### Potentiometer Comparison of EMF's and Determination of Internal Resistance

Potentiometer is a device used to compare the Emf’s of two cells and also used to find the internal resistance of a given cell.It works on a principle that the potential drop across a wire is directly proportional to the length of the wire through which the current is passing.

The device consists of two parts called primary and secondary circuit. The primary circuit consists of a strong battery to supply the potential requirement of the circuit. The connection from the cell is given to a long wire. This long wire is divided into pieces of wires each of one meter length and they are connected with small copper pieces of negligible length. They behaves like multiple wires connected in series and the total length is available between the copper strips.A galvanometer is connected from the wire with a connecting wire.

Comparison of EMF's of two cells

The secondary circuit consists of cells whose electromotive forces has to be compared. There is key that acts like a on and off switch and it can be used to control the flow of current through a particular cell.

In two different cases the two cells are connected in the secondary circuit separately and corresponding balancing lengths are measured with it. When the emf of secondary circuit is balanced with that of primary, the galvanometer shows zero deflection. This happens at a particular length of the wire and that length is called balancing length. We will find the balancing length with the second cell whose EMF has to be compared.

As per the principle, the ratio of EMF’s is nothing but the ratio of the balancing lengths in the two cases. Thus we are able to compare the EMF’s of two cells using the Potentiometer.

Determination of internal resistance of a cell

We need to connect cell alone first whose internal resistance has to be measured. We can find the balancing length in the circuit. In the next case, the same cell is connected to a external resistance in parallel and again balancing length is measured using the potentiometer. There we will get one more balancing length. The ratio of emf of that cell and its potential drop across a resistor is nothing but the ratio of balancing lengths.

Basing on the definition of potential drop, we can get one more relation between emf and voltage and by comparing both of them, we can measure the internal resistance of a cell as shown below.

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