Question

Resistance of a wire of length 0.5 m and area of cross-section 10 mm 2 is 1 Ω. The resistivity (in Ω-m) of the wire is

• A. \(2\times 10^{-3}\)
• B. \(10^{-3}\)
• C. \(2\times 10^{-6}\)
• D. \(10^{-6}\)

Answer 1

The Correct Option is C

The resistivity \( \rho \) of a wire is related to its resistance \( R \), length \( L \), and area of cross-section \( A \) by the formula: \[ R = \rho \frac{L}{A}. \] We are given:
Resistance \( R = 1 \, \Omega \),
Length \( L = 0.5 \, \text{m} \),
Area of cross-section \( A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2 \).
Rearranging the formula to solve for resistivity \( \rho \): \[ \rho = \frac{R A}{L}. \] Substituting the known values: \[ \rho = \frac{1 \times 1 \times 10^{-6}}{0.5} = 2 \times 10^{-6} \, \Omega \cdot \text{m}. \] Thus, the resistivity of the wire is \( 2 \times 10^{-6} \, \Omega \cdot \text{m} \).

The correct option is (C): \(2\times 10^{-6}\)