
+6 in :
+7 a :
+8 path :
+9 with :
+10 the :
+11 battery :
+12 and :
+13 bulb. :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+6 7 8 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// 4, 5, and 6 are connected to the positive side
+// Terminals 4, 5 and 6 are connected to the positive battery terminal
+
+1 4, :
+2 5, :
+3 and :
+4 6 :
+5 are :
+6 connected :
+7 to :
+8 the :
+9 positive :
+10 side :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 connected :
+8 to :
+9 the :
+10 positive :
+11 battery :
+12 terminal :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 <==> 6 7 // EQUI // 5 //
+7 8 9 10 <==> 8 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// a voltage reading of 0 volts indicates a gap in the circuit.
+// there is no gap between the terminals
+
+1 a :
+2 voltage :
+3 reading :
+4 of :
+5 0 :
+6 volts :
+7 indicates :
+8 a :
+9 gap :
+10 in :
+11 the :
+12 circuit. :
+
+
+1 there :
+2 is :
+3 no :
+4 gap :
+5 between :
+6 the :
+7 terminals :
+
+
+8 9 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// 4 5 and 6 are not connected to negative battery terminal
+// Terminals 4, 5 and 6 are not connected to the negative battery terminal
+
+1 4 :
+2 5 :
+3 and :
+4 6 :
+5 are :
+6 not :
+7 connected :
+8 to :
+9 negative :
+10 battery :
+11 terminal :
+
+
+1 Terminals :
+2 4, :
+3 5 :
+4 and :
+5 6 :
+6 are :
+7 not :
+8 connected :
+9 to :
+10 the :
+11 negative :
+12 battery :
+13 terminal :
+
+
+1 2 3 4 <==> 1 2 3 4 5 // EQUI // 5 //
+5 6 7 <==> 6 7 8 // EQUI // 5 //
+8 9 10 11 <==> 9 10 11 12 13 // EQUI // 5 //
+
+
+
+
+
+// bulbs a and b are still contained on a closed path with the battery
+// If C burns out then A and B are still in a closed path with the battery
+
+1 bulbs :
+2 a :
+3 and :
+4 b :
+5 are :
+6 still :
+7 contained :
+8 on :
+9 a :
+10 closed :
+11 path :
+12 with :
+13 the :
+14 battery :
+
+
+1 If :
+2 C :
+3 burns :
+4 out :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+8 9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+12 13 14 <==> 15 16 17 // EQUI // 5 //
+
+
+
+
+
+// bulbs a, b, and c are all in the same path.
+// A and C are in the same path
+
+1 bulbs :
+2 a, :
+3 b, :
+4 and :
+5 c :
+6 are :
+7 all :
+8 in :
+9 the :
+10 same :
+11 path. :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+8 9 10 11 <==> 5 6 7 8 // EQUI // 5 //
+
+
+
+
+
+// a and c are on the same closed path with the battery
+// A and C are in the same closed path
+
+1 a :
+2 and :
+3 c :
+4 are :
+5 on :
+6 the :
+7 same :
+8 closed :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 2 3 <==> 1 2 3 // EQUI // 5 //
+4 <==> 4 // EQUI // 5 //
+5 6 7 8 9 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// "if the switch is included in the bulb""s closed path, then the switch being open will affect the bulb"
+// If a bulb and a switch are in the same path the switch affects the bulb
+
+1 "if :
+2 the :
+3 switch :
+4 is :
+5 included :
+6 in :
+7 the :
+8 bulb""s :
+9 closed :
+10 path, :
+11 then :
+12 the :
+13 switch :
+14 being :
+15 open :
+16 will :
+17 affect :
+18 the :
+19 bulb" :
+
+
+1 If :
+2 a :
+3 bulb :
+4 and :
+5 a :
+6 switch :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+12 the :
+13 switch :
+14 affects :
+15 the :
+16 bulb :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 <==> 2 3 4 5 6 // EQUI // 5 //
+4 5 <==> 7 // EQUI // 5 //
+9 10 <==> 8 9 10 11 // EQUI // 5 //
+12 13 <==> 12 13 // EQUI // 5 //
+16 17 <==> 14 // EQUI // 5 //
+18 19 <==> 15 16 // EQUI // 5 //
+
+
+
+
+
+// because the outcome of the bulb will not affect each other
+// A and C are not in the same path with the battery
+
+1 because :
+2 the :
+3 outcome :
+4 of :
+5 the :
+6 bulb :
+7 will :
+8 not :
+9 affect :
+10 each :
+11 other :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 path :
+10 with :
+11 the :
+12 battery :
+
+
+4 5 6 <==> 10 11 12 // EQUI // 5 //
+10 11 <==> 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// not seperated by a gap
+// Terminal 6 and the positive terminal are not separated by the gap
+
+1 not :
+2 seperated :
+3 by :
+4 a :
+5 gap :
+
+
+1 Terminal :
+2 6 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 not :
+9 separated :
+10 by :
+11 the :
+12 gap :
+
+
+1 2 <==> 7 8 9 // EQUI // 5 //
+3 4 5 <==> 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// because terminal 1 and the neavtive terminal are seperated.
