Impedance Calculator

FAQ

How does impedance change with frequency?

In a series RLC circuit the impedance is lowest at the resonant frequency and rises on both sides: below resonance the capacitor dominates, above it the inductor. A parallel RLC circuit is the opposite, with the highest impedance at resonance. The Frequency Sweep table shows the magnitude and phase at frequencies from a hundredth to a hundred times the resonance, so you can see the whole curve from one calculation.

What capacitor do I need for resonance at a given frequency?

Rearrange f = 1/(2π√(LC)) to C = 1/((2πf)²L). Enter your inductor and the target frequency, and the Design Hints list the capacitor (or, from a capacitor, the inductor) that resonates there, plus the cutoff frequency of an RC or RL circuit.

What is impedance in an AC circuit?

Impedance (Z) is the total opposition a circuit presents to alternating current. It combines resistance (R), which opposes current flow, with reactance (X), which arises from inductors and capacitors. Unlike pure resistance, impedance is a complex quantity with both magnitude and phase angle, expressed as Z = R + jX in ohms.

What is the difference between impedance and resistance?

Resistance opposes current equally at all frequencies and dissipates energy as heat. Impedance includes resistance plus reactance from inductors and capacitors, which varies with frequency. Resistance is a real number measured in ohms, while impedance is a complex number with magnitude and phase angle.

How is impedance calculated for a series RLC circuit?

For a series RLC circuit, impedance Z = R + j(X_L − X_C), where X_L = 2πfL is inductive reactance and X_C = 1/(2πfC) is capacitive reactance. The magnitude is |Z| = √(R² + (X_L − X_C)²) and phase angle is θ = arctan((X_L − X_C)/R).

What happens at the resonant frequency of an RLC circuit?

At resonance, inductive reactance equals capacitive reactance (X_L = X_C), so they cancel out. In a series RLC circuit, impedance drops to its minimum value (Z = R). In a parallel RLC circuit, impedance reaches its maximum. The resonant frequency is f₀ = 1/(2π√(LC)).

What is the quality factor (Q) of a circuit?

The quality factor Q measures how sharply a circuit resonates. Higher Q means a narrower bandwidth and more selective frequency response. For series RLC, Q = (2πf₀L)/R. For parallel RLC, Q = R/(2πf₀L). Q also equals the ratio of resonant frequency to bandwidth: Q = f₀/BW.

What is a phasor diagram?

A phasor diagram is a graphical representation of impedance as a vector in the complex plane. The horizontal axis represents resistance (real part) and the vertical axis represents reactance (imaginary part). The length of the vector is the impedance magnitude, and the angle from the horizontal is the phase angle between voltage and current.

What is the impedance of a 100 ohm resistor and 0.1 H inductor in series at 60 Hz?

For an ideal series RL circuit, inductive reactance is 2πfL. At 60 Hz and 0.1 H, that is about 37.7 ohms. The impedance magnitude is √(100² + 37.7²), or about 106.9 ohms, with a phase angle of about 20.7 degrees inductive. This is an estimate based on ideal components; real inductors also have winding resistance and other frequency-dependent effects.

What happens if I enter zero frequency for an RLC impedance calculation?

Zero frequency is a special case, because the ideal reactance formulas divide by frequency for a capacitor and multiply by frequency for an inductor. As frequency approaches zero, an ideal capacitor behaves like an open circuit and an ideal inductor like a short circuit. For a practical AC impedance calculation, enter the actual operating frequency; DC behavior may require a separate circuit analysis.

Will an RLC calculation give the exact impedance of a loudspeaker?

Not usually. A loudspeaker’s impedance changes with frequency and includes mechanical resonance, voice-coil inductance, and other effects; its labeled impedance is a nominal rating. An RLC model can illustrate frequency-dependent behavior when you have suitable equivalent component values, but entering only the nominal speaker resistance will not capture its full impedance curve. Use measured or manufacturer-provided frequency data when that detail matters.