Question

A series LCR circuit with inductance $10 \,H$, capacitance $10 \,\mu F$, resistance $50 \,\Omega$ is connected to an ac source of voltage, $V=200 \,\sin (100 \,t )$ volt. If the resonant frequency of the LCR circuit is $\nu_{ o }$ and the frequency of the ac source is $\nu$, then :

• A. $v=100 \,Hz ; v_{0}=\frac{100}{\pi} \,Hz$
• B. $v_{ 0 }=\nu=50\, Hz$
• C. $v_{0}=v=\frac{50}{\pi} Hz$
• D. $v_{0}=\frac{50}{\pi} \,Hz , \nu=50\, Hz$

Answer 1

Answer: (C)

$\omega=100$
$v=\frac{\omega}{2 \pi}=\frac{100}{2 \pi}=\frac{50}{\pi} Hz$
Resonance frequency
$v_{0}=\frac{1}{2 \pi \sqrt{ LC }}=\frac{1}{2 \pi} \sqrt{\frac{1}{10 \times 10 \times 10^{-6}}} $
$=\frac{50}{\pi} Hz$