Complex Impedance Magnitude (RLC)
|Z| = √(R² + (ωL − 1/(ωC))²)
Quick answer
This calculator solves |Z| = √(R² + (ωL − 1/(ωC))²) for Impedance Magnitude. With Resistance 1.03 kΩ, Frequency 1 kHz, Inductance 10 mH, Capacitance 100 µF, the result is 1.032 kΩ.
Calculator
Formula
Description
The magnitude of the impedance of a series RLC circuit combines resistance with the net reactance. Inductive reactance XL = ωL increases with frequency, while capacitive reactance XC = 1/(ωC) decreases. At resonance, XL = XC and the impedance equals R alone (minimum impedance). Below resonance the circuit is capacitive; above resonance it is inductive. This formula is essential for understanding filter behavior, resonant circuits, and the frequency-dependent impedance of any circuit containing R, L, and C elements.
Variables
- |Z| — Impedance magnitude (Ω)
- R — Resistance (Ω)
- f — Frequency (Hz)
- L — Inductance (H)
- C — Capacitance (F)
Practical Notes
At resonance, f₀ = 1/(2π√(LC)), the impedance is purely resistive and equal to R. The quality factor Q = (1/R)√(L/C) determines the sharpness of the resonance. High-Q circuits (low R) have narrow bandwidth and high selectivity. For parallel RLC circuits, the impedance is maximum at resonance.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Z | Impedance Magnitude | Ω | mΩ, Ω, kΩ, MΩ |
| R | Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| f | Frequency | Hz | Hz, kHz, MHz, GHz |
| L | Inductance | mH | nH, µH, mH, H |
| C | Capacitance | µF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Resistance 1.03 kΩ, Frequency 1 kHz, Inductance 10 mH, Capacitance 100 µF
- 2. The relation: |Z| = √(R² + (ωL − 1/(ωC))²)
- 3. Substitute: R = 1.03 kΩ, f = 1 kHz, L = 10 mH, C = 100 µF
- 4. Result: Impedance Magnitude = 1.032 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 1 kΩ | 3.1% |
| E24 | 1 kΩ | 3.1% |
Worked examples
Minimum range
Given: Resistance 2.2 Ω, Frequency 5 Hz, Inductance 100 µH, Capacitance 100 nF
Result: Impedance Magnitude = 0.3183 MΩ
Low range
Given: Resistance 22 Ω, Frequency 50 Hz, Inductance 1 mH, Capacitance 1 µF
Result: Impedance Magnitude = 3.183 kΩ
Typical
Given: Resistance 1.03 kΩ, Frequency 1 kHz, Inductance 10 mH, Capacitance 100 µF
Result: Impedance Magnitude = 1.032 kΩ
High range
Given: Resistance 10.3 kΩ, Frequency 20 kHz, Inductance 100 mH, Capacitance 1 mF
Result: Impedance Magnitude = 16.25 kΩ
Maximum range
Given: Resistance 103 kΩ, Frequency 0.2 MHz, Inductance 1 H, Capacitance 10 mF
Result: Impedance Magnitude = 1.261 MΩ
How Impedance Magnitude changes with Resistance
| Resistance (input) | Impedance Magnitude (result) |
|---|---|
| 0.227 kΩ | 0.377 kΩ |
| 0.5675 kΩ | 0.6424 kΩ |
| 1.135 kΩ | 1.174 kΩ |
| 1.703 kΩ | 1.729 kΩ |
| 2.27 kΩ | 2.29 kΩ |
| 3.405 kΩ | 3.418 kΩ |
| 4.54 kΩ | 4.55 kΩ |
| 9.08 kΩ | 9.085 kΩ |
| 15.89 kΩ | 15.89 kΩ |
| 22.7 kΩ | 22.7 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 1032000 |
| Ω | 1032 |
| kΩ | 1.032 |
| MΩ | 0.001032 |
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<p><a href="https://vbatpower.com/formulas/complex-impedance-mag/">Complex Impedance Magnitude (RLC)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Complex Impedance Magnitude (RLC)?
Use |Z| = √(R² + (ωL − 1/(ωC))²). With Resistance 1.03 kΩ, Frequency 1 kHz, Inductance 10 mH, Capacitance 100 µF, Impedance Magnitude works out to 1.032 kΩ.
What is the formula for Complex Impedance Magnitude (RLC)?
The formula is |Z| = √(R² + (ωL − 1/(ωC))²). The magnitude of the impedance of a series RLC circuit combines resistance with the net reactance.
What units does Complex Impedance Magnitude (RLC) use?
Impedance Magnitude is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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