Rms And Peak Values

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: $V_{rms}=\frac{311}{\sqrt{2}}=\frac{311}{1.414}\approx 220\text{V}$. 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.