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Question

When the diameter of a wire is doubled, its resistance becomes:

(a) double
(b) four times
(c) one-half
(d) one-fourth

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Solution

(d) one-fourth
R = ρ lA

When the diameter is doubled, d' = 2d

Radius, r' = 2r

Area of cross-section, A'=πr'2=π(2r)2=4πr2=4A

The area of cross-section will increase by four times.

Then the new resistance,R'=ρlA'

R'=ρl4A

R'=R4

Thus, the resistance will get reduced by four times.


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