AC Circuit Phasor Visualizer Online
Animate rotating AC voltage and current phasors in the complex plane. Compute RLC impedance, phase angle, and power factor with synchronized sinusoidal waveforms.
What is an AC Circuit Phasor Diagram?
A phasor diagram is a graphical representation used in electrical engineering to analyze steady-state Alternating Current (AC) circuits. It transforms complex time-varying sinusoidal waveforms into rotating vectors in the complex Cartesian plane, simplifying differential equations into straightforward algebraic vector geometry.
By mapping resistive, inductive, and capacitive voltages onto orthogonal real and imaginary axes, phasors effortlessly resolve phase shifts, power factors, and reactive power imbalances in electric power distribution grids and audio filters.
How to Use the AC Circuit Phasor Visualizer
Model RLC networks and evaluate phase angles in four intuitive steps.
Set Source Voltage & Freq
Adjust AC voltage (V_RMS) and frequency (f) to model mains power (50/60 Hz) or audio frequencies.
Tune RLC Components
Slide Resistance (R), Inductance (L), and Capacitance (C) to modify inductive and capacitive reactances.
Observe Phasor Rotation
Watch the complex vectors rotate counterclockwise at angular velocity ω = 2πf while projecting sine waves.
Hit Resonance
Click 'Tune to Resonance' to align net reactance to zero and verify unity power factor (cos θ = 1.0).
Key Engineering Features
Engineered for electrical engineering students and power systems technicians.
Synchronized Projections
Real-time projection from rotating phasors directly onto time-domain sine waves for voltage and current.
Impedance Triangle
Computes inductive reactance XL, capacitive reactance XC, net impedance Z, and phase angle θ.
Power Quality Metrics
Calculates Real Power (Watts), Reactive Power (VAR), Apparent Power (VA), and power factor.
Governing AC Circuit Equations
In a series RLC circuit excited by an angular frequency \(\omega = 2\pi f\), the inductive and capacitive reactances are:
The net impedance \(Z\) and phase angle \(\theta\) form a right-angled impedance triangle:
The power factor is PF = cos(θ) = R / Z. When XL = XC, the circuit enters electrical resonance at frequency f0 = 1 / (2π√(LC)), where impedance is purely resistive and current reaches its maximum.
Practical Power & RF Applications
Power Grid Power Factor Correction
Industrial factories running large AC induction motors cause highly inductive lagging power factors. Utility companies install automatic capacitor banks to supply leading reactive power (VARs), canceling the inductive reactance and restoring the power factor close to 1.0.
Radio Frequency (RF) Tuners & Crossover Filters
AM/FM radio receivers and audio speaker crossover networks use resonant LC circuits. By tuning the capacitor, the circuit's resonant frequency matches the target radio station, passing that frequency while rejecting adjacent carrier waves.
Frequently Asked Questions
A phasor is a rotating vector in the complex plane whose length represents the peak or RMS amplitude of a sinusoidal quantity (voltage or current) and whose angle relative to the positive horizontal axis represents its phase angle.
In an inductive circuit (XL > XC), current lags behind voltage because an inductor opposes changes in current (CIVIL mnemonic). In a capacitive circuit (XC > XL), current leads voltage because voltage builds up only after charge accumulates.
Electrical resonance occurs at the frequency f0 = 1 / (2π√(LC)) where inductive reactance XL equals capacitive reactance XC. At this point, the net reactance is zero, impedance reaches its minimum value Z = R, and the power factor equals 1.0 (purely resistive).
Real Power (Watts, W) is the actual energy consumed by resistors doing useful work. Reactive Power (Volt-Amps Reactive, VAR) is non-dissipative energy oscillating between magnetic and electric fields in inductors and capacitors. Apparent Power (Volt-Amps, VA) is the vector hypotenuse product of total RMS voltage and current.