Power Demo — AC Real, Reactive, and Apparent Power

How this works

An AC source drives a load: v(t) = V_m·cos(2πft) and i(t) = (V_m/R)·cos(2πft − θ), with θ = φ_V − φ_I.

Reactive loads are simulated by phase-shifting the current — its magnitude stays V_m/R, so you can see what phase alone does to power without computing complex impedance. Every power quantity uses RMS values: V_rms = V_m/√2.

ELI the ICEman: E leads I in an inductor (ELI); I leads E in a capacitor (ICE) — E is the old notation for voltage (EMF).

Source & Load

Peak voltage V_m 17.0 V

1 V20 V

Resistance R 10.0 Ω

1 Ω20 Ω

Frequency f 60 Hz

10 Hz100 Hz

Phase difference θ = φ_V − φ_I 0°

−90° (leading)+90° (lagging)

Things to try

With θ = 0°, write out v(t) and i(t) from the current slider values, then check the plots match your equations.
Will p(t) ever be negative while θ = 0°? Now drag θ away from zero — a negative lobe appears. What is the circuit doing with that energy?
Watch P and S while you drag θ: which one moves? Why do you pay for watts but size hardware for volt-amperes?
Set θ = +60°: confirm pf = 0.50 and P = S·pf on the readouts, and that S² = P² + Q².
Which way does the triangle flip for a capacitive load? Match the pill's ELI/ICE mnemonic to which waveform peaks first.
At θ = ±90°, where did the real power go? What kind of load is this?

Voltage & Current v(t) [V] · i(t) [A]

Instantaneous Power p(t) = v(t)·i(t)

Power Triangle P Q S

Power Factor pf = cos θ = P/S

1.00

θ = 0°

V_rms—

I_rms—

S—

P—

Q—

pf—

θ—

Unity — resistive