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 because :
+2 terminal :
+3 1 :
+4 and :
+5 the :
+6 neavtive :
+7 terminal :
+8 are :
+9 seperated. :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+2 3 4 5 6 7 <==> 1 2 3 4 5 6 // EQUI // 5 //
+8 9 <==> 7 8 // EQUI // 5 //
+
+
+
+
+
+// Because their is a gap between A and C now.
+// there is an incomplete circuit
+
+1 Because :
+2 their :
+3 is :
+4 a :
+5 gap :
+6 between :
+7 A :
+8 and :
+9 C :
+10 now. :
+
+
+1 there :
+2 is :
+3 an :
+4 incomplete :
+5 circuit :
+
+
+4 5 <==> 3 4 5 // EQUI // 5 //
+
+
+
+
+
+// Bulb A and bulb b are still contained in closed paths with the battery
+// If C burns out then A and B are still in a closed path with the battery
+
+1 Bulb :
+2 A :
+3 and :
+4 bulb :
+5 b :
+6 are :
+7 still :
+8 contained :
+9 in :
+10 closed :
+11 paths :
+12 with :
+13 the :
+14 battery :
+
+
+1 If :
+2 C :
+3 burns :
+4 out :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery :
+
+
+1 2 3 4 5 <==> 6 7 8 // EQUI // 5 //
+6 <==> 9 // EQUI // 5 //
+7 <==> 10 // EQUI // 5 //
+9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+12 13 14 <==> 15 16 17 // EQUI // 5 //
+
+
+
+
+
+// B and C are not in the same circuit as A.
+// each bulb is in its own path
+
+1 B :
+2 and :
+3 C :
+4 are :
+5 not :
+6 in :
+7 the :
+8 same :
+9 circuit :
+10 as :
+11 A. :
+
+
+1 each :
+2 bulb :
+3 is :
+4 in :
+5 its :
+6 own :
+7 path :
+
+
+6 7 8 9 <==> 4 5 6 7 // EQUI // 5 //
+10 <==> 3 // EQUI // 5 //
+11 <==> 1 2 // EQUI // 5 //
+
+
+
+
+
+// there terminals are separated by a gap when the voltage jumps from 0 to 1.5.
+// the terminals are separated by a gap
+
+1 there :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+8 when :
+9 the :
+10 voltage :
+11 jumps :
+12 from :
+13 0 :
+14 to :
+15 1.5. :
+
+
+1 the :
+2 terminals :
+3 are :
+4 separated :
+5 by :
+6 a :
+7 gap :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+3 4 <==> 3 4 // EQUI // 5 //
+5 6 7 <==> 5 6 7 // EQUI // 5 //
+
+
+
+
+
+// bulbs a b and c are on a closed path
+// A and C are in the same closed path
+
+1 bulbs :
+2 a :
+3 b :
+4 and :
+5 c :
+6 are :
+7 on :
+8 a :
+9 closed :
+10 path :
+
+
+1 A :
+2 and :
+3 C :
+4 are :
+5 in :
+6 the :
+7 same :
+8 closed :
+9 path :
+
+
+1 2 3 4 5 <==> 1 2 3 // EQUI // 5 //
+7 8 9 10 <==> 5 6 7 8 9 // EQUI // 5 //
+
+
+
+
+
+// I think the red X means that this is dangerous and should never happen unless something is seriously wrong.
