Question

A potentiometer wire is 4 m long and potential difference of 3 V is maintained between the ends. The e.m.f. of the cell which balances against a length of 100 cm of the potentiometer wire is

• A. 0.50 V
• B. 0.60 V
• C. 0.75 V
• D. 0.25 V

Hint:

In potentiometer problems, the e.m.f. is proportional to the length of the wire that balances the cell.

Answer 1

The Correct Option is C

Step 1: Understanding the potentiometer principle.
The potential difference across the wire is proportional to its length. Hence, the e.m.f. of the cell can be calculated using the formula: \[ E = \frac{l}{L} \times V \] where \( E \) is the e.m.f., \( l \) is the balancing length, \( L \) is the total length of the potentiometer wire, and \( V \) is the potential difference across the wire.

Step 2: Applying the formula.
Substitute the given values: \[ E = \frac{100 \, \text{cm}}{400 \, \text{cm}} \times 3 \, \text{V} = 0.75 \, \text{V} \]
Step 3: Conclusion.
The correct answer is (C) 0.75 V.