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Three copper wires of lengths and cross-sectional areas are (l, A), (2l, A/2) and (l/2, 2A). Resistance is minimum in

Asked in CBSE AIPMT 1997 · Resistance of a wire and stretching

• (1) wire of cross-sectional area 2A
• (2) wire of cross-sectional area A/2
• (3) wire of cross-sectional area A
• (4) same in all three cases.

Step-by-step solution

Why the other options are wrong

• (2) This wire has the largest resistance, 4ρ l/A; the question asks for the minimum.
• (3) This wire sits in the middle, at ρ l/A.
• (4) All three have the same volume lA, but equal volume does not mean equal resistance; R goes as l/A.

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