+// there is a short circuit
+
+1 I :
+2 think :
+3 the :
+4 red :
+5 X :
+6 means :
+7 that :
+8 this :
+9 is :
+10 dangerous :
+11 and :
+12 should :
+13 never :
+14 happen :
+15 unless :
+16 something :
+17 is :
+18 seriously :
+19 wrong. :
+
+
+1 there :
+2 is :
+3 a :
+4 short :
+5 circuit :
+
+
+19 <==> 2 // EQUI // 5 //
+
+
+
+
+
+// because there was no gap from the positive terminal of the battery
+// Terminal 1 and the positive terminal are separated by the gap
+
+1 because :
+2 there :
+3 was :
+4 no :
+5 gap :
+6 from :
+7 the :
+8 positive :
+9 terminal :
+10 of :
+11 the :
+12 battery :
+
+
+1 Terminal :
+2 1 :
+3 and :
+4 the :
+5 positive :
+6 terminal :
+7 are :
+8 separated :
+9 by :
+10 the :
+11 gap :
+
+
+4 5 <==> 9 10 11 // EQUI // 5 //
+6 7 8 9 <==> 1 2 3 4 5 6 // EQUI // 5 //
+
+
+
+
+
+// bulbs A and B are still connected to the closed path containing the battery
+// If C burns out then A and B are still in a closed path with the battery
+
+1 bulbs :
+2 A :
+3 and :
+4 B :
+5 are :
+6 still :
+7 connected :
+8 to :
+9 the :
+10 closed :
+11 path :
+12 containing :
+13 the :
+14 battery :
+
+
+1 If :
+2 C :
+3 burns :
+4 out :
+5 then :
+6 A :
+7 and :
+8 B :
+9 are :
+10 still :
+11 in :
+12 a :
+13 closed :
+14 path :
+15 with :
+16 the :
+17 battery :
+
+
+1 2 3 4 <==> 6 7 8 // EQUI // 5 //
+5 <==> 9 // EQUI // 5 //
+6 <==> 10 // EQUI // 5 //
+8 9 10 11 <==> 11 12 13 14 // EQUI // 5 //
+12 13 14 <==> 15 16 17 // EQUI // 5 //
+
+
+
+
+
+// if the switch and the bulb are in the same path
+// When the switch and the bulb are contained in the same path
+
+1 if :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 in :
+9 the :
+10 same :
+11 path :
+
+
+1 When :
+2 the :
+3 switch :
+4 and :
+5 the :
+6 bulb :
+7 are :
+8 contained :
+9 in :
+10 the :
+11 same :
+12 path :
+
+
+1 <==> 1 // EQUI // 5 //
+2 3 4 5 6 <==> 2 3 4 5 6 // EQUI // 5 //
+7 <==> 7 8 // EQUI // 5 //
+8 9 10 11 <==> 9 10 11 12 // EQUI // 5 //
+
+
+
+
+
+// bulb c and switch z are in the same closed path
+// there is a path containing both Z and C
+
+1 bulb :
+2 c :
+3 and :
+4 switch :
+5 z :
+6 are :
+7 in :
+8 the :
+9 same :
+10 closed :
+11 path :
+
+
+1 there :
+2 is :
+3 a :
+4 path :
+5 containing :
+6 both :
+7 Z :
+8 and :
+9 C :
+
+
+1 2 3 4 5 <==> 7 8 9 // EQUI // 5 //
+6 <==> 6 // EQUI // 5 //
+7 8 9 10 11 <==> 3 4 // EQUI // 5 //
+
+
+
+
+
+// the bulb only has one terminal connected
+// The battery is contained in a path which does not contain any other components
+
+1 the :
+2 bulb :
+3 only :
+4 has :
+5 one :
+6 terminal :
+7 connected :
+
+
+1 The :
+2 battery :
+3 is :
+4 contained :
+5 in :
+6 a :
+7 path :
+8 which :
+9 does :
+10 not :
+11 contain :
+12 any :
+13 other :
+14 components :
+
+
+1 2 <==> 1 2 // EQUI // 5 //
+4 <==> 9 10 11 // EQUI // 5 //
+
+
+
+