With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is
(A) directly proportional to the length of the potentiometer wire
(B) directly proportional to the potential gradient of the wire
(C) inversely proportional to the potential gradient of the wire
(D) inversely proportional to the length of the potentiometer wire
Choose the correct option for the above statements :

Solution

Physics sir · 4 steps

Sensitivity means small balancing length changes are easy to see, so you want a small potential gradient.

1. What sensitivity means. A potentiometer is more sensitive when a tiny change in emf shifts the balance point by a large, easily measured length. If the emf changes by Δ E, the balance point moves by Δ l.

   Δ E = k Δ l ⇒ Δ l = (Δ E)/k

2. Role of gradient. Here k is the potential gradient (potential drop per unit length of wire). For the same Δ E, a smaller k gives a larger Δ l. So sensitivity is inversely proportional to the potential gradient, and statement C is correct while B is wrong.
3. Role of length. With a fixed potential V across the wire, k = V/L. A longer wire spreads the same voltage over more length, so k drops and sensitivity rises. Sensitivity is directly proportional to the length, so statement A is correct while D is wrong.
4. So. Statements A and C are true, which is option (c).

The idea to keep. To make a potentiometer more sensitive, reduce the potential gradient: use a longer wire, or lower the current in the main circuit with a rheostat.

Answer from the NTA final answer key. Solution by PrepWiser.