Question

In a series resonant $LCR$ circuit, the voltage across $R$ is $100$ volts and $R = 1\,\Omega$ with $C = 2\mu F$. The resonant frequency $\omega$ is $200$ rad/s. At resonance the voltage across $L$ is :

• A. $2.5\times10^{-2}\,V$
• B. $40\,V$
• C. $250\,V$
• D. $4\times10^{-3}\,V$

Answer 1

Answer: (C)

$250\,V$

Answer 2

At resonance, $\omega L=\frac{1}{\omega C}$ Current flowing through the circuit, $I=\frac{V_{R}}{R}=\frac{100}{1000}=0.1A$ So, voltage across $L$ is given by $V_{L}=I\,X_{L}=I\omega\,L$ but $\omega L=\frac{1}{\omega C}$ $\therefore V_{L}=\frac{I}{\omega C}=\frac{0.1}{200\times2\times10^{-6}}=250\,V$