Electrical Impedance (Z

Electrical Engineering: AC Impedance, Reactance & Resonance

In alternating current (AC) circuits, resistance is generalized to complex Impedance (Z), combining ohmic resistance with frequency-dependent reactances:

• Inductors vs. Capacitors:

• Inductive Reactance): Directly proportional to frequency. At high frequencies, inductors act as open circuits, resisting rapid current changes.

• Capacitive Reactance): Inversely proportional to frequency. At low frequencies, capacitors block DC steady-state current.

• Electrical Resonance (f_0): When the inductive and capacitive reactive energies cancel each other out completely), collapsing series impedance to pure resistance) and maximizing current transfer (the operating principle of radio receivers and wireless power transmitters).

• Power Factor (θ): Measures how effectively electrical power is converted into useful work. Low power factors (due to large industrial motor inductive loads) require power factor correction capacitor banks.

How to Use This Calculator

Enter your RLC Circuit Topology — choose from Series RLC Circuit (Z = √(R² + (X_L - X_C)²)), Parallel RLC Circuit (1/Z = √(1/R² + (1/X_L - 1/X_C)²)), AC Signal Frequency (f in Hz) (e.g. 60 (US grid 60Hz / EU grid 50Hz)), Resistance (R in Ohms Ω) (e.g. 50), Inductance (L in millihenries mH) (e.g. 150 (1 mH = 10⁻³ H)), Capacitance (C in microfarads μF) (e.g. 47 (1 μF = 10⁻⁶ F)), and Applied AC Voltage (V_rms in Volts) (e.g. 120 (RMS Voltage)). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

AC Circuit Electrical Impedance \& RLC equations:

ω = 2 π f

X_L = ω L = 2 π f L, X_C = (1) / (ω C) = (1) / (2 π f C)

Series RLC Impedance: Z = √(R^2 + (X_L - X_C)^2), θ = ((X_L - X_C) / (R))

Parallel RLC Impedance: (1) / (Z) = √(((1) / (R))^2 + ((1) / (X_L) - (1) / (X_C))^2)

Resonant Frequency: f_0 = (1) / (2 π √(L C))

AC RMS Current: I_rms = V_rmsZ, Power Factor = (θ) = (R) / (Z)

Worked Example

For example, analyzing a series RLC circuit connected to a 120V, 60 Hz AC source with \ (0.15 H), and \ (4.7 × 10^-5 F): Inductive reactance is 0.15) = 56.55 Ω. Capacitive reactance is 4.7 × 10^-5) = 56.44 Ω. Net reactance is . Total impedance is . Resonant frequency is . Because 60 Hz ≈ f_0, the circuit is in near-perfect resonance with a unity Power Factor of 1.000 drawing .

Understanding Your Result

Industry average CTR benchmarks: Google Search ads average 2–5%; Display ads 0.1–0.3%. Organic search position 1 averages 27–35% CTR; position 10 averages 1–2%. Email CTR benchmarks: industry average 2–5%, excellent 5%+. For social media, LinkedIn average post CTR is 0.2–0.5%, Facebook 0.5–1.0%. CTR below benchmark typically indicates weak headlines, poor audience targeting, or ad fatigue — A/B test subject lines or headlines before adjusting bids.