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Question
(i) State the principle on which a potentiometer works. How can a given potentiometer be made more sensitive?
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Solution
(i) Potentiometer is an apparatus used for measuring the emf of a cell or potential difference between two points in an electric circuit accurately.
Principle of potentiometer
The working of potentiometer is based on the fact that the fall of potential across any portion of the wire is directly proportional to the length of that portion provided the wire is of uniform area of cross-section and a constant current is flowing through it.
If V is the potential drop across the portion of wire of length l whose resistance is R. Then
\[V = I \times R = I \times \frac{\rho l}{A}\]
where A, l and \[\rho\] are respectively the area of cross-section, length and specific resistance of the material of the wire.
\[\frac{V}{l} = I \frac{\rho}{A} = K\]
where K is called the potential gradient, i.e. the fall of potential per unit length of wire.
To make the potentiometer sensitive, the potential gradient should be low. So by increasing the length of the wire,potential gradient reduces as it is inversely proportional to the length of the wire and hence in this the potentiometer can be made more sensitive.
(ii) A potentiometer is called sensitive if fall of potential per unit length i.e potential gradient is small. The slope of V-l graph gives potential gradient which is smaller for the potentiometer B than for potentiometer A. Hence, potentiometer B is more sensitive than A.
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