Impedance (RLC Series)
Z = √(R² + (XL − XC)²)
Quick answer
This calculator solves Z = √(R² + (XL - XC)²) for Z. With Resistance 0.47 kΩ, Inductive Reactance 1.03 kΩ, Capacitive Reactance 2.21 kΩ, the result is 1.27 kΩ.
Calculator
Formula
Description
Impedance is the AC equivalent of resistance and represents the total opposition to alternating current in a circuit containing resistance and reactance. It is calculated as the magnitude of the complex impedance vector Z = R + j(XL - XC), where resistance forms the real component and net reactance forms the imaginary component. The Pythagorean relationship arises because resistance and reactance are orthogonal in the phasor domain: resistive voltage is in phase with current while reactive voltage is 90 degrees out of phase. When XL equals XC the circuit is at resonance and impedance equals pure resistance.
Variables
- Z — Impedance magnitude in ohms (Ω)
- R — Resistance in ohms (Ω)
- XL — Inductive reactance in ohms (Ω)
- XC — Capacitive reactance in ohms (Ω)
Practical Notes
The phase angle of impedance is arctan((XL - XC) / R). Positive angles indicate net inductive behavior (current lags voltage), negative angles indicate net capacitive behavior (current leads voltage). Impedance matching is critical in RF design to maximize power transfer.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R | Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| XL | Inductive Reactance | Ω | mΩ, Ω, kΩ, MΩ |
| XC | Capacitive Reactance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Resistance 0.47 kΩ, Inductive Reactance 1.03 kΩ, Capacitive Reactance 2.21 kΩ
- 2. The relation: Z = √(R² + (XL - XC)²)
- 3. Substitute: R = 0.47 kΩ, XL = 1.03 kΩ, XC = 2.21 kΩ
- 4. Result: Z = 1.27 kΩ
Worked examples
Minimum range
Given: Resistance 1 Ω, Inductive Reactance 2.2 Ω, Capacitive Reactance 4.7 Ω
Result: Z = 2.693 Ω
Low range
Given: Resistance 10 Ω, Inductive Reactance 22 Ω, Capacitive Reactance 47 Ω
Result: Z = 26.93 Ω
Typical
Given: Resistance 0.47 kΩ, Inductive Reactance 1.03 kΩ, Capacitive Reactance 2.21 kΩ
Result: Z = 1.27 kΩ
High range
Given: Resistance 4.7 kΩ, Inductive Reactance 10.3 kΩ, Capacitive Reactance 22.1 kΩ
Result: Z = 12.7 kΩ
Maximum range
Given: Resistance 47 kΩ, Inductive Reactance 103 kΩ, Capacitive Reactance 0.221 MΩ
Result: Z = 127 kΩ
How Z changes with Resistance
| Resistance (input) | Z (result) |
|---|---|
| 47 Ω | 1.181 kΩ |
| 117.5 Ω | 1.186 kΩ |
| 0.235 kΩ | 1.203 kΩ |
| 0.3525 kΩ | 1.232 kΩ |
| 0.47 kΩ | 1.27 kΩ |
| 0.705 kΩ | 1.375 kΩ |
| 0.94 kΩ | 1.509 kΩ |
| 1.88 kΩ | 2.22 kΩ |
| 3.29 kΩ | 3.495 kΩ |
| 4.7 kΩ | 4.846 kΩ |
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<p><a href="https://vbatpower.com/formulas/impedance/">Impedance (RLC Series)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Impedance (RLC Series)?
Use Z = √(R² + (XL - XC)²). With Resistance 0.47 kΩ, Inductive Reactance 1.03 kΩ, Capacitive Reactance 2.21 kΩ, Z works out to 1.27 kΩ.
What is the formula for Impedance (RLC Series)?
The formula is Z = √(R² + (XL - XC)²). Impedance is the AC equivalent of resistance and represents the total opposition to alternating current in a circuit containing resistance and reactance.
Related Concepts
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