How to use the rlc circuit calculator
- Choose a series or parallel circuit.
- Type the resistance, inductance, capacitance and frequency. You can add a prefix and unit: 4.7k, 10 mH, 100 nF, 1 kHz.
- Enter a source voltage if you want the current and power. The default is an example.
- Read the impedance, phase angle, resonant frequency, Q and bandwidth, then the table that sweeps the frequency around resonance.
Formula
X(L) = 2 pi f L and X(C) = 1 / (2 pi f C)
series: Z = R + j (X(L) - X(C))
parallel: Y = 1/R + j (2 pi f C - 1 / (2 pi f L)) and Z = 1 / Y
resonant frequency f0 = 1 / (2 pi sqrt(L C)) and bandwidth = f0 / Q
Series Q = sqrt(L / C) / R and parallel Q = R x sqrt(C / L). The phase angle is positive when the circuit is inductive and negative when it is capacitive. At resonance the reactances cancel, so the series impedance falls to R and the parallel impedance rises to R.
50 ohms, 10 mH and 1 uF at 1 kHz
In series, X(L) = 62.832 ohms and X(C) = 159.155 ohms, so Z = 50 - j96.323, which has a size of 108.527 ohms and a phase of -62.567 degrees: the circuit behaves as a capacitor. The resonant frequency is 1591.55 Hz, Q is 2 and the bandwidth is 795.77 Hz. With 10 V the current is 0.092143 A and the real power is 0.42452 W at a power factor of 0.4607.
The same parts in parallel give a size of 45.0477 ohms at +25.716 degrees, which is inductive, a Q of 0.5, a bandwidth of 3183.1 Hz and a real power of 2 W. At the resonant frequency both circuits show exactly 50 ohms with a phase of zero.
What the numbers mean
Reactance is the opposition of a coil or capacitor to alternating current. It grows with frequency for a coil and shrinks for a capacitor. At low frequency the capacitor dominates, and at high frequency the coil does, and in between there is one frequency where they cancel: resonance.
Q describes how sharp the resonance is. A high Q gives a narrow peak, and the bandwidth is the width between the half-power points. In a series circuit a high Q also means the voltage across the coil or capacitor can be larger than the source voltage.
Limits of the ideal model
The parts are treated as ideal, with no resistance in the coil and no leakage in the capacitor. Real parts lower Q, and a coil can have its own stray capacitance. For the basic relations of voltage, current and power, see the Ohm's Law Calculator, and to decode a capacitor marking use the Capacitor Code Calculator.
More science and electronics tools
For other science and electronics questions, try the Resistor Combination Finder, Room Modes Calculator and pH Calculator.
Assumptions and limits
- The source is a steady sine wave at one frequency, and the voltage is an RMS value.
- Resistors, coils and capacitors are ideal: no parasitic effects, no temperature drift.
- Series means all three parts share one current. Parallel means all three share one voltage.
- The prefix letters mean pico, nano, micro (u), milli (m), kilo, mega and giga.
Frequently asked questions
Why is the series impedance smallest at resonance?
The coil and capacitor reactances have opposite signs and cancel, leaving only the resistance. Current is therefore at its largest for a given voltage.
What does a negative phase angle mean?
The circuit is capacitive: the current leads the voltage. A positive angle means the circuit is inductive and the current lags the voltage.
Why does the parallel circuit peak at resonance instead?
In parallel, the coil and capacitor currents cancel, so little current flows into the pair and the total impedance rises to the resistance alone.
What is the power factor?
It is the cosine of the phase angle, the share of the apparent power that does real work. At resonance it is 1.