Two wires $A$ and $B $ of same material and same mass have radius $2r$ and $r$ . If resistance of wire $A$ is $34\,\Omega $, then resistance of $B$ will be ............ $\Omega$
Medium
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(a) $R = \rho \frac{l}{A}$ and mass $m =$ volume ($V$) $×$ density ($d$) $=$ ($A l$) $d$
Since wires have same material so $r$ and $d$ is same for both.
Also they have same mass $ \Rightarrow $ $Al$ $=$ constant $ \Rightarrow $ $l \propto \frac{1}{A}$
$ \Rightarrow $ $\frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}} \times \frac{{{A_2}}}{{{A_1}}} = {\left( {\frac{{{A_2}}}{{{A_1}}}} \right)^2} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^4}$
$ \Rightarrow $ $\frac{{34}}{{{R_2}}} = {\left( {\frac{r}{{2r}}} \right)^4}$ $ \Rightarrow $ ${R_2} = 544\,\Omega $
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