Question

What is the peak voltage across capacitor at resonance frequency in the given circuit ?

• A. $100V$
• B. $10V$
• C. $5V$
• D. $50V$

Answer 1

The correct option is A $100V$

For resonance in a series $LCR$ circuit, $X_L=X_C$

i.e $\omega L=\frac{1}{\omega C}$
$\Rightarrow \omega =\frac{1}{\sqrt{LC}}$

and Impedance at resonance $Z=\sqrt{R^2+(X_L-X_C{)}^2}=R$

Peak current $i_0=\frac{V_0}{Z}=\frac{10}{2}=5A$

Therefore, peak voltage across capacitor $=i_0{X}_C$
$=5\times 20=100V$