Question

In potentiometer experiment, the balancing length with cell $E_1$ of unknown e.m.f. is $\ell_1$ cm. By shunting the cell $E_1$ with resistance $R$ which is equal to internal resistance $r$ of the cell $E_1$, the balancing length $\ell_2$ is

• A. $\ell_1$
• B. $\dfrac{\ell_1}{4}$
• C. $\dfrac{\ell_1}{2}$
• D. $2\ell_1$

Hint:

In potentiometer problems, balancing length is directly proportional to emf.

Answer 1

The Correct Option is C

Step 1: Relation between emf and balancing length.
In a potentiometer, emf is directly proportional to balancing length: \[ E \propto \ell \] Step 2: Effect of shunting the cell.
When the cell is shunted with resistance equal to its internal resistance, the effective emf becomes half of its original value.
Step 3: Find new balancing length.
\[ \dfrac{E_2}{E_1} = \dfrac{\ell_2}{\ell_1} = \dfrac{1}{2} \] \[ \ell_2 = \dfrac{\ell_1}{2} \]