Question

A potentiometer having a wire of $4\,m$ length is connected to the terminals of a battery with a steady voltage. A leclanche cell has a null point at $1\,m$ . If the length of the potentiometer wire is increased by $1\,m$ , the position of the null point is
A. $1.5\,m$
B. $1.25\,m$
C. $10.05\,m$
D. $1.31\,m$

Answer 1

Hint: Consider the gradient of potential difference. The emf of the cell is the same in both the given conditions. As the length is increased, the potential gradient will decrease. In the second case, assume the null point is at some distance. Balance the equation to get the null point.

Complete step by step answer:
A potentiometer is an instrument which is used for measuring an electromotive force by balancing it against the potential difference produced by passing a known current through a known variable resistance. Let the emf of the battery be $E$ .
The initial potential gradient of the cell will be emf divided by the length of the potentiometer, this is given as:
$\dfrac{E}{4}$
The null point is obtained at length, ${l_i} = 1\,m$ , therefore the emf in the first case will be:
$\dfrac{E}{4} \times {l_1}$
$ \Rightarrow \dfrac{E}{4} \times 1 = \dfrac{E}{4}$
For the second case, when the length is increased let the null point be at some location $x$
Therefore, the emf of the cell can be written as potential gradient multiplied by the null point of the wire.
$\dfrac{E}{{4 + 1}} \times x$
The emf of the cell in both the cases must be equal.
$ \Rightarrow \dfrac{E}{4} \times 1 = \dfrac{E}{{4 + 1}} \times x$
$ \Rightarrow \dfrac{1}{4} = \dfrac{1}{{4 + 1}} \times x$
$ \Rightarrow x = \dfrac{5}{4}$
$ \Rightarrow x = 1.25\,m$
Therefore, the position of the null point is $1.25\,m$ .

So, the correct answer is “Option B”.

Note:
The emf in the cell of a potentiometer remains constant unless mentioned. For problems involving potentiometers, we use potential gradient instead of potential difference. The null point is the point where the galvanometer shows zero deflection. It is used to determine the emf of an unknown cell. In practical experiments, as length increases, the resistance also increases and there is potential drop due to increase in length.