Question

A wire X is half the diameter and half the length of a wire Y of similar material. The ratio of resistance of X to that of Y is:

• A. \(8:1\)
• B. \(4:1\)
• C. \(2:1\)
• D. \(1:1\)

Hint:

Resistance increases if length increases or cross-sectional area decreases.

Answer 1

The Correct Option is A

Step 1: Resistance of a wire: \[ R = \rho \frac{L}{A} \]
Step 2: For wire X: \[ L_X = \frac{L_Y}{2}, \quad d_X = \frac{d_Y}{2} \Rightarrow A_X = \frac{A_Y}{4} \]
Step 3: \[ \frac{R_X}{R_Y} = \frac{L_X}{L_Y} \cdot \frac{A_Y}{A_X} = \frac{1}{2} \times 4 = 8 \]