The Potentiometer-Internal resistance of a cell

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

Potentiometer is a device used to measure the internal resistance of a cell, to compare the e.m.f. of two cells and potential difference across a resistor. It consists of a long wire of uniform cross sectional area and of 10 m in length. The material of wire should have a high resistivity and low temperature coefficient. The wires are stretched parallel to each other on a wooden board. The wires are joined in series by using thick copper strips. A metre scale is also attached on the wooden board.

It works on the principle that when a constant current flows through a wire of uniform cross sectional area, potential difference between its two points is directly proportional to the length of the wire between the two points.

**Relation between e.m.f., potential difference, and internal resistance of a cell**

If a cell of emf E and internal resistance r, connected to an external resistance R, then the circuit has the total resistance (R+r). The current I in the circuit is given by,

or

Hence,

This means, V is less than E by an amount equal to the fall of potential inside the cell due to its internal resistance.

From the above equation,

Or; The internal resistance of the cell,

Using a potentiometer, we can adjust the rheostat to obtain the balancing lengths l_{1} and l_{2} of the potentiometer for open and closed circuits respectively.

Then, E= k l_{1} and V = k l_{2} ; where k is the potential gradient along the wire.

Now we can modify the equation for getting the internal resistance of the given cell, by using the above relations as;

- Students get the idea of potentiometer apparatus and its parts.
- Students are able to construct circuits based on circuit diagrams.
- Students understand the different component used in the experiment.