Question

The radius of potentiometer wire is doubled without changing its length. The value of potential gradient.
A. increases four times
B. increase two times
C. does not change
D. become half

Answer 1

Hint: A potentiometer can act as voltage divider or a rheostat. It has three terminals, when all the three terminals are used it acts as a voltage terminal due to sliding or rotation contact of the pointer. It acts as a rheostat or variable resistance when two terminals are used the other is left free.

Formula used:
$k=\dfrac{V}{l}$

Complete step-by-step answer:
The potentiometer uses the following principle, when a constant current is flowing through a wire of uniform cross-section, then the potential drop across a segment of the wire is directly proportional to the length of the wire. And thus potentiometers can be used to measure the potential drop across two points. In labs they are used to find the emf of any given cell. The potentiometer is generally used in electrical devices to control the system volumes. They are also used in the television sets to adjust the brightness, contrast and other colour responses.
We know that the potential drop across any two points is the emf of the given cell. Also we know that potential gradient $k$ is the potential drop $V$ per unit length $l$, and is given as $k=\dfrac{V}{l}$.
Clearly, the potential gradient depends on the length and not the radius. Since here the length of wire remains constant, we can say that there is no change in the potential gradient.

So, the correct answer is “Option C”.

Note: Clearly, potential gradient of a potentiometer is independent of the cross-sectional area and is hence independent of the radius of the wire. But the potential drop or the emf depends on the cross-sectional area of the wire.