Q 12-07-157JEE MainJEE Main 2025 (7 Apr, Shift 1)Medium
An ac current is represented as $i = 5\sqrt2 + 10\cos\left(650\pi t + \dfrac\pi6\right)\ \text{A}$. The r.m.s. value of the current is:
Answer: (C) $10\ \text{A}$
$$i^2 = 50 + 100\cos^2\theta + 100\sqrt2\cos\theta,\qquad \theta = 650\pi t + \frac\pi6$$
Over a full cycle $\langle\cos^2\theta\rangle = \tfrac12$ and $\langle\cos\theta\rangle = 0$:
$$\langle i^2\rangle = 50 + 50 = 100 \Rightarrow i_{\text{rms}} = 10\ \text{A}$$
Solution by Sreeraj P, M.Sc Physics