Q. A series LCR circuit with inductance 10 H, capacitance 10 μF, resistance 50 Ω is corrected to an ac source of voltage, V = 200 sin(100t) volt. If resonant frequency of the LCR circuit is $v_0$ and the frequency of the ac source is v, then :
A) $v = 100$ Hz; $v_0 = \frac{100}{\pi}$ Hz
B) $v_0 = v = 50$ Hz
C) $v_0 = v = \frac{50}{\pi}$ Hz
D) $v_0 = \frac{50}{\pi}$ Hz, $v = 50$ Hz
Explanation
[Solution] $\omega_0 = 1/\sqrt{LC} = 1/\sqrt{10 \times 10^{-5}} = 100$ rad/s and source ω = 100 rad/s, so $v_0 = v = 100/2\pi = 50/\pi$ Hz. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.