# GCSE Science/Parallel and series circuits

GCSE Science/Electricity
You will have already studied series and parallel circuits before, so should be familiar with what a series and parallel circuit is and their basic properties.But in this module we will be looking at them in a little more detail. We will apply Ohm's law to see how we can work out the resistance of a whole circuit that is made up of a large number of components. Before we begin You might want to try some revision questions. Follow the link then come back here when you are finished.

## Resistors in Series Circuits

As we know, in a series circuit the current in all parts of the circuit is the same and the current has a one way system. The current depends on the applied voltage and the number of and nature of other components in the circuit.
Consider two resistors in a series circuit with a battery. As you might expect the total resistance in this circuit is higher than the resistance of each resistor, because the battery has to "push" the charge through both resistors one after the other. So the total potential difference of the supply is "shared" between the two resistors.
Think about what is happening to the current as it flows around the circuit. There are no branches, nowhere for the electric current to escape to, so obviously the same current must flow through both resistors. Let's call this current I.
The total resistance for the whole circuit is very simple. It's just R$_1$ plus R$_2$.

### Formula for resistance of two resistors in series

R$_{Total}$ = R$_1$ + R$_2$
The total resistance in a series circuit is the sum of the resistances of all the components.
Using this formula we can calculate the voltage across each resistor. But it could depend on how many resistors there are.

### Example: Calculating voltages in a series circuit

Question:
Suppose R$_1$ = 1Ω and R$_2$= 4Ω. If the battery supplies 2.5 Volts what is the voltage across each resistor.
Answer:
First use the total resistance of the circuit to work out how much current is flowing through the circuit.
Step 1: Work out the total resistance
* identify formula: R$_{Total}$ = R$_1$ + R$_2$
* insert numbers and units R$_{Total}$ = 1Ω + 4Ω = 5Ω
Step 2: Use Ohms's law to calculate the current in the circuit. Decide which resistance to use.
* identify formula(using the triangle): I = V / R (Ohms's law)
* decide which resistance to use: Use R$_{Total}$; so formula becomes I = V / R$_{Total}$
* insert numbers and units I amps = 2.5V / 5Ω = 0.5A
Now we know how much current is flowing through both resistors, we can work out the voltage across each resistor.
Step 3: Use Ohm's law to calculate the voltage across each resistor:
* identify formula(using the triangle): V = I x R
* insert numbers for resistor 1: V$_1$ volts = 0.5A x 1Ω = 0.5 Volts
* insert numbers for resistor 2: V$_2$ volts = 0.5A x 4Ω = 2.0 Volts

### Practice questions

* Q1)Let R$_1$ = 2Ω, R$_2$= 3Ω, and V=5V what is the voltage across R$_1$ and R$_2$ ?
* Q2)Let R$_1$ = 3Ω, R$_2$= 3Ω, and V=6V what is the voltage across R$_1$ and R$_2$ ?
* Q3)Let R$_1$ = 2Ω, V=5V and I= 1A what is the value of resistor R$_2$ ?

## Resistors in Parallel Circuits

Parallel circuits are a bit more complicated than series circuits, because they contain a branch - the electric current will take more than one route. Look at the diagram. At point X the current splits into 2 paths, and flows through both resistor R$_1$ and resistor R$_2$. It may not split in equal amounts. When several(two or more) components are connected in parallel branches, the voltage (potential difference) across each parallel branch is the same. And this is the same as the voltage across the battery.
The current through each component is the same as if it were the only component present. So the total current flowing through the battery is the sum of the currents flowing through each branch. Here is the formula for the currents flowing through a parallel circuit.
I$_{Main}$ = I$_1$ + I$_2$
Because the voltage is the same for all branches, the branch with the lowest resistance has the highest current flowing through it. Because there are more paths for the charge to flow along, the total resistance is less than either of the two paths on their own. And therefore (with the same battery) the current is bigger.
To find out the resistance of the whole circuit , we can't just add together the resistors as we did in the series circuit, we have to apply Ohm's law to each branch of the circuit.
Imagine we replaced the resistors with bulbs. You should now be able to answer the following questions from your previous knowledge.
* Q4)You disconnect one of the bulbs, does the other stay lit?
* Q5)You reconnect the disconnected bulb, does the other dim or brighten?
* Q6)Would it be reasonable to say "each branch of the circuit behaves as if the other branch weren't there" ?
If you answered the above questions correctly you should find this next section easy!

### Example: Calculating the resistance of several resistors in parallel

It's best to break the process down into a number of simple steps. Some books may give you a formula to use, but you shouldn't use any formula without understanding where it comes from (otherwise you are likely to remember it incorrectly or apply it inappropriately). By using a simple step by step method instead you can get a feel for why it works, and you will be far less likely to make a mistake in the exam.
Step1 considering each branch on its own, as if the other branch didn't exist use Ohm's law to work out the current flowing through each branch.
Step 2 Add the currents together to find out the total amount of current flowing through the whole circuit.
Step 3 Apply Ohm's law again to work out the total resistance of the circuit.

### Example

Suppose V=2V R$_1$ = 1Ω and R$_2$= 1Ω.
Applying Ohm's law to the branch containing R$_1$ gives
I$_1$=V/R$_1$ =2/1 =2A
Applying Ohm's law to the branch containing R$_2$ gives I$_2$=V/R$_2$ =2/1 =2A
Total current = I$_1$+I$_2$ = 4A
Applying Ohm's law again, to the whole circuit.
R$_{Total}$ =V/I$_{total}$ = 2/4 =0.5Ω
Notice that the resistance of the whole circuit is lower than the resistance of either branch!

### Practice questions

* Q7) Calculate the resistance of the above pair of resistors if they had been in series rather than parallel.
* Q8) A parallel circuit has two resistors, one is 2Ω the other is 3Ω. The voltage is 6V. What is the total resistance of the circuit?
* Q9) Three resistors are in parallel (three separate branches) their resistances are 2Ω, 2Ω and 3Ω. The voltage is 6V. What is the resistance of the circuit?
* Summary
* Series Circuits The current through each component is the same. To find the total resistance just add the individual ones up. The total voltage is the sum of the voltages across the individual components.
* Parallel Circuits Each branch acts as if the other branches were not there. The Voltage across each branch is the same. Ohm's law can be applied to each branch separately. The total current, is just the sum of the currents through each branch.
Answers | Three useful components>>