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  4. The rms value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is

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Q. The $ rms $ value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is

VMMC MedicalVMMC Medical 2011

Solution:

Heat produce by DC $ H=i_{DC}^{2}Rt $ ?(i) $ =4Rt $ Heat produced by AC $ 4H=i_{rms}^{2}Rt $ ?(ii) $ \therefore $ $ \frac{4H}{H}=\frac{i_{rms}^{2}Rt}{4Rt} $ or $ {{i}_{rms}}=4A $