Question

In case of four wires of same material, the resistance will be minimum if the diameter and length of the wire respectively are

• A. D/2 and L/4
• B. D/4 and 4L
• C. 2D and L
• D. 4D and 2L

Answer 1

The Correct Option is D

The resistance \( R \) of a wire is given by the formula:
\[R = \rho \frac{L}{A}\]
where:
- \(\rho\) is the resistivity,
- \(L\) is the length of the wire,
- \(A\) is the cross-sectional area.
The area \(A\) is proportional to the square of the diameter (\(A \propto D^2\)). So, to minimize resistance, we need to maximize the cross-sectional area and minimize the length.
- If the diameter is increased by a factor of 4 (i.e., \(4D\)), and the length is reduced by a factor of 2 (i.e., \(2L\)), the resistance will be minimized.