AC circuits – phase difference and power factor (cos φ)
Design & TechnologyElectrical Engineering & SafetyAges 17–18Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Electrical Engineering & Safety
An AC source u = U√2·sin(ωt) supplies a purely resistive load, an R–L load (motor, ballast), an R–C load, or a series R–L–C load. Real-time graphs of u(t) and i(t) show the current lagging the voltage in an inductive load and leading it in a capacitive load, while the phasor diagram alongside plots U_R, U_L, U_C and the phase angle φ. Drag the R, L, C sliders to see the impedance Z, power factor cos φ and real power P = UIcos φ change, including at resonance. An Oscilloscope screen measures peak, peak-to-peak, period and frequency from the trace, and an Equal heating screen compares V_rms = V₀/√2 with a DC supply that heats a resistor at the same rate.
Lesson: Introduction to alternating current: RMS value, frequency, phase angle, impedance, power and power factor
What it shows
In an AC circuit, voltage and current are both sinusoidal but not always in step. A resistor keeps them in phase; an inductor, with reactance X_L = 2πfL, makes the current lag the voltage; a capacitor, with reactance X_C = 1/(2πfC), makes it lead. In a series circuit the impedance is Z = √(R² + (X_L − X_C)²) and tan φ = (X_L − X_C)/R. Only part of the apparent power S = UI does useful work: the real power is P = UI cos φ. A low power factor needs a larger current for the same power, so inductive loads such as motors are compensated with capacitors. For a sine wave of peak V₀ the RMS value is V₀/√2: the DC voltage that heats a resistor at the same rate. An oscilloscope shows the peak and the period as divisions on a grid.
How to use
Choose a Load type and compare the u(t) and i(t) graphs with the phasor diagram; press Pause to line up the peaks. With the R–L load, increase Inductance L and watch the phase angle grow and cos φ fall. Then select the series R–L–C load and adjust Capacitance C or Frequency f until X_L equals X_C: the current reaches its maximum, φ becomes zero and cos φ reaches 1. Compare P, Q and S in the readout each time. On Oscilloscope, choose a Signal, set Y-gain and Time base so the trace fits the screen, read the height and one period in divisions and press Check. On Equal heating, set the two voltages, press Switch on and compare the temperature rises.
Parameters you can change
- Load type Purely resistive load R (stove, incandescent lamp), R–L load (motor, ballast), R–C load (compensating capacitor), Series R–L–C load
- RMS voltage U 100–380 V
- Frequency f 40–70 Hz
- Resistance R 10–200 Ω
- Inductance L 20–500 mH
- Capacitance C 10–300 µF
- Screen Circuit, Oscilloscope, Equal heating
Questions to explore
- For the R–L load, does the current lead or lag the voltage, and how does φ change as L increases?
- How do X_L and X_C change when the frequency is raised from 40 Hz to 70 Hz?
- What value of C makes the series R–L–C circuit resonate, and what happens to I and cos φ?
- What are the peak, peak-to-peak value, period and frequency of Unknown signal A?
- With an AC peak of 12 V, what DC voltage gives the same temperature rise, and how does it compare with V₀/√2?
