AC Impedance Calculator: Series and Parallel RLC Circuits
The Impedance Calculator computes total impedance (Z) in ohms for AC circuits containing resistance (R), inductance (L), and capacitance (C). Impedance is the complex opposition to current flow, combining resistance and reactance.
Impedance Formula
Z = R + j(X_L - X_C)
Magnitude: |Z| = √(R² + (X_L - X_C)²)
Phase: θ = tan⁻¹((X_L - X_C)/R)
Reactance Formulas
X_L = 2πfL (inductive)
X_C = 1/(2πfC) (capacitive)
Series RLC
Z_series = R + j(2πfL - 1/(2πfC))
Reactances add algebraically.
Parallel RLC
1/Z_parallel = 1/R + 1/(j2πfL) + j2πfC
Admittances add (Y = 1/Z).
Key Values Table
| Component | Symbol | Unit | Formula |
|---|---|---|---|
| Resistance | R | Ω | — |
| Inductive Reactance | X_L | Ω | 2πfL |
| Capacitive Reactance | X_C | Ω | 1/(2πfC) |
| Impedance | Z | Ω | √(R² + X²) |
Examples
- R=10Ω, L=50mH, C=100μF, f=60Hz (series) → Z ≈ 12.1Ω
- R=100Ω, L=0, C=10μF, f=50Hz (parallel) → Z ≈ 318Ω
Applications
- Power factor correction
- Filter design
- Motor circuits
- Audio crossovers
Resonance
At resonance, X_L = X_C → Z = R (minimum in series, maximum in parallel).
f_res = 1/(2π√(LC))
Conclusion
Accurate impedance calculation ensures proper circuit performance. Use with Reactance and Resonance tools.