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  4. What is the (rms) value of an alternating current which when passed through a resistor produces heat which is thrice that of produced by a direct current of 2 A in the same resistor?

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Q. What is the (rms) value of an alternating current which when passed through a resistor produces heat which is thrice that of produced by a direct current of 2 A in the same resistor?

Rajasthan PMTRajasthan PMT 2010

Solution:

Heat produced by $ AC=3\,\,\,\times $ Heat produced by $ DC $ $ \therefore $ $ i_{rms}^{2}Rt=3\times {{i}^{2}}Rt $ $ \Rightarrow $ $ i_{rms}^{2}=3\times {{2}^{2}} $ $ {{i}_{rms}}=2\sqrt{3}=3.46A $