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Question

(A) The heat produced by a steady $DC$ current $I$ in a resistor $R$ over time $t$ is given by $H_{DC} = I^2 R t$.The heat produced by an $AC$ current

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$2 : 1$

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(A) The heat produced by a steady $DC$ current $I$ in a resistor $R$ over time $t$ is given by $H_{DC} = I^2 R t$.The heat produced by an $AC$ current with peak value $I$ in the same resistor $R$ over the same time $t$ is given by $H_{AC} = I_{rms}^2 R t$.Since $I_{rms} = \frac{I}{\sqrt{2}}$,we have $H_{AC} = \left(\frac{I}{\sqrt{2}}\right)^2 R t = \frac{I^2 R t}{2}$.Therefore,the ratio of heat produced is $\frac{H_{DC}}{H_{AC}} = \frac{I^2 R t}{I^2 R t / 2} = \frac{2}{1}$.

$A$ steady current of magnitude $I$ and an $AC$ current of peak value $I$ are allowed to pass through identical resistors for the same time. The ratio of heat produced in the two resistors will be

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