Question

$\text{Statement}1$: The wire of a potentiometer should be of uniform area of cross-section.
$\text{Statement}2$: It satisfies the requirement of the principle of a potentiometer.

• A. $\text{Statement}1$ is True, $\text{Statement}2$ is True; $\text{Statement}2$ is a correct explanation for $\text{Statement}1$.
• B. $\text{Statement}1$ is True, $\text{Statement}2$ is True; $\text{Statement}2$ is not a correct explanation for $\text{Statement}1$.
• C. $\text{Statement}1$ is True, $\text{Statement}2$ is False.
• D. $\text{Statement}1$ is False, $\text{Statement}2$ is True.

Answer 1

The correct option is A $\text{Statement}1$ is True, $\text{Statement}2$ is True; $\text{Statement}2$ is a correct explanation for $\text{Statement}1$.

The principle of potentiometer is,

$V\propto l$

$\Rightarrow IR\propto l-\left(1\right)$

Now, resistance of a wire is given by,
$R=\frac{\rho l}{A}$

$\Rightarrow R\propto l-\left(2\right)$

The above equation is valid only when $A$ is constant.
Also, equation $\left(1\right)$ is valid only when $\left(2\right)$ is obeyed, i.e. the wire has uniform cross-section.

Hence, option $\left(A\right)$ is the correct answer.

Key concept: Principle : The potentiometer is based upon the principle that when a constant current is passed through a wire of uniform area of cross-section, the potential drop across any portion of the wire is directly proportional to the length of that portion.