Impedance Builder

Build any series RLC combination and see its impedance take shape on the complex plane as you tune each value. Readouts for $X_L$ , $X_C$ , $|Z|$ , and the phase angle $\\varphi$ update live. Add a source voltage to see the current magnitude and whether it leads or lags the supply.

Resistance R (Ω)100 Ω

Inductance L (mH)10.0 mH

Capacitance C (µF)1.00 µF

Frequency f (Hz)1.00 kHz

Source V_s (V_rms)10.0 V

X_L

62.83 Ω

X_C

159.15 Ω

|Z|

138.85 Ω

φ (V_s vs I)

-43.9°

Source → current

I = V_s / |Z|=10.0 / 138.85=72.02 mA

Current leads / lags the source voltage by 43.9° (leads)

Resonance at f₀ = 1.59 kHz

Quick experiments

Find resonance. Keep L = 10 mH and C = 1 µF — the readout shows f₀ just under 1.6 kHz. Move the frequency slider onto that value and the triangle flattens to the real axis.
Sweep through resonance. From 500 Hz upward, the triangle flips from net capacitive (points down) to net inductive (points up) as you cross f₀ ≈ 1.59 kHz.
Pure element limits. Set L and C to zero-ish for a pure resistive line; crank up L with a tiny C for a near-inductive load; swap for a near-capacitive load. The triangle swings through every orientation.
Build the classic 3-4-5 triangle. Set R = 30 Ω and X = 40 Ω. The magnitude is exactly 50 Ω at an angle of 53.1°. It is the right triangle from school, drawn in the complex plane.
Confirm the 45° rule. Make X equal R. Whatever the value, the angle is exactly 45° and the magnitude is R√2. With R = X = 100 Ω the impedance is 141 Ω.
Read power factor straight off the angle. Power factor is cos φ. At 53.1° that is 0.6, meaning only 60 % of apparent power does useful work — the number utilities charge for.

Complex impedance

Impedance Z extends resistance to AC circuits by including reactance: Z = R + jX, where R is resistance and X is reactance (positive for inductors, negative for capacitors). The magnitude |Z| = √(R² + X²) gives the peak voltage-to-current ratio; the phase angle θ = arctan(X/R) gives the phase shift between them.

Series vs parallel combinations

Series: Z_total = Z₁ + Z₂ (add complex numbers directly)
Parallel: 1/Z_total = 1/Z₁ + 1/Z₂ (or use admittance Y = 1/Z)

Series RLC resonance

Z = R + j(ωL − 1/ωC). At resonance ω₀ = 1/√(LC), the imaginary parts cancel and Z = R — minimum impedance, maximum current. Q = ω₀L/R measures sharpness; bandwidth BW = f₀/Q.

Learn more → Impedance — Learn

Formula reference

Impedance in rectangular form: $Z = R + jX$
R is the real (dissipative) part; X is the imaginary (energy-storing) part.
Magnitude: $|Z| = \sqrt{R^2 + X^2}$
R = 30 Ω, X = 40 Ω → |Z| = 50 Ω.
Phase angle: $\phi = \arctan\!\left(\frac{X}{R}\right)$
Positive is inductive (current lags), negative is capacitive (current leads).
Power factor: $PF = \cos\phi = \frac{R}{|Z|}$
Unity only when X = 0.

Symbol	Meaning	Unit
$Z$	Complex impedance	Ω
$R$	Resistance, the real part	Ω
$X$	Net reactance, the imaginary part	Ω
$\phi$	Phase angle of voltage relative to current	°

Common mistakes

Adding impedance magnitudes in series.
Add the real parts and the imaginary parts separately, then take the magnitude. 50 Ω at 53° in series with 50 Ω at −53° totals 60 Ω, not 100 Ω, because the reactances cancel.
Dropping the sign of the reactance.
The sign is what distinguishes inductive from capacitive. Treat −j40 as +j40 and a circuit that should cancel to resistive instead doubles its reactance.
Believing high impedance always means low current.
Current is V/|Z| at the frequency of interest. Impedance varies with frequency, so a network that looks high-impedance at 1 kHz may be near a short at 1 MHz.
Confusing impedance matching with equal resistance.
Maximum power transfer needs the complex conjugate: the load must be R − jX to match a source of R + jX. Matching magnitudes alone leaves reactive power sloshing back and forth.
Using the phase angle without stating the reference.
By convention φ is the angle of voltage relative to current. Reverse the reference and every sign flips, turning inductive results into capacitive ones.

Frequently asked questions

What is the difference between impedance and resistance?

Resistance opposes current and dissipates power, and it does not change with frequency. Impedance is the total opposition in an AC circuit, combining resistance with reactance, so it has both a magnitude and a phase angle and it does vary with frequency.

How do I calculate the magnitude of impedance?

For a series R and X, the magnitude is the square root of R squared plus X squared, and the phase angle is the arctangent of X over R. With R = 30 ohms and X = 40 ohms the magnitude is 50 ohms at an angle of about 53 degrees.

What does a positive or negative impedance angle mean?

A positive angle means the circuit is inductive and current lags voltage. A negative angle means it is capacitive and current leads voltage. An angle of zero means the reactances have cancelled and the circuit looks purely resistive.

What happens to impedance at resonance?

At resonance the inductive and capacitive reactances are equal and cancel. A series RLC circuit falls to its minimum impedance, just the resistance, while a parallel RLC circuit rises to its maximum impedance.