# Potentiometer

An ideal voltmeter should have infinite resistance so that it does not draw any current when connected across a source of emf. Practically it is not possible to manufacture a voltmeter which will not draw any current. To overcome this difficulty, a potentiometer is used, which draws no current from it. It employs a null method.

The potentiometer can also be used for measurement of internal resistance of a cell, the current flowing in a circuit and comparison of resistances.

### Description of Potentiometer

A potentiometer consists of a wooden board on which a number of resistance wires (usually ten) of uniform cross-sectional area are stretched parallel to each other. The wire is of maganin or nichrome. These wires are joined in series by thick copper strips. In this way, these wires together act as a single wire of length equal to the sum of the lengths of all the wires. The end terminals of the wires are provided with connecting screws.

A metre scale is fixed on the wooden board parallel to wires. A jockey (a sliding contact maker) is provided with the arrangement. It makes a knife edge contact at any desired point on a wire. Jockey has a pointer which moves over the scale. It determines the position of the knife edge contact.

### Measurements with Potentiometer

A steady source of e.m.f. E (say an accumulator) is connected across a uniform wire AB of length l. Positive terminal of the accumulator is connected at end A. A steady current I flows through the wire. The potential difference across AB is given by

VAB = RI If r is the resistance per unit length of the wire, and k is the potential drop across unit length of the wire, then

R = rl

E = kl

k = E/l

For length l1 of wire, potential drop is given by

V1 = kl1= El1/l

Thus, potential falls linearly with distance along the wire from the positive to the negative end.

The positive terminal of the cell is connected to end A of the wire and negative terminal through a galvanometer to the jockey having variable contact Y. For V > E, it will not be possible to obtain a null point. So, use a standard cell of emf E (> V). To check this, insert keys K and K1 and tap at ends A and B. The galvanometer should show deflection in opposite directions. If so, all is well with the circuit.

Insert key K1 and start moving jockey from A towards B. Suppose that at position Y′ potential drop across the length AY of the wire is less than voltage V. The current in the loop AY′XA due to voltage V exceeds the current due to potential difference across AY′. Hence galvanometer shows some deflection in one direction.

Then jockey is moved away, say to Y′′ such that potential drop across AY′′ is greater than the voltage V. If galvanometer shows deflection in the other direction, the voltage drop across AY′′ is greater than that across AY′. Therefore, the jockey is moved slowly between Y′ and Y′′. A stage is reached, say at point Y, where potential drop across AY is equal to voltage V. Then points X and Y will be at the same potential and hence the galvanometer will not show any deflection, i.e. null point is achieved.

Thus, the unknown voltage V is measured when no current is drawn.