Question

The resistivity of the material of a potentiometer wire is \(5 \times 10^{-6}\,\Omega m\) and its area of cross section is \(5 \times 10^{-6}\,m^2\). If \(0.2\,A\) current is flowing through the wire, then the potential drop per metre length of the wire is

• A. 0.1 Vm\(^{-1}\)
• B. 0.5 Vm\(^{-1}\)
• C. 0.25 Vm\(^{-1}\)
• D. 0.2 Vm\(^{-1}\)
• E. 0.01 Vm\(^{-1}\)

Hint:

Potential gradient = current × resistance per unit length.

Answer 1

The Correct Option is D

Concept: Resistance per unit length: \[ R = \frac{\rho}{A} \] Potential gradient: \[ V = IR \]

Step 1: Find resistance per metre. \[ R = \frac{5\times10^{-6}}{5\times10^{-6}} = 1\,\Omega/m \]

Step 2: Use Ohm’s law. \[ V = IR = 0.2 \times 1 = 0.2\,V/m \]

Step 3: Conclusion. \[ \boxed{0.2\,V/m} \]