A constant voltage is applied between the two ends of a metallic wire. If both the length and the radius of the wire are doubled, the rate of heat developed in the wire
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$H \propto \frac{1}{R}$ (If $V =$ constant) $ \Rightarrow $ $\,\frac{{{H_1}}}{{{H_2}}} = \frac{{{R_2}}}{{{R_1}}}$$ = \frac{{{l_2}{A_1}}}{{{l_1}{A_2}}}$$ = \frac{{{l_2}r_1^2}}{{{l_1}r_2^2}}$
$ \Rightarrow $ ${H_2} = 2{H_1}$
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