JEE Main · PhysicsHard
An AC source with voltage $V = V_0 \sin(\omega t)$ is connected to a series LCR circuit. If the frequency of the source is varied, the power factor of the circuit is $1/\sqrt{2}$ at two angular frequencies $\omega_1$ and $\omega_2$. Find the value of $|\omega_1 - \omega_2|$.
- A.$R/L$
- B.$R/(2L)$
- C.$2R/L$
- D.$L/R$
Show correct answer & step-by-step solution
Correct answer: A — $R/L$
Solution
The power factor is when the impedance , which implies the reactance . Solving the quadratic equation leads to the difference between roots being .
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