What is the peak value of an alternating current that produces three times the heat per second as a direct current of 2.0 A in a resistance R?
MPPSC Forest Service - 2023,
Answer: B
The peak current is about 4.9 A.
The heating effect of an alternating current depends on its rms value. To produce three times the heat of 2.0 A DC in the same resistance:
\[ \begin{aligned} I_{rms}^{2}R &= 3(2.0)^{2}R \\ I_{rms} &= \sqrt{12} = 3.46\ \text{A} \\ I_{0} &= \sqrt{2}\,I_{rms} = 4.9\ \text{A} \end{aligned} \]
3.46 A is the rms value, not the peak asked for. 2.45 A and 2.0 A would produce less than three times the heat.
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