Impedance Formula
Calculate the total opposition to current flow in AC circuits.
Combines resistance, capacitance, and inductance effects.
The Formula
Z = √(R² + (X_L - X_C)²)
Impedance is the total opposition to alternating current (AC) in a circuit. It combines resistance (R) with reactance from inductors (X_L) and capacitors (X_C).
Variables
| Symbol | Meaning |
|---|---|
| Z | Impedance (Ohms, Ω) |
| R | Resistance (Ohms) |
| X_L | Inductive reactance = 2πfL (Ohms) |
| X_C | Capacitive reactance = 1/(2πfC) (Ohms) |
Example 1
R = 30 Ω, X_L = 50 Ω, X_C = 10 Ω
Z = √(30² + (50 - 10)²)
Z = √(900 + 1600)
Z = √2500 = 50 Ω
Example 2
R = 100 Ω, X_L = 80 Ω, X_C = 80 Ω (resonance)
Z = √(100² + (80 - 80)²) = √(10000 + 0)
Z = 100 Ω (at resonance, impedance equals pure resistance)
When to Use It
Use the impedance formula when:
- Analyzing AC circuits with resistors, capacitors, and inductors
- Calculating current flow in AC power systems
- Designing audio equipment and radio frequency circuits
- Matching impedance between source and load for maximum power transfer