Determine Internal Resistance of a Cell Using a Potentiometer

Aim

To determine the internal resistance of a given primary cell using a potentiometer.

Apparatus Required

Potentiometer, the given primary cell, an ammeter, a battery, resistance box, two one-way keys, galvanometer, rheostat, jockey, and connecting wires.

Theory

In the circuit, a cell of emf E and internal resistance r supplies current I when the key is closed:

[ E = I(R + r) ]

So,

[ E = IR + Ir = V + Ir ]

Where V is the potential difference across resistance R.

Thus,

[ r = \frac{E - V}{I} = \left(\frac{E}{V} - 1\right) R ]

If

• l₁ = balancing length for emf E
• l₂ = balancing length for potential difference V

Then:

[ r = \left(\frac{l_1}{l_2} - 1\right) R ]

[ r = \frac{(l_1 - l_2)R}{l_2} ]

Circuit Diagram

Procedure

1. Clean the ends of the connecting wires using sandpaper.
2. Set up the circuit as shown in the figure with keys K₁ and K₂ open.
3. Close K₁. Touch the jockey near ends A and B of the potentiometer wire—ensure opposite galvanometer deflections. Adjust the rheostat if needed.
4. Move the jockey along the wire to find the balancing point and note balancing length l₁.
5. Close K₂, introduce resistance R using the resistance box, and repeat the steps to get balancing length l₂.
6. Repeat the experiment for at least five different values of R.

Observation Table Image

Precautions

1. Clean wire ends with sandpaper before making connections.
2. Ensure all connections are tight.
3. Connect positive terminals of the battery and primary cell to the same end of the potentiometer wire.
4. The emf of the battery must be greater than that of the primary cell.
5. Do not slide the jockey—touch gently and momentarily.
6. Use current for the shortest time to prevent heating.

Sources of Error

1. Loose connections.
2. The emf of the battery may be less than that of the primary cell.
3. Keys may remain inserted for too long, heating the potentiometer wire.