The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then
AIPMT 2004, Easy
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(b) $R \propto \frac{l}{{{r^2}}}$
$ \Rightarrow $ $\frac{{{R_2}}}{{{R_1}}} = \frac{{{l_2}}}{{{l_1}}} \times \frac{{{r_1}^2}}{{{r_2}^2}}=\left( {\frac{2}{1}} \right) \times {\left( {\frac{1}{2}} \right)^2}$ $ = \frac{1}{2}$
$ \Rightarrow $ ${R_2} = \frac{{{R_1}}}{2},$ specific resistance doesn't depend upon length, and radius.
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