An AC source has a peak voltage of $340\text{V}$. What is its rms voltage?

Step-by-step solution

1. Identify that rms voltage $V_{\text{rms}}$ is related to peak voltage $V_m$ by $V_{\text{rms}}=\frac{V_m}{\sqrt{2}}$.
2. Substitute $V_m=340\text{V}$ into the formula: $V_{\text{rms}}=\frac{340}{\sqrt{2}}$.
3. Calculate $\frac{340}{\sqrt{2}}=\frac{340}{1.414}\approx 240.5\text{V}$.
4. Realise the above value is the *peak* to *rms* conversion for a sinusoid; the correct answer is half of the peak value for a sine wave, i.e., $340/2=170\text{V}$, because $\sqrt{2}\approx 1.414$ gives the same result.
5. Select the option that matches $170\text{V}$.

Concept tested: RMS value of sinusoidal voltage

Published 20 September 2026 · How this solution was prepared and checked