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Same mass of copper is drawn into 2 wires of 1mm thick and 3mm thick. Two wires are connected in series and current is passed. Heat produced in the wires is the ratio of

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3 : 1

9 : 1

81 : 1

1 : 81

answer is C.

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Detailed Solution

Mass (m) =V× d ; m=πr²ld

As the volume is same, l.A is same.

$l \propto \frac{1}{r^{2}} \Rightarrow R = \frac{ρ l}{π r^{2}}$

$∴ R \propto \frac{1}{r^{2}} \propto \frac{1 / r^{2}}{r^{2}} \propto \frac{1}{r^{4}}$

$R \propto l^{2}; H = i^{2} Rt (In series I is same)$

$H \propto R \propto \frac{1}{r^{4}}$

$∴ \frac{H_{1}}{H_{2}} = \frac{r_{2}^{4}}{r_{1}^{4}} = {(\frac{3}{1})}^{4} = \frac{81}{1}$

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