Series RLC Impedance Calculator
Enter your circuit values to calculate Z, XL, XC and phase angle.
What Is an Impedance Calculator?
An impedance calculator determines the total opposition an AC circuit presents to current. Impedance includes both ordinary resistance and frequency-dependent reactance produced by inductors and capacitors.
This calculator is designed for a series RLC circuit. It uses resistance, inductance, capacitance, and frequency to calculate the impedance magnitude as well as inductive reactance, capacitive reactance, net reactance, and phase angle.
Series RLC Impedance Formula
For a series resistor-inductor-capacitor circuit, impedance depends on resistance and the difference between inductive and capacitive reactance.
XC = 1 / (2πfC)
X = XL - XC
|Z| = √(R² + (XL - XC)²)
Here, R is resistance, XL is inductive reactance, XC is capacitive reactance, and Z is the magnitude of the total series impedance.
How to Use the Impedance Calculator
- Enter the circuit resistance and choose its unit.
- Enter the AC frequency and select Hz, kHz, MHz, or GHz.
- Enter inductance and choose nH, µH, mH, or H.
- Enter capacitance and choose pF, nF, µF, mF, or F.
- Enter zero for L or C if that component is not present.
- Click Calculate Impedance.
The result includes the total impedance magnitude, XL, XC, net reactance, and the circuit phase angle.
Impedance Calculation Example
Consider a series RLC circuit with a resistance of 100 Ω, an inductance of 10 mH, a capacitance of 10 µF, and a frequency of 1 kHz.
XC = 1 / (2π × 1000 × 0.00001) ≈ 15.92 Ω
X = 62.83 - 15.92 ≈ 46.92 Ω
|Z| = √(100² + 46.92²) ≈ 110.46 Ω
Because XL is greater than XC in this example, the circuit has a net inductive reactance and a positive phase angle.
Understanding Resistance, Reactance and Impedance
Resistance
Resistance opposes current and converts electrical energy into other forms such as heat. Ideal resistance does not change with frequency.
Reactance
Reactance is frequency-dependent opposition created by inductors and capacitors. It can be inductive or capacitive.
Impedance
Impedance combines resistance and reactance and describes the overall opposition of an AC circuit to current.
Inductive and Capacitive Circuits
Net Inductive
When XL is greater than XC, net reactance is positive and the circuit behaves inductively.
Net Capacitive
When XC is greater than XL, net reactance is negative and the circuit behaves capacitively.
Resonance
When XL equals XC, their reactances cancel in an ideal series RLC circuit and impedance is equal to resistance.
Phase Angle Formula
The phase angle describes the relationship between voltage and current in the series AC circuit.
A positive phase angle indicates net inductive behavior, while a negative phase angle indicates net capacitive behavior. A phase angle near zero indicates a mainly resistive or resonant condition.
Common Units Used in Impedance Calculations
| Quantity | Common Units |
|---|---|
| Resistance / Impedance | mΩ, Ω, kΩ, MΩ |
| Frequency | Hz, kHz, MHz, GHz |
| Inductance | nH, µH, mH, H |
| Capacitance | pF, nF, µF, mF, F |
| Phase Angle | Degrees (°) |
Frequently Asked Questions
What is impedance?
Impedance is the total opposition a circuit presents to alternating current. It combines resistance with inductive and capacitive reactance and is measured in ohms.
What is the impedance formula for a series RLC circuit?
The magnitude of series RLC impedance is Z = √(R² + (XL − XC)²), where XL is inductive reactance and XC is capacitive reactance.
What unit is impedance measured in?
Impedance is measured in ohms (Ω), the same unit used for resistance and reactance.
What happens when XL equals XC?
When inductive and capacitive reactance are equal, they cancel each other in an ideal series RLC circuit. The circuit is at resonance and the impedance magnitude equals its resistance.
Can I calculate an RL circuit with this tool?
Yes. Set capacitance to zero and the calculator will treat capacitive reactance as zero, allowing an RL impedance calculation.
Can I calculate an RC circuit?
Yes. Set inductance to zero and the calculator will calculate the impedance using resistance and capacitive reactance.