Impedance Calculator

Impedance is the total opposition to current flow in an AC (alternating current) circuit. It extends the concept of resistance to include the effects of capacitors and inductors, which store and release energy rather than dissipating it.

The formula for series RLC impedance:

Z = √(R² + (X_L − X_C)²)

Where:

• Z = impedance (in Ohms, Ω)
• R = resistance (in Ohms)
• X_L = inductive reactance = 2πfL (in Ohms)
• X_C = capacitive reactance = 1 / (2πfC) (in Ohms)
• f = frequency (in Hertz)
• L = inductance (in Henrys)
• C = capacitance (in Farads)

Phase angle:

φ = arctan((X_L − X_C) / R)

The phase angle tells you whether the circuit is inductive (positive angle, current lags voltage) or capacitive (negative angle, current leads voltage).

Resonant frequency: When X_L = X_C, the inductive and capacitive reactances cancel each other out, and impedance equals pure resistance. This occurs at the resonant frequency: f₀ = 1 / (2π√(LC)). Resonance is the principle behind radio tuning, filters, and many oscillator circuits.

Complex impedance notation: Engineers often write impedance as a complex number: Z = R + j(X_L − X_C), where j is the imaginary unit. The magnitude is |Z| and the angle is φ.

Practical applications:

• Audio crossover networks use impedance to split frequencies between speakers (woofers, tweeters).
• Radio tuners adjust capacitance to match the resonant frequency of a desired station.
• Power factor correction in industrial settings uses capacitors to offset inductive loads from motors.
• Filter circuits (low-pass, high-pass, band-pass) rely on frequency-dependent impedance.

Tips:

• At DC (frequency = 0), capacitors have infinite reactance (open circuit) and inductors have zero reactance (short circuit).
• At very high frequencies, capacitors approach zero reactance (short circuit) and inductors approach infinite reactance (open circuit).
• Enter 0 for inductance or capacitance if the component is not present in your circuit.