Physics - EMI/AC Question with Solution | TestHub

The impedance of a series LCR circuit is given by $Z=\sqrt{R^2+(X_L-X_C{)}^2}$, where $X_L=\omega L$ is the inductive reactance and $X_C=\frac{1}{\omega C}$ is the capacitive reactance.

At resonance, $X_L=X_C$. This means the term $(X_L-X_C{)}^2$ becomes zero. Consequently, the impedance becomes $Z=\sqrt{R^2+0}=R$.

Since $R$ is the purely resistive component, and $X_L$ and $X_C$ are frequency-dependent, $Z=R$ is the minimum possible impedance for the circuit. Thus, both assertion and reason are true, and the reason correctly explains why the impedance is minimum at resonance.