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Q.

If the diameter of a wire is doubled, the resistance changes by


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a

Decrease to half

b

Decrease to one-fourth

c

Increase to four times

d

Increase to double 

answer is B.

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Detailed Solution

If the diameter of a wire is doubled, the resistance will decrease to one-fourth.
We know that,
 R=ρlA
⇒R=ρlπ×d22
= ρlπ×4d2
Let us assume that after doubling the diameter of the wire, the resistance of the wire is R’.
⇒R'= ρlA
=ρl1×1π2d22    ( d becomes 2d)
⇒R'= ρlπ×44d2
⇨      14×ρlπ×4d2
⇨      14R
 
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