Current Electricity

## Current

Current is the flow of charge per unit time through a cross sectional area .

I = Q/t

I = neAVd

Current and charge remain the same in series . Voltafe is lost so that current remains the same .

## Potential Difference

THe work done in moving a test positive charge from one point to another in an electric field is calld as Potential Difference .

V = W / Q

Voltage remains same in parallel combination . The current gets distributed according to voltages in the parallel branches .

## Ohm's Law

The Ohm's law states that the current flowing through a metallic conductor is directly proportional to the potential difference across its terminals provided that the physical factors remain constant .

V = RI

## Resistance and Resistivity

The tendency to oppose the flow of current is called as Resistance .
The resistance of a wire of unit length and unit area of cross section is called Resistivity .

Resistivity is the fundamental property of a material . The resistance can be changed by modifying the length and Area of cross section . Resistivity remains constant . Resistivity can change only if temperature is changed considerably .

When a 50 ohm wire is divided into 5 equal parts , the resistance of each part is 10 ohm .

## Drift Velocity

J = nev

v = J/ne

I = neAVd

NOTE : Current flows in opposite direction of drift velocity .

## Temperature Dependence of Resistance

The temperature coefficient of resistance is defined as the rise in resistance per unit rise in temperature per unit original length .

## PTC and NTC

If Resistance/Resistivity increases with increase in temperature (positive slope) , it is PTC (Positive Temperature Co-efficient)

e.g. Metals , Conductors .

If Resistance decreases with increase in temperature (negative slope) , it is NTC (Negative Temperature co-efficient)

e.g. Semiconductors

Note : The resistivity changes with temprature , thus changing the resistance .

## Thermistor

They are also called Thermal Resistors . Resistances which are affected by temperature . Two types NTC , PTC .

Thermisters are made up of metal oxides of high co-efficient of resistivity .

## Thermal Effect of Current

When we have a thermo-couple , one at hot end and other being cold , the variation in EMF is given as :-

e = aθ + bθ2

The temperature at which the EMF is maximum is called as **Neutral Temperature** .

At the **inversion temperature** , the polarity of the emf is reversed . The graph of variation of emf starts from cold junction and goes maximum up to neutral temperature and then starts decreasing as we move towards hot junction .

θn = (θi + θc ) / 2

## Colour Code for Resistors

B
B
R
O
Y
G
B
V
G
W
G
S
N

## Combination of Resistors

Series

Rs = R1 + R2 +... + Rn

Parallel

1/Rp = 1/R1 + 1/R2 + ...... + 1/Rn

## Combination of Cells

Series
The Voltages are added to give effective voltage .

Parallel
The voltages remain same throughout the combination .

## Electro Motive Force

The force provided by voltage source , so as to overcome the resistance of the conductor is called as Electromotive Force .

For ideal Battery , E = V

For a cell with internal resistance r , V = E - ir .

NOTE : For EMF, Internal Resistance has to be considered as well .

## Internal Resistance

If the internal resistance of a cell is zero , then it will supply constant current to the circuit .

## Work Done by Electric

Work done = I2Rt

1 eV is the amount of electric work done when a single electron flows through the conductor when 1 volt of P.D. is applied across its terminals .
1eV = 1.6 x10-19 J

## Heating Effect of Electric Current

H = I2Rt

= V2/R

= VIt

## Electric Power

Electric power is the rate of doing work .
It can also be defined as the rate at which electric energy is consumed .

P = I2R = V2/Rt = VI

## Kirchoff's Laws

**Kirchoff's Current Law**

It states that the sum of current at a junction is zero . The current flowing towards the junction is taken as positive and the current flowing away from the junction is taken as negative .

**Kirchoff's Voltage Law**

It states that the sum of EMFs and Voltages (IR) in a loop is equal to zero .

EMFs in the direction of the loop is taken as positive , while against the loop is taken as negative .

Voltages (IR) in the direction is loop is taken as negative and against the loop is taken as positive .

Note :

For MCQs , whenever there are a large number of voltages , EMFs or currents , use Kirchoof's Loop Laws

## Wheatstone's Network

The Wheatstone's Network consists of four resistances through which a galvanometer is connected . The unknown resistance can be calculated by the formula R1 / R2 = R3 / R4 , . i.e. Left/ Right = Left / Right .

Note : The middle resistance is ignored when the network is balanced .

## Wheatstone's Meterbridge

Wheatstone's Meterbridge and potentiometer work on the principle of Wheatstone,s Network .

Wheatstone's meterbridge consists of two L shaped wooden strips , between which , two resistors are connected . A Jockey , containing a centre - zero deflection galvanometer is connected at a point between the two resistors . A 1 m long wire is connected below the resistors .

The switch is turned on and the jockey is now tapped at point A . It is then tapped at point C . It should give deflections on either sides , if not adjust the rheostat . Now , start tapping the wire till you reach a point , where the deflection is zero . Take this distance as l . hence , the remaining distance is (100 - l) cm .

The wire AC has certain resistance , which is directly proportional to the length of the wire . Using this relation we can find the unknown resistance connected above on one of the wooden planks . The relation in Wheatstone's Meterbridge is :-

R1 / R2 = R3 / R4

## Potentiometer

A potentiometer is like an ideal voltmeter , because it does not draw any current from the circuit .

**Principle**

V α l

... Potential Gradient = Constant

**A) Comparison Method**

E1 / E2 = l1 / l2

**B) Combination Method**

E1 + E2 / E1 - E2 = L1 / L2

**C) Internal Resistance**

r = R [(l1 - l2) / l2]

## Capacitors in Circuit

While in steady state , no current flows through capacitor .

**Capacitors in Series**

1/Cp = 1/C1 + 1/C2 + ...... + 1/Cn

**Capacitors in Parallel**

Cs = C1 + C2 +... + Cn

## Charging and Discharging of Capacitors

THe graph of charge v/s time of Capaitor is exponential .

**Charging :**

q = EC(1 - e-t/CR)

**Discharging :**

q = Qe-t/CR

## Tips & Tricks

1. When n resistors of Resistance R are connected in series , the total resistance is nR .
2. When n series of Resistance R are connected in parallel , the total resistance is R/n .
3. If a wire of resistance R is stretched n (l2/l1) times , The new resistance is n2R
4. When a complicated symmetric circuit is given for finding resistance , it can be divided into halves to simplify the circuit .
5. When simplifying a circuit , plot points on the circuit to guide you .
6. In Wheatstone's network , if the network is balanced , the middle resistance is ignored because no current flows through it .
7. Whenever , a part of circuit confuses you , remove it and see it's role in the circuit .
8. The effective resistance for a balanced Wheatstone's Network is R
9. For equivalent resistances , consider current through each branch .
10. Use Kirchoff's laws for complicated circuits .