Q 12-07-080JEE MainJEE Main 2023 (25 Jan, Shift 2)Easy
A series LCR circuit is connected to an AC source of $220\ \text{V}$, $50\ \text{Hz}$. The circuit contains a resistance $R=80\ \Omega$, an inductor of inductive reactance $X_L=70\ \Omega$, and a capacitor of capacitive reactance $X_C=130\ \Omega$. The power factor of circuit is $\dfrac x{10}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 8
$Z=\sqrt{80^2+60^2}=100\ \Omega$; $\cos\phi=\dfrac RZ=0.8=\dfrac8{10}$. So $x=8$.
Solution by Sreeraj P, M.Sc Physics