#### Question

Explain the principle of potentiometer.

#### Solution

Principle:

The potential difference between any two points of the potentiometer wire is directly proportional to the length of wire between these two points.

The fall of potential per unit length of potentiometer wire (potential gradient of wire) is

constant.

Explanation:

a) Suppose a potentiometer wire AB of length L and resistance R is stretched on the

rectangular wooden board. The source of e.m.f E and negligible internal resistance is

connected to the wire AB through a key K as shown in figure.

b) Resistance per unit length of wire AB is given by, σ = R/L

∴ R = σL

c) Let ‘V_{AB}’ be the P.D across the wire. There is uniform fall of potential along the wire

from A to B.

d) By Ohm’s law, the current ‘I’ passing through the wire is given by,

e) Let ‘P’ be any point on the wire, such that AP = ‘l’. The resistance of wire AP of

length ‘l’ is R_{AP} = σl. So the potential difference ‘V’_{AP} between points A and P is given

by,

f) But, V_{AB} and L are constant,

∴ V_{AP} ∝ L

∴ `V_(AP)/L` = K = constant

where, K is called potential gradient of wire.