# Internal Resistance of a Cell Using Potentiometer Experiment

Experiment: Determine the internal resistance of a primary cell using a potentiometer.

A cell is characterised by its emf ε. When current is drawn from a cell, there is a movement (flow) of ions in the electrolyte between the electrodes of the cell. Resistance offered by the electrolyte to the flow of ions in it is called the internal resistance of the cell and is denoted by r.

Schematically, internal resistance r of a cell is shown as part of a cell of emf ε whose terminals A and B only are available to us for making connections.

When a resistance R is put across a cell of emf s and internal resistance r, the current drawn from the cell will be

I = E/(R+r)

The terminal potential difference V across the terminal A and B of the cell and hence across R will be

V = IR

V(R+r) = εr

r = (ε/V - 1)R

When a constant current is maintained in a wire of uniform cross-sectional area, potential difference between any two points on the wire is directly proportional to the length of the wire between the two points.

Null point is a condition which refers to zero deflection shown by a galvanometer connected in an electrical network. On either side of the null point the galvanometer deflection is on opposite side of zero.

In the circuit arrangement, l1 is the length of the potentiometer wire between the terminal P and the null point when the cell is in open circuit then

E α l1

E = kl1

If the null point is obtained at a length l2 when the cell is in close circuit then

V α l2

V = kl2

ε/V = l1/l2

r = (l1/l2 - 1)R

Material Required

A 4m wire / 10 m wire potentiometer, a battery, two one-way keys, a rheostat of low resistance, a high resistance box RB (H), a low resistance box RB (L), a voltmeter, a Leclanche cell, a jockey, a galvanometer, connecting wires, sand paper.

### How to Set Up

1. Clean the ends of the connecting wires with the sand paper and make tight connections as per the circuit diagram. 2. Before connecting a key in the circuit, remove the plug from it.

### How To Perform Experiment

1. After having assembled the circuit, check it once again with the circuit diagram.

2. Keep the rheostat resistance at its maximum and then insert the plug in key K1.

3. Take out some high resistance plug (say 5000Ω) from the resistance box RB(H).

4. Place the jockey J first at terminal P of the potentiometer wire and then at terminal Q of the potentiometer wire. The galvanometer deflection must be on opposite sides of zero in the two cases. If it is so, the null point will be obtained somewhere on the potentiometer wire. If the galvanometer deflection is on one side of the zero only, adjust the rheostat to a lower resistance value till you get deflection on opposite sides of the zero. Rheostat should be so adjusted that the null point is preferably on the last wire of the potentiometer.

Note: To get null point somewhere on the potentiometer wire, the voltmeter reading must be greater than the emf of the experimental cell.

5. Starting from the terminal P gently slide the jockey J along the potentiometer wire till you get zero deflection in the galvanometer. This is a rough adjustment of null point, because with 5000 Ω resistance in series galvanometer is quite insensitive. This step is necessary for safety of the galvanometer.

6. Now make resistance 0 ohm in the resistance box RB(H) and adjust the Jockey J again, if required, to make fine adjustment of null point position. Measure the distance of this null point (called the balancing length l1 from the terminal P along the potentiometer wire and record it. Take 2 or 3 observations for l1, in this manner.

7. Take out 5000 Ω plug resistance again from the resistance box RB(H). Take out some resistance R (say 5 Ω) from the resistance box RB (L) and insert the plug in key K2. Repeat steps 5 and 6 above to obtain null point. Measure the distance of this null point (called the balancing length l2) from the terminal P along the potentiometer wire and record it. In this manner take 2 or 3 observations for l2 also.

8. Repeat step 7 for several R’s say 6Ω, 7Ω, 8Ω, 9Ω and 10Ω. All through the observations, the voltmeter reading should remain constant. Adjust rheostat, if required, to keep the voltmeter reading constant. For this purpose battery B should be fully charged. Also during these observations key K2 should be closed for as little time as possible.

9. In the end repeat measurement of l1 with K2 open to check up if emf of cell changed in the process of doing the experiment. Take l1, as the mean of all the readings taken in the beginning and in the end.

### Sources of Error

1. Primary cells cannot deliver large currents for long duration. This is due to the increase in their internal resistance. So while finding balancing length l2 for a particular R, if the key K2 is kept closed for a longer duration, l2 will be affected. Hence calculated value of internal resistance will not be exact.
2. Calculation of r is based on the measured values of l1 and l2 for some value of R. Error in measurement of l1 and l2, will introduce error in r.