Question

When the frequency of the AC source in an LCR circuit equals the resonant frequency, the reactance of the circuit is zero. Does it mean that there is no current through the inductor or the capacitor?

Answer 1

The condition for resonance is:
$\frac{1}{\omega C}=\omega L$
The peak current through the circuit is given by,
$i_0=\frac{V_0}{{\sqrt{R^2+\left({\displaystyle \frac{1}{\omega C}}-\omega L\right)}}^2}$
From the condition of resonance, we get:
$i_0=\frac{V_0}{R}$
The current will flow through the all circuit elements. But since the reactance of the capacitor and inductor are equal, the potential difference across them will be equal and opposite and will cancel each other.