The E.m.f of a cell, cells in series, cells in parallel

The E.m.f of a cell, cells in series, cells in parallel

The E.m.f of a cell is the potential difference across the inside of the cell and the external circuit.

E.M.F = Voltage across the inside of a cell + voltage across the external circuit

E= Ir + IR

Where r is the internal resistance of the cell and

R is the total External resistance.

Example 1

A cell of e.m.f  30v  is connected across an external resistance of 10Ω.  If the current in the circuit is 2A. what is the internal resistance of the cell ?

Solution

E=Ir + IR

30=2r + 2 x 10

30=2r +20

30-20=2r

10=2r

r=5Ω

CELLS IN SERIES

Battery  is a combination of two or more cells connected together in series..

The positive terminal of the first cell is connected to the negative terminal of the second cells as shown in figure 1  above

The total e.m.f is the sum of individual E.m.f of the cells and the total internal resistance is the sum  of individual internal resistance.

Example

Five cells are connected in series. If the E.m.f  and internal resistance of the cells are 2v and 0,5Ω respectively. What is the total E,m.f and internal resistance ?

Solution

CELLS IN PARALLEL

When two or more identical cells are connected in parallel, all the positive terminals of the cells are connected together and all the negative terminals are also connected together. This means positive terminal of the first cell is connected to the positive terminal of the second cell. Negative terminal of the first cell is connected to the negative terminal of the second cell. See fig 2 above

The total E.m.f of the cells is equal to the E.m.f of one of the cells

If there are three identical cells in parallel

The total internal resistance is the resultant of the internal resistance of the cells in parallel

Example

Three torch light batteries are used to power a light bulb . Calculate the current in the circuit if

1. They are connected in series
2. They are connected in parallel

The E.m.f of each of the cells is 2v and the internal resistance of each of the cells is 1Ω. The bulb resistance is 10Ω

Solution

Series connection

Parallel connection

Total e.m.f  =  2v

Total internal resistance

                                Total resistance =

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