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 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:
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Resistance increases if length increases or cross-sectional area decreases.
Updated On: Apr 5, 2026
- \(8:1\)
- \(4:1\)
- \(2:1\)
- \(1:1\)
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The Correct Option is A
Solution and Explanation
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: \[ \frac{R_X}{R_Y} = \frac{L_X}{L_Y} \cdot \frac{A_Y}{A_X} = \frac{1}{2} \times 4 = 8 \]
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