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 ohmGiven : 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 R∝1A2∝1d4 ⇒R1R2=(d2d1)4 ⇒24R2=⎛⎜ ⎜ ⎜⎝dd2⎞⎟ ⎟ ⎟⎠4=16 R2=1.5 ohm Hence, option (C) is correct.

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