Q Factor of a Series Resonant Circuit
Worked example: 100 µH, 250 pF, 5 Ω → Q ≈ 126.5 — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
Resonance →
UniversityCircuits & Electrical Power
Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning.
share your results
Q Factor of a Series Resonant Circuit explained
Q is the ratio of energy stored to energy lost per radian of oscillation, and for a series circuit that works out to . 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.
Q Factor of a Series Resonant Circuit formula
- = Quality factor
- = Series resistance (Ω)
- = Inductance (mH)
- = Capacitance (μF)
Missing one of these? Work it out first, then come back
- Quality factor — Bandwidth from Q and Centre Frequency, Overall Equipment Effectiveness (OEE)
- Series resistance — LED Series Resistor, Conductor Resistance Temperature Correction
- Inductance — RL Cutoff Frequency, Two Inductors in Series
- Capacitance — Power-Factor Correction Capacitance, RC Cutoff Frequency