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Q.

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


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a

Double

b

Four times

c

One- half

d

One-fourth 

answer is D.

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Detailed Solution

The resistance of a conductor is inversely proportional to its area of cross-section. That is,
     Resistance, R= ρ×lA
Where,
A is area of cross-section of wire
ρ is resistivity of the wire and l is length of the wire
(Where R is resistance and A is area of cross-section of conductor).
The resistance of a wire is inversely proportional to the square of its diameter. If the diameter becomes double, the area increases by the square of the diameter, i.e. 4 times; therefore, resistance becomes one-fourth.
 
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