An AC source produces a sinusoidal voltage with peak (maximum) value $V_m=200\text{V}$. What is its rms value?

Step-by-step solution

1. Recall that for a sinusoidal voltage the rms value is $V_{\text{rms}}=\frac{V_m}{\sqrt{2}}$.
2. Substitute $V_m=200\text{V}$: $V_{\text{rms}}=\frac{200}{\sqrt{2}}$ V.
3. Calculate $\frac{200}{\sqrt{2}}=200\times \frac{\sqrt{2}}{2}=100\sqrt{2}\text{V}$.
4. Since $\sqrt{2}\approx 1.414$, $100\sqrt{2}\approx 141.4\text{V}$.

Concept tested: RMS value of sinusoidal voltage

Published 7 September 2026 · How this solution was prepared and checked