Question

The potentiometer wire is 5 m long and potential difference of 4 V is maintained between the ends. The e.m.f. of the cell which balances against a length of 200 cm of the potentiometer wire is ______.

• A. 0.4 V
• B. 0.8 V
• C. 1.2 V
• D. 1.6 V

Hint:

Ensure your units match! If you use the gradient in V/m ($0.8$), you MUST convert the balancing length to meters ($200 \text{ cm} = 2 \text{ m}$) before multiplying ($0.8 \times 2 = 1.6 \text{ V}$).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The principle of a potentiometer is that the potential drop across any length of the wire is directly proportional to that length, provided the wire is uniform and the current is constant ($V \propto l$).

Step 2: Formula Application:
Potential Gradient ($K$) = $\frac{V}{L}$.
e.m.f. ($E$) = $K \times l = \frac{V}{L} \times l$.

Step 3: Explanation:
Total length $L = 5$ m, Total Voltage $V = 4$ V.
Balancing length $l = 200$ cm $= 2$ m.
$E = \frac{4}{5} \times 2 = \frac{8}{5} = 1.6$ V.
Wait, let me re-check the calculation: $4/5 = 0.8$ V/m. For $2$ meters, $0.8 \times 2 = 1.6$ V.
Looking at the options, if the question meant 100 cm, it would be 0.8 V. Given the data provided:
$E = (4/5) \times 2 = 1.6$ V.

Step 4: Final Answer:
The e.m.f. is 1.6 V. (Option D).