Basics calculator
RLC circuit
The resistor decides how long an LC keeps ringing; Q counts the swings.
Free. It runs in your browser: nothing to install.
The example, worked out
Given
- Arrangement
- R, L and C in series
- Resistance R
- 10 Ω
- Inductance L
- 1 mH
- Capacitance C
- 1 µF
- Frequency of interest
- 5 kHz
Working
- the same in series and in parallel
- a small R lets it ring
- at 5 kHz
Results
The formulas
- f0 = 1 / (2π √(L C))the same for both
- Q = Z0 / R (series), R / Z0 (parallel)the resistor damps one and loads the other
- BW = f0 / Qbetween the two half-power points
The usual traps
- In series the impedance is lowest at f0; in parallel it is highest.
- Q above 0.5 (ζ below 1) means it rings on a step: the overshoot grows fast with Q.
- The coil's own resistance counts as part of R.
Questions
How do I calculate the resonance and Q of an RLC circuit?
f0 = 1 / (2π √(L C)): the same for both. Q = Z0 / R (series), R / Z0 (parallel): the resistor damps one and loads the other. BW = f0 / Q: between the two half-power points.
What does it give for typical values?
F0 = 5.03 kHz, Q = 3.16, series: 10 Ω, 1 mH, 1 µF. Resonance f0: 5.03 kHz; Quality factor Q: 3.16.
What are the usual mistakes?
In series the impedance is lowest at f0; in parallel it is highest. Q above 0.5 (ζ below 1) means it rings on a step: the overshoot grows fast with Q. The coil's own resistance counts as part of R.
In the app
Your circuit, drawn live
Change a value: the schematic redraws with your numbers on the parts.
The part you can buy
Results rounded to standard values (E12, E24, E96) and power ratings.
The working, shown
Every step written out. Try it first by hand, then check.
Into your notebook
One click puts the circuit on a sheet of your project.
Open the calculatorOpens in the app on 1 December, with Circuit Notebook 1.0
Also in Basics
- Ohm's law & power Any two of V, I, R, P give the other two.
- LED resistor The series resistor, in a value you can buy.
- Voltage divider What two resistors give, loaded or not; or the pair to build one.
- Series & parallel Resistors, capacitors or inductors together, and how they share.
- Resistor colour code A value to its bands, or the bands to a value.
- RC time constant τ, the cutoff, and how long to reach a level.
- Reactance & resonance XL and XC at a frequency, and where L and C meet.
- Wheatstone bridge The output of a bridge, the value that balances it, the unknown from a reading.
- Capacitive divider Two capacitors in series: the ratio, the tap, the load that spoils it.
- RL time constant τ = L / R, the final current, and the kick when the switch opens.