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  4. The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then

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Q. The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then

JIPMERJIPMER 2015Current Electricity

Solution:

Resistance of wire $=\rho \frac{l}{A}$
$R \propto \frac{l}{A}=\frac{l}{\pi r^{2}}$
When length and radius are both doubled
$R_{1} \propto \frac{2 l}{\pi(2 r)^{2}}$
$ \Rightarrow R_{1} \propto \frac{1}{2} R$
The specific resistance of wire is independent of geometry of the wire, it only depends on the material of the wire.