The sensitivity of a potentiometer can be increased by:

The correct answer is Option (3) → Decreasing the potential gradient of the potentiometer wire of fixed length.

A potentiometer is more sensitive when a small potential difference gives a long balancing length. The balancing length for a potential difference \( V \) is

    \( \displaystyle l = \frac{V}{k} \)

where \( k \) is the potential gradient (potential drop per unit length) of the wire. A smaller \( k \) gives a longer \( l \) for the same \( V \), so the sensitivity rises when the potential gradient is decreased.

Option (1) Decreasing the length of potentiometer wire only. — Incorrect. With the same voltage across a shorter wire, the potential gradient becomes larger, which lowers the sensitivity.

Option (2) Increasing the potential gradient of the potentiometer wire of fixed length. — Incorrect. A larger potential gradient shortens the balancing length and lowers the sensitivity.

Option (4) Increasing the current in the potentiometer wire circuit. — Incorrect. A larger current increases the drop \( IR \) across the wire, so the potential gradient increases and the sensitivity falls.