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A constant wire has resistance $R$ . If the wire is doubled on it, find the new resistance in terms of original resistance.

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\frac{R}{2}

\frac{R}{4}

\frac{R}{2}

R

answer is B.

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Detailed Solution

The new resistance will be

\frac{R}{4}

.
A wire's resistance is inversely proportional to its area and directly proportional to its length.
It means resistance

R \propto \frac{l}{A}

R = ρ \frac{l}{A}

where

l

is the length of the wire,

A

is the cross-sectional area of the wire,

ρ

is the resistivity of the wire. Let the initial resistance of the wire is

R = ρ \frac{l}{A}

When the wire is doubled, its length becomes

\frac{l}{2}

and the wire’s cross-sectional area becomes

2 A

, then resistance

R = ρ \frac{\frac{l}{2}}{2 A}

That is new resistance

R = ρ \frac{l}{4 A}

\Rightarrow

R = \frac{R}{4}

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