Question

A potentiometer wire has length 4 m and resistance 5 \( \Omega \). It is connected in series with 495 \( \Omega \) resistance and a cell of e.m.f. 4V. The potential gradient along the wire is

• A. 0.03 V/m
• B. 0.01 V/m
• C. 0.02 V/m
• D. 0.04 V/m

Hint:

In potentiometer problems, the potential gradient is the potential difference per unit length of the wire. Make sure to calculate the current first to determine the potential across the wire.

Answer 1

The Correct Option is B

Step 1: Understanding the potential gradient.
The potential gradient \( k \) is given by the formula: \[ k = \frac{V}{L} \] where \( V \) is the potential difference across the potentiometer wire and \( L \) is the length of the wire. The total resistance in the circuit is \( 495 \, \Omega + 5 \, \Omega = 500 \, \Omega \). The current \( I \) in the circuit is: \[ I = \frac{V_{\text{emf}}}{R_{\text{total}}} = \frac{4}{500} = 0.008 \, \text{A} \] The potential difference across the 5 \( \Omega \) wire is: \[ V = I \times R = 0.008 \times 5 = 0.04 \, \text{V} \] Step 2: Calculating the potential gradient.
The potential gradient is: \[ k = \frac{0.04}{4} = 0.01 \, \text{V/m} \] Step 3: Conclusion.
Thus, the correct answer is (B) 0.01 V/m.