Question

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

• A. $4$ x ${10}^{-3}V$
• B. $2.5$ x ${10}^{-2}V$
• C. $40V$
• D. $250V$

Answer 1

Answer: (D)

$250V$

The resonant angular frequency , $\omega =\frac{1}{\sqrt{LC}}$

$L=\frac{1}{{\omega }^{2}C}=\frac{1}{{200}^2\times 2\times {10}^{-6}}=12.5H$

At resonance , impedance $Z=R$ so the current in the circuit is

$I=\frac{V}{Z}=\frac{V}{R}=\frac{100}{1000}=0.1A$

Voltage across inductor, $V_L=I{X}_L=I\omega L=0.1\times 200\times 12.5=250V$