Problem

The RMS value of current in an AC circuit is $10 \, \mathrm{A}$. What is the peak current?

Data

• RMS current: $I_{\text{rms}} = 10 \, \mathrm{A}$
• To find: Peak current $I_{\text{max}}$

Prerequisite Concepts

The RMS current ($I_{\text{rms}}$) is related to the peak current ($I_{\text{max}}$) by the formula:

$$I_{\text{rms}} = \frac{I_{\text{max}}}{\sqrt{2}}$$

Rearranging to find $I_{\text{max}}$:

$$I_{\text{max}} = \sqrt{2} \times I_{\text{rms}}$$

Solution

Substitute the given values into the formula:

$$I_{\text{max}} = \sqrt{2} \times 10 \, \mathrm{A}$$ $$I_{\text{max}} = 1.41 \times 10 \, \mathrm{A}$$ $$I_{\text{max}} = 14.1 \, \mathrm{A}$$

Answer

The peak current is $14.1 \, \mathrm{A}$.

---