Impedance is the complex opposition to alternating current, equal to the phasor ratio of voltage to current. Its magnitude combines resistance and net reactance, and its argument is the phase angle between voltage and current.
Learning objectives
- Calculate impedance magnitude and phase from resistance and reactance
- Apply I = V/Z to a series AC circuit
- Distinguish impedance, resistance and reactance
- Explain resonance in terms of impedance
- Measure impedance correctly with an appropriate instrument
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
Impedance is not simply R + XL + XC arithmetically because the parts are not in step. They add as vectors: resistance is the horizontal component and net reactance the vertical component.
Intermediate How it behaves in a circuit
Parallel impedances combine as 1/Z = 1/Z1 + 1/Z2 + …, which is often easier with admittances Y = 1/Z.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Impedance | Z | ohm (Ω) |
| Resistance | R | ohm (Ω) |
| Reactance | X | ohm (Ω) |
| Phase angle | φ | degree (°) |
Worked examples
Series R–L circuit
Problem. A coil with R = 30 Ω and XL = 40 Ω is connected to 230 V RMS. Find the impedance, current and phase angle.
Solution. Z = √(30² + 40²) = √2500 = 50 Ω. I = 230/50 = 4.6 A. φ = arctan(40/30) = 53.1°.
Series R–C circuit
Problem. A circuit has R = 8 Ω and XC = 6 Ω. It is supplied with 12 V RMS. Find Z, I and the phase angle.
Solution. Z = √(8² + 6²) = √100 = 10 Ω. I = 12/10 = 1.2 A. φ = arctan(−6/8) = −36.9°.
Resonant frequency
Problem. A series circuit has L = 100 mH and C = 100 µF. At what frequency does the net reactance become zero?
Solution. f0 = 1/(2π√(LC)) = 1/(2π√(0.100 × 0.000100)).
Practical applications
- Cable and source impedance in fault calculations
- Loudspeaker and audio system matching
- Filter and antenna design
- Motor and transformer equivalent circuits
- Protection and relay settings
- Electromagnetic compatibility analysis
Automotive applications
Sensor inputs and communication buses have characteristic impedances that must be respected to avoid reflections and noise. Audio systems use impedance matching between amplifiers and speakers, and high-voltage EV cables and connectors are specified with impedance and shielding requirements for EMC.
Industrial applications
Fault-loop impedance determines the prospective short-circuit current and therefore the disconnection time of protective devices. Variable-frequency drives, line reactors and power-factor correction all rely on impedance calculations, and impedance is central to protection coordination studies.
Measurement procedure
- Use an LCR meter or impedance analyser at the frequency of interest.
- Measure voltage and current together and calculate Z = V/I, adding a phase measurement for the angle.
- Use four-wire measurement for low impedances to remove lead resistance.
- Keep test leads short and consistent, and discharge reactive components before connecting.
Common mistakes
- Adding resistance and reactance arithmetically instead of as vectors.
- Ignoring the phase angle and treating impedance as a scalar resistance in every context.
- Using the DC resistance of a winding as its AC impedance.
- Assuming impedance is constant with frequency or with temperature.
Safety considerations
- Low impedance means high fault current; verify protective device ratings before working on such circuits.
- Reactive equipment can retain energy after isolation; discharge and verify before touching.
- High-frequency and high-power circuits can cause RF burns and arcs; use rated probes and keep clear.