Physics

At resonance in an LC circuit, the inductive and capacitive reactances cancel each other out perfectly, so the impedance is minimized and current is maximized. The key is setting $X_L = X_C$—that is, $\omega L = \frac{1}{\omega C}$—then solving for the unknown inductance using the given frequency and capacitance. This resonance condition is independent of resistance and depends only on $L$, $C$, and $\omega$.

At resonance in an LC circuit, the inductive and capacitive reactances cancel each other out perfectly, so the impedance is minimized and current is maximized. The key is setting $X_L = X_C$—that is, $\omega L = \frac{1}{\omega C}$—then solving for the unknown inductance using the given frequency and capacitance. This resonance condition is independent of resistance and depends only on $L$, $C$, and $\omega$.