Enter branches with R, L, C and sinusoidal EMFs — get complex currents and voltages, the power balance S = P + jQ and a phasor diagram. Below: resonant frequency, Q factor and resonance curve of an RLC circuit.
Phasor method
Sinusoids become complex numbers I = I·e^{jψ}; impedances: resistor R, inductor jωL, capacitor −j/(ωC). A series R-L-C branch: Z = R + j(ωL − 1/(ωC)). Ohm’s and Kirchhoff’s laws, mesh and nodal methods work as for DC, with complex numbers. Results are shown as a + jb and |I|∠ψ.
Power balance
Source complex power S = E·I* = P + jQ, load power Σ|I|²Z = Σ|I|²R + jΣ|I|²X. P in watts, Q in var, |S| in VA.
Resonance
A series circuit resonates when ωL = 1/(ωC): f₀ = 1/(2π√(LC)), characteristic impedance ρ = √(L/C), Q = ρ/R. In a parallel circuit the input impedance peaks, Q = R/ρ.
FAQ
How do I solve an AC circuit with complex numbers?
Replace elements with complex impedances (R, jωL, −j/(ωC)) and sources with complex EMFs, then solve as a DC circuit. The calculator does this automatically.
How do I convert rectangular to polar form?
|I| = √(a² + b²), ψ = atan2(b, a). Both forms are shown for each current.
How do I find the resonant frequency?
f₀ = 1 / (2π√(LC)). Enter L and C in the “Resonance” block.
Why is source power complex?
The real part of S = E·I* is active power (heat in resistors), the imaginary part reactive power exchanged with L and C.
Which units for L and C?
Inductance in millihenries (mH), capacitance in microfarads (µF), EMF and currents as RMS values, phase in degrees.