In an AC circuit, the root mean square value of the current is related to the peak current by which factor?

Solution

1. For a sinusoidal alternating current, the instantaneous current is given by $I(t)=I_0\sin (\omega t)$, where $I_0$ is the peak current.
2. The root mean square (RMS) value is defined as the square root of the mean of the squared current over one complete cycle.
3. Calculating this integral yields $$\begin{array}{rl}{I}_{\text{rms}}& =\sqrt{\frac{1}{T}{\int }_0^T{I}_0^2{\sin }^2(\omega t)dt}\\ & =\frac{I_0}{\sqrt{2}}\end{array}$$.
4. Hence the answer is (C).