Question

In a potentiometer experiment, a cell of emf 1.5 V gives a balance point at 75 cm. If the cell is replaced by another cell and the balance point is at 60 cm, the emf of the second cell is:

• A. 1.2 V
• B. 1.0 V
• C. 1.8 V
• D. 2.0 V

Hint:

In a potentiometer, the emf is directly proportional to the balance length: \( V \propto l \). Use the ratio of lengths to find the unknown emf.

Answer 1

The Correct Option is A

- In a potentiometer, the emf of a cell is proportional to the balance length. If \( V_1 \) and \( V_2 \) are the emfs of the two cells, and \( l_1 \) and \( l_2 \) are the corresponding balance lengths: \[ \frac{V_1}{V_2} = \frac{l_1}{l_2} \]
- Given \( V_1 = 1.5 \, \text{V} \), \( l_1 = 75 \, \text{cm} \), \( l_2 = 60 \, \text{cm} \), find \( V_2 \): \[ \frac{1.5}{V_2} = \frac{75}{60} \]
- Simplify the ratio: \[ \frac{75}{60} = \frac{5}{4} \]
- So: \[ \frac{1.5}{V_2} = \frac{5}{4} \implies V_2 = 1.5 \times \frac{4}{5} = 1.5 \times 0.8 = 1.2 \, \text{V} \]
- This matches option (A).