Q Factor of a Series Resonant Circuit

Q is the ratio of energy stored to energy lost per radian of oscillation, and for a series circuit that works out to √(L/C)/R. It sets the bandwidth — BW = f₀/Q — so a 100 µH coil with 250 pF and 5 Ω of loss gives Q ≈ 126, meaning a 1 MHz resonance only 8 kHz wide. That selectivity is what lets a receiver hear one station while ignoring its neighbour.

The startling part is voltage magnification: at resonance the voltage across the inductor (and across the capacitor) is Q times the applied voltage, even though they cancel each other in the sum. Feed 10 V into that circuit and the coil sits at 1.26 kV. Bench technicians have destroyed capacitors this way, and power engineers watch for the same effect when a capacitor bank resonates with system inductance at a harmonic frequency.