Impedance
The key idea
Impedance (Z) is how hard a circuit pushes back against AC current. It has two parts: resistance (R), which turns current into heat, and reactance (X), which pushes back without losing anything. They combine at a right angle, not by simple addition.
The idea
In a DC circuit, only resistance opposes current. In an AC circuit there is a second opponent.
Resistance, R (ohms). The friction of the conductor itself. Current through resistance loses energy as heat — this is where network losses come from.
Reactance, X (ohms). The push-back from magnetic and electric fields. A transformer winding or a long line builds a magnetic field as current rises, and that field resists the change. No energy is lost — the field gives it back every half cycle — but the current is opposed and delayed all the same.
The two do not add directly, because their pushes are a quarter-cycle apart in time. They add like the two short sides of a right triangle: Z = √(R² + X²). A circuit with R = 3 Ω and X = 4 Ω has an impedance of 5 Ω, not 7 Ω.
Try it
R and X do not add directly — they add at a right angle. A circuit with R = 3 Ω and X = 4 Ω has Z = 5 Ω, not 7 Ω. Grab the corner and drag it around to feel how Z and the angle respond. Cables are mostly R. Transformers and long overhead lines are mostly X.
Why it matters
- Every branch in a network model is, at its core, an impedance. A missing or zero impedance is the most common reason a power flow fails to converge.
- Impedance sets the fault current. A short circuit is the network voltage driving current through nothing but the impedance on the way to the fault. Less impedance, more fault current.
- The X/R ratio shapes the fault's first moments. A fault fed through mostly reactance (high X/R — near transformers and generators) carries a large DC offset, which raises the peak current that switchgear must survive mechanically. That is why the widget shows X/R.
- Character differs by equipment. Cables are mostly R. Transformers and overhead lines are mostly X. This is why the same load produces different voltage drops on different feeders.
The math, if you want itOptional — the page reads completely without it
Impedance is a complex number, colored here to match the triangle above:
impedance
Z = R + jX
magnitude and angle
|Z| = √( R² + X² ) · φ = tan⁻¹ XR
Inductive reactance grows with frequency, XL = 2πfL; capacitive reactance shrinks with it, XC = 1/(2πfC). Ohm's law keeps its familiar shape with phasors —
Ohm's law
V = Z · I
— and the current lags the voltage by the impedance angle φ.
See it in Phasor
Every line, cable and transformer you place in Phasor carries its impedance data — R, X, and the sequence values fault studies need. The short circuit study reports the X/R ratio and the peak-current factor κ at every fault location.