How this calculator works
Impedance combines resistance and reactance as a complex quantity. Series impedances add directly. Parallel branches add as admittances, then the total is inverted. Positive imaginary impedance is inductive and negative imaginary impedance is capacitive. The phase is the voltage phase relative to current for the passive load convention. Results assume sinusoidal steady state and frequency-independent ideal components.
Formula
Zseries = R + j(omega L - 1/(omega C)); Yparallel = 1/R + j(omega C - 1/(omega L)); Zparallel = 1/Yparallel; omega = 2 pi f.
Worked example
At omega = 1 rad/s, R = 3 ohm, L = 2 H and C = 1 F in series give Z = 3+j1 ohm, with magnitude 3.16227766 ohm. A parallel RLC at ideal resonance has impedance equal to its shunt resistance.
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Frequently asked questions
What does a negative imaginary value mean?
The equivalent load is capacitive at this frequency, so current leads voltage.
Why is the parallel impedance not the reciprocal of the series value?
The individual branch admittances must be added before inverting; the circuit topology is different.
Can I include parasitic coil loss?
This model does not include an internal series resistance in the inductor branch. Use a more complete circuit model for that topology.