Rms And Peak Values

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An alternating voltage supplied to a household appliance has a peak value of 311 volts and oscillates sinusoidally at 50 hertz. What is the root-mean-square value of this voltage that a standard meter would display?

RankGuru · Accepted Answer

According to NCERT Class 12, Chapter 7 (Alternating Current), for a sinusoidal voltage the root-mean-square value relates to the peak value by $V_{rms} = \frac{V_0}{\sqrt{2}}$, because the rms value represents the equivalent steady voltage that delivers the same average power. Substituting the peak value: $V_{rms} = \frac{311}{\sqrt{2}} = \frac{311}{1.414} \approx 220\ 	ext{V}$. The option 311 V simply repeats the peak value and ignores the averaging factor. The option 440 V multiplies by $\sqrt{2}$ instead of dividing, doubling toward the peak-to-peak scale. The option 156 V erroneously halves the peak value rather than dividing by $\sqrt{2}$. As a sanity check, the rms of a sinusoid must lie between zero and the peak, and 220 V is indeed less than 311 V and matches the familiar mains supply value, confirming the result is physically reasonable. Meters and appliance ratings quote rms values precisely because they determine actual power dissipation.

Rms And Peak Values

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