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Question

We have two wires A and B of the same mass and the same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will be

A
1.5 ohm
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B
None of the above
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C
12 ohm
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D
3.0 ohm
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Solution

The correct option is A 1.5 ohm
Given :
Same mass, same material, i.e., volume is the same Al= constant
R1=24 ohm
Let diameter of B is d and diameter of A is d2.
Resistance is given by
R=ρlA
R=ρlA×AA=ρVA2
R1A21d4
R1R2=(d2d1)4
24R2=⎜ ⎜ ⎜dd2⎟ ⎟ ⎟4=16
R2=1.5 ohm
Hence, option (C) is correct.

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