Question

In a series $LCR$ circuit, $R=1\Omega ,C=2\mu F$ and voltage across $R$ is $100V$. The resonant frequency of the circuit $\omega$ is $200rad{s}^{-1}$. Calculate the value of voltage across $L$ at resonance.

Answer 1

Given, $V_R=100,R=1\Omega$

$w=200rad/s,C=2\mu F$

$w^2=\frac{1}{LC}$

⇒$(200{)}^2=\frac{1}{L\times 2\times {10}^{-6}}$

$L=\frac{1}{8\times {10}^{-2}}$

$L=12.5H$

Current through $R=\frac{100}{1}=100A$

At resonance,

Voltage across $L$= Voltage across $C$

$\Rightarrow$ $I\times X_C$

$=100\times \frac{1}{200\times 2\times {10}^{-6}}$

= $250\times {10}^{3}volts$