Problem

The peak voltage of an AC supply is 300 V. What is the RMS voltage?

Data

• Maximum voltage: $\mathrm{V}_{\text{max}} = 300 \, \mathrm{V}$
• To find: Root mean square voltage $\mathrm{V}_{\text{rms}}$

Prerequisite Concepts

The RMS voltage ($\mathrm{V}_{\text{rms}}$) is related to the peak voltage ($\mathrm{V}_{\text{max}}$) by the formula:

$$\mathrm{V}_{\text{rms}} = \frac{\mathrm{V}_{\text{max}}}{\sqrt{2}}$$

Solution

Substitute the given value into the formula:

$$\mathrm{V}_{\text{rms}} = \frac{\mathrm{V}_{\text{max}}}{\sqrt{2}} = 0.707 \, \mathrm{V}_{\text{max}}$$ $$\mathrm{V}_{\text{rms}} = 0.707 \times 300 \, \mathrm{V}$$ $$\mathrm{V}_{\text{rms}} = 212.1 \, \mathrm{V}$$

Answer

The RMS voltage is $212.1 \, \mathrm{V}$.

---