Question

A potentiometer consists of a wire of length 4 m and resistance $10\, \Omega$ It is connected to a cell of e.m.f. 2 V. The potential difference per unit length of the wire will be

• A. 5 V/m
• B. 2 V/m
• C. 0.5 V/m
• D. 10 V/m

Answer 1

The Correct Option is C

The problem involves finding the potential difference per unit length of a potentiometer wire. Let's solve this step-by-step.

1. First, understand the concept of a potentiometer. A potentiometer measures the voltage or potential difference by comparing it with a known voltage.
2. In this problem, we have a wire length L = 4\, \text{m} and a resistance R = 10\, \Omega. The wire is connected to a cell with an electromotive force (e.m.f.) E = 2\, \text{V}.
3. The total potential difference (voltage) across the potentiometer wire is equal to the e.m.f. of the cell, which is 2\, \text{V}.
4. We need to find the potential difference per unit length of the wire. This is given by the formula:

V_{\text{per unit length}} = \frac{E}{L}

5. Substitute the given values into the formula:

V_{\text{per unit length}} = \frac{2\, \text{V}}{4\, \text{m}} = 0.5\, \text{V/m}

6. Thus, the potential difference per unit length of the wire is 0.5\, \text{V/m}.
7. Comparing this with the given options, the correct answer is 0.5 V/m.

Let’s rule out the incorrect options:

• 5 V/m: This is incorrect as the calculated value is lower than this option.
• 2 V/m: This is incorrect as it would imply the potential difference across the entire wire is 8 V (which exceeds the e.m.f.).
• 10 V/m: This is incorrect for similar reasons as it exceeds the possible values given the constraints.

Therefore, the option 0.5 V/m correctly represents the potential drop per meter of the potentiometer wire.