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The masses of three copper wires are in the ratio 5:3:1 and their lengths are in the ratio 1:3:5. The ratio of their electrical resistances is ______.

Asked in GUJCET 2011 · Resistance of a wire and stretching

• (1) 5:3:1
• (2) 125:15:1
• (3) 1:15:125
• (4) 1:3:5

Step-by-step solution

Why the other options are wrong

• (1) Follows the masses, as if more metal meant more resistance. For a given length, more metal means a thicker wire and less resistance.
• (2) Has the right numbers in the reverse order, which is what comes out if the two ratios are swapped (the first wire given length 5 and mass 1).
• (4) Follows the lengths only, R∝ L. The masses fix the cross-sections too: A=m/(dL), which makes R∝(L²)/m.

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