Q 12-07-151JEE MainJEE Main 2018 (8 Apr)Medium
In an A.C. circuit, the instantaneous e.m.f. and current are given by $E = 100\sin30t$, $I = 20\sin\left(30t - \dfrac\pi4\right)$. In one cycle of A.C., the average power consumed by the circuit (in watt) and the wattless current (in ampere) are, respectively:
Answer: (C) $\dfrac{1000}{\sqrt2},\ 10$
$$P = \frac{E_0I_0}{2}\cos\phi = \frac{100\times20}{2}\cos45^\circ = \frac{1000}{\sqrt2}\ \text{W}$$
The wattless component of the current (rms) is
$$I_{\text{rms}}\sin\phi = \frac{20}{\sqrt2}\times\frac{1}{\sqrt2} = 10\ \text{A}$$
Solution by Sreeraj P, M.Sc Physics