Q 12-07-065JEE MainJEE Main 2024 (30 Jan, Shift 1)Medium
A series $LR$ circuit connected with an ac source $E = (25\sin1000t)\ \text{V}$ has a power factor of $\dfrac1{\sqrt2}$. If the source of emf is changed to $E = (20\sin2000t)\ \text{V}$, the new power factor of the circuit will be:
Answer: (C) $\dfrac1{\sqrt5}$
$\cos\phi = \dfrac{R}{\sqrt{R^2 + \omega^2L^2}} = \dfrac1{\sqrt2}$ at $\omega = 1000$ gives $\omega L = R$.
Doubling $\omega$ makes $X_L = 2R$:
$$\cos\phi' = \frac{R}{\sqrt{R^2 + 4R^2}} = \frac1{\sqrt5}$$
Solution by Sreeraj P, M.Sc Physics