Question

If the specific resistance of a wire of length 2 m and area of cross-section 1 mm² is 10^–8 Ω-m, then calculate the resistance.

• A. 10^–2 Ω
• B. 2 Ω
• C. \(2 × 10^{–5} Ω\)
• D. \(2 × 10^{–2} Ω\)

Answer 1

The Correct Option is D

To find the resistance \( R \) of a wire, we use the formula:

\[ R = \rho \frac{L}{A} \]

where \( \rho \) is the specific resistance of the material, \( L \) is the length of the wire, and \( A \) is the cross-sectional area.

Given:

• \(\rho = 10^{-8} \, \Omega \cdot \text{m}\)
• \(L = 2 \, \text{m}\)
• \(A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2\)

Insert these values into the formula:

\[ R = 10^{-8} \times \frac{2}{1 \times 10^{-6}} \]

Simplify the expression:

\[ R = 10^{-8} \times 2 \times 10^6 \]

\[ R = 2 \times 10^{-2} \, \Omega \]

Thus, the resistance of the wire is \(2 \times 10^{-2} \, \Omega\).

Answer 2

We use the formula for resistance:

\[ R = \rho \cdot \frac{l}{A} \]

Given:

• Specific resistance \( \rho = 10^{-8} \, \Omega \cdot \text{m} \)
• Length \( l = 2 \, \text{m} \)
• Area of cross-section \( A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2 \)

Substitute the values:

\[ R = 10^{-8} \cdot \frac{2}{1 \times 10^{-6}} = 10^{-8} \cdot 2 \times 10^6 = 2 \times 10^{-2} \, \Omega \]

Final Answer: \(2 \times 10^{-2} \, \Omega\)