Atomic Energy Education Society, Mumbai

Chapter-3 CURRENT ELECTRICITY

Module - 3

By

Girish Kumar

PGT (Physics) AECS Narora

1) Resistances in series 2) Resistances in parallel 3) Joules heating effect current 4) Power in series and in parallel 5) Transmission through conducting wire 6) Source of emf 7) Internal resistance 8) Relationship between E,V,r and R 9) Cells in Series combination 10) Cells in parallel combination

Current Electricity

Topics covered in Module - 3

Resistance in Series

If a number of resistances are connected end to end so that the same current flows through each one of them in succession then resistances are said to be connected in series.

By Ohms law, the potential drops across the three resistances are

V1= IR1, V2 = IR2, V3 = IR3

V = V1 + V2 + V3

IReq= I(R1 + R2 + R3)

Req = R1 + R2 + R3

Equivalent resistance is more than maximum of the individual resistance

Resistance in parallel

If number of resistances are connected in between two common points so that each of them provides a separate path for current then resistances are said to be connected in parallel.

Since all the resistance have been connected between same two points A and B, therefore, potential drop V is same across each of them.

The total Current in the main circuit is given by

I = I1 + I2 + I3

By Ohms law,

I1 = V/R1 , I2 = V/R2 , I3 = V/R3

V/Req = V(1/R1 + 1/R2 + 1/R3)

1/Req = 1/R1 + 1/R2 + 1/R3

Equivalent resistance is less than the least value among individual resistances.

Joule’s heating effect The law state that heat ‘H’ produced in a resistor of resistance R is

i) directly proportional to the square of electric current flowing through it, H α I2

ii) directly proportional to resistance of the circuit, H α R iii) directly proportional to the time t

H α t H = I2RT

H = {V2/R}t H = VIt

Electric power: The rate at which work is done by source of emf in maintaining an electric current through a circuit is called electric power of the circuit.

P = W/t = VI = I2R = V2/R

Electric power = Current x Voltage SI unit of Power is Watt

Power Consumption by a series combination

Power Consumption by a parallel combination

The resistance of three bulb, R1 = V2/P1 R2 = V2/P2 R3 = V2/P3

In series, R = R1 + R2 + R3

V2/P = V2/P1 + V2/P2 + V2/P3

1/P = 1/P1 + 1/P2 + 1/ P3

As, R α 1/P

The resistance of three bulb, R1 = V2/P1 R2= V2/P2 R3 = V2/P3

In parallel, 1/R = 1/R1 + 1/R2 + 1/R3

P = P1 + P2 + P3

Application of power transmission Electric power is transmitted from power station to homes and factories which

may be hundreds of miles. One obviously want to minimize the power loss in transmission cables connecting the power stations to home and factories.

Consider a device R, to which a power P to be delivered via transmission cable having a resistance Rc to be dissipated by it finally. If V is the voltage across R and I , current through it , then

P = VI

The connecting wires from the power station to the device has a finite resistance Rc. The power dissipated in the connecting wire, which is wasted is Pc with

Pc = I2Rc

Pc = P2Rc/V2

To drive a device of power P, the power wasted in the connected wires is inversely proportional to V2.

To reduce Pc, these wires carry current at enormous value of V. This is the reason for the high voltage danger signs on transmission lines.

Sources of emf: The electro motive force is the maximum potential difference between the

two electrodes of the cell when no current is drawn from the cell.

Comparison of EMF and P.D:

EMF Potential Difference

1 EMF is the maximum potential

difference between the two

electrodes of the cell when no

current is drawn from the cell

i.e. when the circuit is open.

P.D is the difference of potentials

between any two points in a closed

circuit.

2 It is independent of the

resistance of the circuit.

It is proportional to the resistance

between the given points.

3 The term ‘emf’ is used only for

the source of emf.

It is measured between any two

points of the circuit.

4 It is greater than the potential

difference between any two

points in a circuit.

However, p.d. is greater than emf

when the cell is being charged.

Internal Resistance of a cell: The opposition offered by the electrolyte of the cell to the flow ofelectric

current through it is called the internal resistance of the cell.

Factors affecting Internal Resistance of a cell:

i) Larger the separation between the electrodes of the cell, more the length

of the electrolyte through which current has to flow and consequently a

higher value of internal resistance.

ii) Greater the conductivity of the electrolyte, lesser is the internal resistance

of the cell. i.e. internal resistance depends on the nature of the electrolyte.

iii) The internal resistance of a cell is inversely proportional to the common

area of the electrodes dipping in the electrolyte.

iv) The internal resistance of a cell depends on the nature of the electrodes.

E = V + v

= IR + Ir

= I (R + r)

I = E / (R + r)

This relation is called circuit equation.

Internal Resistance of a cell in terms of E,V and R:

Determination of Internal Resistance of a cell by voltmeter method:

E = V + v

= V + Ir

Ir = E - V

Dividing by IR = V,

r = ( - 1) R E

V

Ir E – V

IR V =

Cells in Series combination:

Cells are connected in series when they are joined end to end so that the

same quantity of electricity must flow through each cell.

NOTE:

1. The emf of the battery is the

sum of the individual emfs

2. The current in each cell is the

same and is identical with the

current in the entire

arrangement.

3. The total internal resistance of

the battery is the sum of the

individual internal resistances.

Total emf of the battery = nE

Total Internal resistance of the battery = nr

Total resistance of the circuit = nr + R

Conclusion: When internal resistance is negligible in

comparison to the external resistance, then the cells are

connected in series to get maximum current.

(i) If R << nr, then I = E / r (ii) If nr << R, then I = n (E / R)

(for n no. of identical cells)

Current I = nE

nr + R

Cells in Parallel combination: Cells are said to be connected in parallel when they are joined positive to

positive and negative to negative such that current is divided between the

cells.

1. The emf of the battery is the same as that of a

single cell.

2. The current in the external circuit is divided equally

among the cells.

3. The reciprocal of the total internal resistance is the

sum of the reciprocals of the individual internal

resistances.

NOTE:

Total emf of the battery

Total Internal resistance of the battery

Total resistance of the circuit

= E

= r / n

= (r / n) + R

(i) If R << r/n, then I = n(E / r) (ii) If r/n << R, then I = E / R

Conclusion: When external resistance is negligible in

comparison to the internal resistance, then the cells are

connected in parallel to get maximum current.

Current I = nE

nR + r