Question

A potentiometer wire is 4m long and potential difference of 2V is maintained between the ends. The e.m.f. of the cell which balances against a length of 80 cm of the potentiometer wire is

• A. \(0.25\) V
• B. \(0.30\) V
• C. \(0.40\) V
• D. \(0.80\) V

Hint:

EMF = potential gradient x balancing length.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The potential gradient of a potentiometer wire is \(k = \dfrac VL\). A cell balances at length \(\ell\) when \(E = k\ell\).

Step 2: Compute
\[ k = \frac{2}{4} = 0.5 \text{ V/m} \]
\[ E = 0.5 \times 0.8 = 0.4 \text{ V} \]
Using 80 cm without converting to metres gives 40, which is not an option, and 0.8 V would need the full 1.6 m of wire.

Final Answer:
The e.m.f. is 0.4 V, option (C). \[ \boxed{0.4 \text{ V}} \]