Question

The sensitivity of a potentiometer can be increased by

• A. Increasing the emf of the cell
• B. Decreasing the emf of the cell
• C. Increasing the length of the potentiometer wire
• D. Decreasing the length of the potentiometer wire

Hint:

Potentiometer sensitivity increases when potential gradient decreases. Increasing the length of the potentiometer wire decreases potential gradient.

Answer 1

The Correct Option is C

Concept:
A potentiometer is an instrument used to measure potential difference accurately. Its working is based on the principle that potential difference across a wire is directly proportional to the length of the wire, provided current remains constant. The potential gradient of a potentiometer is given by: \[ k=\frac{V}{L} \] where, \[ k=\text{potential gradient} \] \[ V=\text{potential difference across the potentiometer wire} \] \[ L=\text{length of potentiometer wire} \] The sensitivity of a potentiometer increases when the potential gradient decreases.

Step 1: Understand what sensitivity means.
Sensitivity means how accurately a potentiometer can detect a small potential difference. If the potential gradient is small, then a small change in voltage will correspond to a larger change in length. This makes the measurement more accurate. So: \[ \text{Sensitivity} \propto \frac{1}{\text{Potential gradient}} \]

Step 2: Relate potential gradient with length.
Potential gradient is: \[ k=\frac{V}{L} \] If the length \(L\) of the potentiometer wire is increased while the applied voltage remains the same, then: \[ k \downarrow \] That means the potential drop per unit length decreases.

Step 3: Understand why increasing length helps.
If potential gradient is smaller, then the balancing length for the same unknown voltage becomes larger. A larger balancing length reduces percentage error in measurement. Therefore, increasing the length of the potentiometer wire increases sensitivity.

Step 4: Check the options.
Option (A) Increasing the emf of the cell increases potential gradient, so sensitivity decreases.
Option (B) Decreasing the emf can increase sensitivity, but the best and standard method among the options is increasing the wire length.
Option (C) Increasing the length of the potentiometer wire decreases potential gradient and increases sensitivity.
Option (D) Decreasing the length increases potential gradient and decreases sensitivity. Hence, the correct answer is: \[ \boxed{(C)\ \text{Increasing the length of the potentiometer wire}} \]