AC Power and Impedance

These tools assume sinusoidal steady state. For a sine wave, RMS magnitude equals peak magnitude divided by √2. A 120 V RMS sine wave therefore has a peak near 170 V. This conversion does not apply to every waveform.

For three-phase input, specify line-to-line RMS voltage and line RMS current. The AC power calculator assumes a balanced load; it does not infer balance from a single pair of measurements.

For single-phase sinusoidal operation, apparent power S = VI, active power P = VI cosφ and reactive power Q = VI sinφ. The calculator uses positive Q for an inductive load and negative Q for a capacitive load. Its power factor is the nonnegative displacement factor cosφ for a passive load.

For balanced three phase, total S = √3 VL IL and total P = S cosφ. Here φ is the load's per-phase impedance angle, not the angle between an arbitrarily selected line-to-line voltage waveform and a line current waveform.

Constructed example: 400 V line-to-line, 10 A line current and 0.8 lagging power factor gives 6.928 kVA, 5.543 kW and 4.157 kvar. Choosing 0.8 leading reverses Q's sign while preserving P and S.

These relations and the power triangle are developed in the DOE Electrical Science handbook, ES-09. For distorted waveforms, true power factor P/S can differ from displacement power factor. This calculator does not derive harmonic or unbalanced-system power.

In a series RLC circuit, X = ωL − 1/(ωC), with ω = 2πf. The complex impedance is R + jX and its magnitude is √(R² + X²). RMS current is source RMS voltage divided by that magnitude. The series RLC calculator reports current, phase, power and each component's RMS voltage.

Component voltages add as phasors. Their magnitudes do not simply add to the source magnitude: V² = VR² + (VL − VC)². Positive reactance gives lagging current; negative reactance gives leading current. See MIT's AC-circuit derivation, sections 12.3–12.4.

Enter capacitance in farads: 100 µF is 0.0001 F. The tool's special zero-capacitance input bypasses the capacitor; it does not model a physical zero-capacitance component. Resistance must remain positive.

Constructed example: R = 10 Ω, L = 0.1 H, C = 100 µF and source = 10 V RMS. The ideal resonance frequency is 50.329 Hz. Hold the components fixed while changing the frequency:

At resonance, current is 1 A and each reactive component has about 31.623 V RMS across it, despite the 10 V RMS source. Their reactive voltages cancel in the series sum. This ideal example does not select component voltage, current or thermal ratings.

Switching transients, component tolerances, inductor saturation and frequency-dependent losses can change actual behavior. Neither tool selects wire ampacity, protective devices or a compliant installation.