Question

What is the resistance of a wire of length $ L = 2 \, \text{m} $ and cross-sectional area $ A = 1 \times 10^{-6} \, \text{m}^2 $ made of a material with resistivity $ \rho = 1.5 \times 10^{-7} \, \Omega \, \text{m} $?

• A. \( 3 \times 10^{-7} \, \Omega \)
• B. \( 3 \times 10^{-6} \, \Omega \)
• C. \( 2 \times 10^{-7} \, \Omega \)
• D. \( 5 \times 10^{-6} \, \Omega \)

Hint:

Remember: The resistance of a wire depends on its length, cross-sectional area, and the resistivity of the material.

Answer 1

The Correct Option is A

Step 1: Apply the resistance formula
The formula for the resistance \( R \) of a wire is: \[ R = \rho \frac{L}{A} \] where: - \( \rho \) denotes resistivity, - \( L \) signifies length, and - \( A \) represents the cross-sectional area.
Step 2: Input provided data
The given values are: 
- Resistivity \( \rho = 1.5 \times 10^{-7} \, \Omega \, \text{m} \), - Length \( L = 2 \, \text{m} \), 
- Cross-sectional area \( A = 1 \times 10^{-6} \, \text{m}^2 \). 
Substituting these into the formula yields: \[ R = 1.5 \times 10^{-7} \times \frac{2}{1 \times 10^{-6}} \] \[ R = 1.5 \times 10^{-7} \times 2 \times 10^6 \] \[ R = 3 \times 10^{-7} \, \Omega \] 
Result:
The calculated resistance of the wire is \( 3 \times 10^{-7} \, \Omega \). This corresponds to option (1).