Neutron STEM Lab

AC Circuit Calculators & Analysis Workbench

Free AC circuit calculators for impedance, phasors, RLC circuits, resonance, real and reactive power, power factor, transformers, and frequency response.

AC Circuits: labelled diagrams and key equations for AC circuits, phasors, impedance, and RLC.
Browser-local interactive workspace
Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

AC Circuits: theory, method, and sources

This electrical engineering workspace publishes 11 governing equations, 4 stated assumptions, 2 documented boundaries, 1 worked example, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyContent reviewed August 11, 2026Calculation & source methodology

How this tool works

Fourteen guided modules progress from sinusoidal waveforms and phasors to complex networks and three-phase power.

Every graph labels its measured quantity and unit, including time, voltage, frequency, impedance, current, gain, and power.

Inputs, imported state, restored state, graph sampling, and complex arithmetic are bounded before calculation and rendering.

Calculators and topics covered

  • AC circuits
  • phasors
  • impedance
  • RLC
  • power factor
  • filters
  • transformers
  • three phase
  • sinusoid
  • RMS
  • complex impedance
  • series RLC
  • parallel RLC
  • real power

Core equations

v(t)=Vpk  sin⁡(ωt+φ)v \left(t\right) = V_{\mathrm{pk}}\; \sin \left(\omega t + \varphi \right)ZR=RZ_{R} = RZL=jωLZ_{L} = j\omega LZC=1jωCZ_{C} = \frac{1}{j\omega C}S=VI∗S = VI^{*}P=∣S∣  cos⁡φP = \left|S\right|\; \cos \varphi Q=∣S∣  sin⁡φQ = \left|S\right|\; \sin \varphi f0=12πLCf_{0} = \frac{1}{2 \pi \sqrt{LC}}fc=12πRCf_{c} = \frac{1}{2 \pi RC}VsVp=NsNp\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}P3φ=3 VLILcos⁡φP_{3\varphi}=\sqrt{3}\,V_L I_L\cos\varphi

Worked examples

Tuning a series RLC branch to unity power factor

A 230 V single-phase branch feeds a 12 Ω resistive load through a 25 mH reactor and a 47 µF capacitor. At the 50 Hz supply frequency the branch draws heavy leading reactive current, so the question is what the branch actually does at 50 Hz and what happens if the source is driven at the resonant frequency instead.

Inputs
  • V = 230 V rms
  • R = 12 Ω, L = 25 mH, C = 47 µF
  • Supply frequency 50 Hz, then swept to resonance
Method
  1. At 50 Hz the reactances are unequal: X_L = 2πfL = 7.854 Ω against X_C = 1/(2πfC) = 67.726 Ω, so the branch is strongly capacitive.
  2. Impedance is therefore Z = 12 − j59.872 Ω, giving |Z| = 61.062 Ω and a phase angle of −78.67°.
  3. Current is I = V/|Z| = 3.767 A at a power factor of 0.197 leading. Only 170.3 W of the 866.3 VA drawn is real power; the remaining 849.4 var is circulating.
  4. Resonance occurs where X_L = X_C, at f₀ = 1/(2π√(LC)) = 146.83 Hz. At that frequency both reactances equal 23.063 Ω and cancel.
  5. At f₀ the impedance collapses to the resistance alone: |Z| = 12 Ω, current rises to 19.167 A, power factor is 1.000, and real power is 4408.3 W.

Result: The same branch draws 3.767 A at pf 0.197 at 50 Hz, but 19.167 A at unity power factor at its 146.83 Hz resonance — a factor of 5.1 increase in current for no change in component values.

Interpretation: This is why series resonance is a hazard as much as a design tool. The branch looks harmless at the supply frequency, yet a harmonic or drive near 147 Hz would push it to over 19 A with nothing but the 12 Ω resistor limiting it. The quality factor Q = (1/R)√(L/C) = 1.922 gives a −3 dB bandwidth of f₀/Q ≈ 76.4 Hz, which is wide enough that ordinary supply harmonics fall inside it. Check the resonant frequency of any power-factor correction branch against the harmonic spectrum it will actually see.

Method and assumptions

Assumptions

  • Signals are sinusoidal and in steady state unless the time-domain sinusoid module is used.
  • Components and transformers are ideal, linear, and lumped.
  • Three-phase systems are balanced.
  • Power-factor correction uses an ideal shunt capacitor estimate.

Limitations and design boundaries

  • Not a substitute for SPICE simulation, protection studies, harmonic analysis, insulation coordination, component thermal design, laboratory measurement, electrical codes, or professional review.
  • The workbench does not model source impedance frequency dependence, parasitics, magnetic saturation, core loss, skin effect, transmission lines, unbalanced three-phase faults, switching transients, or non-sinusoidal harmonics.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy
  • Alexander and Sadiku, Fundamentals of Electric CircuitsSinusoidal steady-state analysis, phasors, impedance, power, resonance, and filters.
  • Nilsson and Riedel, Electric CircuitsAC networks, frequency response, transformers, and three-phase systems.

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