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): $2\times 10^{-6}$