Question

In a series resonant L-C-R circuit, the voltage across R is 100 V and $R=1k\Omega$ with $C=2\mu F$. The resonant frequency is 200 $rad{s}^{-1}$. At resonance the voltage across L is :

• A. $2.5\times {10}^{-2}V$
• B. $4\times {10}^{-8}V$
• C. $250V$
• D. $4\times {10}^{-3}V$

Answer 1

The correct option is C $250V$

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 $\omega L=\frac{1}{\omega C}$

$\therefore V_L=\frac{I}{\omega C}$

$=\frac{0.1}{200\times 2\times {10}^{-6}}$

$=250V$