Calculation
Z = √(R² + (2π·f·L)²)
With no capacitor, impedance follows from the geometric sum of resistance and inductive reactance.
Busch 2006, Abschnitt 5.8.1 Komplexer Widerstand (Beispiel R = 10 Ω, L = 64 mH, 50 Hz → Z = 22,4 Ω)
RL series circuit impedance
With no capacitor, impedance follows from the geometric sum of resistance and inductive reactance.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Impedance Z — Magnitude of the complex AC impedance of the series circuit.
- Resistance R — Resistive part, e.g. choke or motor-winding resistance.
- Inductance L — Effective inductance at the considered frequency without saturation.
- Frequency f — Frequency of the sinusoidal AC supply.
Example
R=10 Ω, L=50 mH and f=50 Hz give XL≈15.71 Ω and Z≈18.62 Ω.
Assumptions and limits
Linear ideal components in sinusoidal steady state with no capacitance in the branch; skin effect, core loss and saturation are excluded.
Understand RL series circuit impedance
This calculator determines the impedance of a series resistor-inductor circuit with no capacitor, the most common practical case of a choke or motor winding on an AC supply.
What does this quantity describe?
For a series R-L circuit, resistance and reactance add geometrically: Z=√(R²+XL²) with XL=2π·f·L.
Formula and variables
Z = √(R² + (2π·f·L)²)
Z = √(R² + (2π·f·L)²)XL = 2π·f·L
| Symbol / input | Meaning |
|---|---|
| Impedance Z | Magnitude of the complex AC impedance of the series circuit. |
| Resistance R | Resistive part, e.g. choke or motor-winding resistance. |
| Inductance L | Effective inductance at the considered frequency without saturation. |
| Frequency f | Frequency of the sinusoidal AC supply. |
Choose the inputs correctly
R is the resistive winding resistance, L the effective inductance and f the mains or operating frequency.
How to use the calculator
Take R from a DC measurement, L from a datasheet or bridge measurement, and use the actual operating frequency.
Worked example
R=10 Ω, L=50 mH and f=50 Hz give XL≈15.71 Ω and Z≈18.62 Ω.
Understand the result and units
At low frequencies R dominates; at high frequencies XL dominates impedance.
R and Z are resistances, L an inductance and f a frequency.
Typical applications
Estimating inrush current of chokes and motor windings on AC supply, and a preliminary step before a full RLC calculation when no capacitor is present.
Assumptions, limits and common mistakes
Linear ideal components in sinusoidal steady state with no capacitance in the branch; skin effect, core loss, saturation and harmonics are excluded.
Common mistake: Do not misuse the existing RLC calculator with C=0; this calculator is more direct and clear for the pure RL case.
Frequently asked questions
What is “RL series circuit impedance” used for?
Estimating inrush current of chokes and motor windings on AC supply, and a preliminary step before a full RLC calculation when no capacitor is present.
Where do the input values come from?
R is the resistive winding resistance, L the effective inductance and f the mains or operating frequency.
What does the result not cover?
Linear ideal components in sinusoidal steady state with no capacitance in the branch; skin effect, core loss, saturation and harmonics are excluded.