AC Impedance and Phase Angle Calculator (Series and Parallel RLC)

What is impedance?

Impedance (Z) is the total opposition a circuit presents to alternating current. A resistor drops voltage in phase with the current. An inductor or capacitor stores energy and returns it, so its voltage is shifted 90 degrees from the current. Reactance measures the size of that effect:

• Inductive reactance: X_L = 2π × f × L (rises with frequency)
• Capacitive reactance: X_C = 1 / (2π × f × C) (falls with frequency)

Series circuit

For R, L and C in series, Z = √(R² + (X_L − X_C)²) and φ = arctan((X_L − X_C) / R). If X_L is larger the circuit is inductive and the current lags the voltage. If X_C is larger the circuit is capacitive and the current leads.

Parallel circuit

In parallel the admittances add: Y = √((1/R)² + (1/X_C − 1/X_L)²) and Z = 1 / Y. Here the branch with the smaller reactance takes more current, so the circuit is inductive when X_L is the smaller one.

Example

Take a 40 Ω resistor, a 40 mH inductor and a 100 µF capacitor in series at an angular frequency of 1000 rad/s. X_L = 1000 × 0.04 = 40 Ω and X_C = 1 / (1000 × 0.0001) = 10 Ω. The net reactance is 30 Ω, the impedance is √(40² + 30²) = 50 Ω, the phase angle is 36.87 degrees and the power factor is 0.8. With 100 V applied the current is 2 A, the active power 160 W, the reactive power 120 var and the apparent power 200 VA.

Powers

Active power (P) is dissipated only in the resistance. Reactive power (Q) flows back and forth between the source and the inductor or capacitor. Apparent power (S) is their vector sum: S² = P² + Q². The power factor is cos φ = P / S.

Limits

The tool is for steady state circuits with ideal components and a single frequency sine source. It does not solve mixed connections other than pure series or pure parallel in one step. For resonant frequency, quality factor and bandwidth use the RLC resonance calculator.