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?

Question

Philoid · Accepted Answer

No, current will flow through both of them.

At resonance, we know that X_L = X_C⇒ … (i), where X_L = inductive reactance, X_C = capacitive reactance, ω = angular frequency, L = inductance, C = capacitance

Current through an LCR circuit is given by … (ii), where i₀ = peak value of current, V₀ = peak value of voltage, R = resistance, ω = angular frequency, L = inductance, C = capacitance

From (i) and (ii), at resonance, the peak value of current is given by … (iii)

This current will flow through all circuit elements. However, since the inductive reactance and the capacitive reactance are equal, the potential difference across the inductor and capacitor will be equal and opposite and they will cancel each other out. (Ans)