Measurement of internal resistance of a cell by potentiometer
To measure the internal resistance of a cell, the circuit connections are made as shown in Figure 2.29. The end C of the potentiometer wire is connected to the positive terminal of the battery Bt and the negative terminal of the battery is connected to the end D through a key K1. This forms the primary circuit.
The positive terminal of the cell ξ whose internal resistance is to be determined is also connected to the end C of the wire. The negative terminal of the cell ξ is connected to a jockey through a galvanometer and a high resistance. A resistance box R and key K2 are connected across the cell ξ. With K2 open, the balancing point J is obtained and the balancing length CJ = l1 is measured. Since the cell is in open circuit, its emf is
A suitable resistance (say, 10 Ω) is included in the resistance box and key K2 is closed. Let r be the internal resistance of the cell. The current passing through the cell and the resistance R is given by
I = ξ / [R +r]
The potential difference across R is
V = ξR [R+r]
When this potential difference is balanced on the potentiometer wire, let l2 be the balancing length.
Substituting the values of the R, l1 and l2 , the internal resistance of the cell is determined. The experiment can be repeated for different values of R. It is found that the internal resistance of the cell is not constant but increases with increase of external resistance connected across its terminals.