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 :

Sensitivity of a potentiometer increases when a small change in emf produces a large balancing length.

Potential gradient is given by :

$$k = \frac{V}{L}$$

Sensitivity is inversely proportional to potential gradient.

Hence, smaller potential gradient gives higher sensitivity.

Also, sensitivity increases with increase in length of potentiometer wire.

Therefore,

(A) directly proportional to the length of potentiometer wire → Correct

(B) directly proportional to the potential gradient → Incorrect

(C) inversely proportional to the potential gradient → Correct

(D) inversely proportional to the length of potentiometer wire → Incorrect

Final Answer :

A and C