AC Impedance Calculator Formula
Understand the math behind the ac impedance calculator. Each variable explained with a worked example.
Formulas Used
Impedance (Z)
impedance = sqrt(pow(resistance, 2) + pow(inductive_reactance - capacitive_reactance, 2))Phase Angle
phase_angle = atan((inductive_reactance - capacitive_reactance) / resistance) * 180 / piVariables
| Variable | Description | Default |
|---|---|---|
resistance | Resistance (R)(Ω) | 100 |
inductive_reactance | Inductive Reactance (XL)(Ω) | 150 |
capacitive_reactance | Capacitive Reactance (XC)(Ω) | 80 |
How It Works
AC Impedance
Impedance is the total opposition to current flow in an AC circuit, including both resistance and reactance.
Formula
Z = sqrt(R² + (XL - XC)²)
where XL = 2*pi*f*L is inductive reactance and XC = 1/(2*pi*f*C) is capacitive reactance. The phase angle is phi = arctan((XL - XC) / R).
Worked Example
A series RLC circuit with R = 100 Ω, XL = 150 Ω, XC = 80 Ω.
- 01Z = sqrt(R² + (XL - XC)²)
- 02Z = sqrt(100² + (150 - 80)²)
- 03Z = sqrt(10000 + 4900)
- 04Z = sqrt(14900) = 122.07 Ω
- 05phi = arctan(70/100) = 34.99°
Frequently Asked Questions
What is the difference between resistance and impedance?
Resistance opposes DC and AC equally. Impedance is the AC equivalent that includes reactance from capacitors and inductors, causing phase shifts.
When is impedance minimized?
When XL = XC (resonance). At resonance, impedance equals pure resistance R, and the circuit passes maximum current.
What does the phase angle mean?
It indicates the time difference between voltage and current peaks. Positive phase means current lags voltage (inductive); negative means current leads (capacitive).
Ready to run the numbers?
Open AC Impedance Calculator