A series LCR circuit with inductance 10 H, capacitance 10 μ F, resistance 50 Ω is connected to an ac source of voltage, V=200 sin (100 t ) volt. If the resonant frequency of the LCR circuit is ν o and the frequency of the ac source is ν, then :

Question

A series LCR circuit with inductance 10 H, capacitance 10 μ F, resistance 50 Ω is connected to an ac source of voltage, V=200 sin (100 t ) volt. If the resonant frequency of the LCR circuit is ν o and the frequency of the ac source is ν, then : (A) v=100 Hz ; v0=(100/π) Hz (B) v 0 =ν=50 Hz (C) v0=v=(50/π) Hz (D) v0=(50/π) Hz , ν=50 Hz

Tardigrade Admin · Accepted Answer

ω=100 v=(ω/2 π)=(100/2 π)=(50/π) Hz Resonance frequency v0=(1/2 π √ LC )=(1/2 π) √(1/10 × 10 × 10-6) =(50/π) Hz

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

$v = 100 Hz; v_{0} = \frac{100}{π} Hz$

$v_{0} = ν = 50 Hz$

$v_{0} = v = \frac{50}{π} Hz$

$v_{0} = \frac{50}{π} Hz, ν = 50 Hz$

$ω = 100$
$v = \frac{ω}{2 π} = \frac{100}{2 π} = \frac{50}{π} Hz$
Resonance frequency
$v_{0} = \frac{1}{2 π L C} = \frac{1}{2 π} \frac{1}{10 \times 10 \times 1 0 ^{- 6}}$
$= \frac{50}{π} Hz$

Q. A series LCR circuit with inductance 10H, capacitance 10μF, resistance 50Ω is connected to an ac source of voltage, V=200sin(100t) volt. If the resonant frequency of the LCR circuit is νo​ and the frequency of the ac source is ν, then :

v=100Hz;v0​=π100​Hz

v0​=ν=50Hz

v0​=v=π50​Hz

v0​=π50​Hz,ν=50Hz