To determine the internal resistance of a cell E using potentiometer, we will be studying the circuit as shown below.
Circuit diagram for measuring internal resistance
Key K is closed and a suitable constant current is maintained in the potentiometer wire with the help of rheostat Rh. Adjust the position of jockey J at different points of the wire and find a point J on the wire where if jockey is pressed, galvanometer shows no deflection. Note the length AJ (=l1) of the potentiometer wire. Now, the emf of the cell E = potential difference across the length l1 of the potentiometer wire.
That is, E = Kl1 ...(iii)
K being the potential gradient across the wire.
Close key
such that the resistance R comes in the cell circuit. Again, find the position of the jockey on the potentiometer wire where galvanometer shows no deflection. Suppose it be at J1. Measure the length of the wire 
.Then, potential difference between two poles of the cell, V = potential difference across the length l1 of the potentiometer wire
i.e. V = Kl2 ...(iv)
Dividing equation (iii) by equation (iv), we get
...(v)We know that the internal resistance r1 of a cell of emf E, when a resistance R is connected in its circuit is given by
...(vi)Substituting the value from equation (v) in equation (vi), we get
Thus, substituting the values l1, l2 and R in above equation, the internal resistance r1 of the cell can be determined.
Procedure:
- Arrange the required materials on a table and make the connections as per the connection diagram.
- Tight the plugs of the resistance box.
- Note the reading on the ammeter.
- To test the connection, insert plug in the one way key k1 and also in between the terminals a and c of the two way key. Introduce a sufficiently high resistance on the resistance box (R.B). Place the jockey at the two end points of the wire. Press the jockey at both end of the potentiometer wire and note the deflection in galvanometer. If the galvanometer shows opposite deflection, the connections are correct.
- Now, gently slide the jockey along the potentiometer wire and stop when null point is obtained.
- Measure the length l1 between this point and the end P of the potentiometer. It is the balancing length for the cell E1.
- Disconnect the cell E1 by removing the plug from the gap ac of the two way key and connect the cell E2 by inserting plug into the gap bc of the two way key.
- Again slide the jockey along the potentiometer wire to obtain the null point. Measure the new balancing length l2 for the cell E2 based on this point.
- Make sure that the reading on the ammeter is constant throughout the observation.
- Repeat the experiment by increasing the current by adjusting the rheostat and record the observations.
- Each time, the ratio between the emf’s of the given cells can be calculated using the relation,
