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Lesson 5 of 6 · 18 minutes · Free

AC Impedance & Phase

Distinguish RMS magnitude from phase, and explain capacitive current lead.

Try the experiment ↓Practice challenge ↓

See the idea

In sinusoidal steady state, a capacitor contributes reactance XC = 1/(2πfC). In a series RC circuit, impedance magnitude is √(R² + XC²). Increasing frequency reduces capacitive reactance.

Current leads the source voltage in this capacitive circuit. The lead angle equals atan(XC/R); it approaches 90° when capacitive reactance dominates and 0° when resistance dominates.

The meters use RMS values. The waveform plot normalizes each trace to its own peak so the phase relationship is easy to see; equal plot heights do not mean voltage and current have equal numerical magnitudes.

XC = 1/(2πfC) |Z| = √(R² + XC²) Irms = Vrms/|Z|

Reactance depends on frequency. Current magnitude and phase both matter.

Work through an example

  1. At 12 V RMS, 50 Hz, R = 1,000 Ω and C = 1 µF: XC ≈ 3,183 Ω.
  2. Impedance magnitude is about 3,336 Ω, giving current ≈ 3.60 mA RMS.
  3. Current leads the supply voltage by about 72.6°. Raising frequency to 500 Hz reduces the lead to about 17.7°.

Watch for this

Do not substitute RMS directly into a peak-voltage equation: a sine wave’s peak is √2 times its RMS value.

Predict, then test

  1. Begin at 50 Hz and compare the current crest with the voltage crest.
  2. Increase frequency to 500 Hz. Watch current rise and its lead angle decrease.

Your virtual bench

Change a setting. See the circuit respond.

Swipe the diagram sideways to explore the connections.

∿12 V RMSR1 1000 ΩC 1 µFReturn reference: 0 V
Current RMS3.597 mA
Current leads by72.559 °
Impedance |Z|3,336.483 Ω
Real power in R0.013 W
0720° (two cycles)+1−1

Indigo: source voltage · Rose: current. Both normalized to their own peak; horizontal axis is phase, not seconds.

Model: Ideal sinusoidal steady-state series RC circuit; RMS meters, no startup transient. Values are calculated, not equipment measurements. Browser simulation only—do not connect live equipment.

Check your understanding

In this series RC circuit, increasing frequency makes capacitive reactance:

Put it to work

At 12 V RMS, 500 Hz, 1,000 Ω and 1 µF, estimate current and phase lead.

Show the worked solution

XC ≈ 318.3 Ω; |Z| ≈ 1,049.4 Ω; Irms ≈ 11.43 mA. Current leads by about 17.7°.

Try the experiment and answer the check, then record your completion.

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