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Question

Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is

A
4Ω when the resistance of wire A is 4.25Ω
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B
5Ω when the resistance of wire A is 4Ω
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C
4Ω when the resistance of wire B is 4.25Ω
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D
5Ω when the resistance of wire B is 4Ω
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Solution

The correct option is A 4Ω when the resistance of wire A is 4.25Ω
Density and masses of wire are same so their volumes are same i.e. A1l1=A2l2
Ratio of resistances of wires A and B RARB=l1l2×A2A1=(A2A1)2=(r2r1)4
Since r1=2r2 so RARB=116RB=16 RA
Resistance RA and RB are connected in parallel so equivalent resistance R=RARBRA+RB=16RA17, By checking correctness of equivalent resistance from options, only option (a) is correct

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