Question

In a potentiometer, the area of cross-section of the wire is 4 cm\(^2\), the current flowing in the circuit is 1 A, and the potential gradient is 7.5 Vm\(^{-1}\). Then the resistivity of the potentiometer wire is

• A. \( 3 \times 10^{-3} \, \Omega \text{m} \)
• B. \( 2 \times 10^{-6} \, \Omega \text{m} \)
• C. \( 2 \times 10^{-2} \, \Omega \text{m} \)
• D. \( 5 \times 10^{-4} \, \Omega \text{m} \)

Hint:

Resistivity can be found using \( \rho = R A / L \) when resistance and dimensions are known.

Answer 1

The Correct Option is A

Ohm’s Law states: \[ E = IR \] Using resistance formula: \[ R = \frac{\rho L}{A} \] Rearrange: \[ \rho = \frac{R A}{L} \] \[ \rho = \frac{(7.5 \times 1) \times (4 \times 10^{-4})}{1} \] \[ = 3 \times 10^{-3} \, \Omega \text{m} \] Thus, the correct answer is \( 3 \times 10^{-3} \) ohm\m.