How do you calculate impedance of an RLC circuit?

Series RLC: Z = √(R² + (XL - XC)²), where XL = 2πfL and XC = 1/(2πfC). Phase angle θ = arctan((XL-XC)/R). Example: R=100Ω, L=10mH, C=1µF at 1kHz: XL=62.83Ω, XC=159.15Ω, Z=√(100²+(-96.3)²) = 138.8Ω at -43.9°.

What is Q factor in RLC circuits?

Q = f₀/bandwidth = (1/R)×√(L/C) for series RLC. Higher Q = sharper resonance peak, more selective filter. Q=1 is critically damped, Q 1 underdamped. Typical values: crystal oscillators Q=10,000-100,000, LC circuits Q=10-100, speaker crossovers Q=0.5-2.

What is the difference between impedance and resistance?

Resistance (R) opposes DC and AC equally — it's purely real. Impedance (Z) is the total opposition to AC current including resistance AND reactance — it's a complex number Z = R + jX. Impedance varies with frequency (due to L and C), while resistance doesn't. At DC (0 Hz), impedance of a pure resistor equals its resistance.

Impedance Calculator — Free RLC Circuit & AC Impedance Tool | AllInOneTools

⚡ Electrical & Energy

Impedance Calculator

Calculate total impedance, phase angle, resonant frequency, and Q factor for series RLC AC circuits. Interactive phasor diagram shows the impedance triangle in real time.

Series RLC Circuit

Resistance (R)

Inductance (L)

Capacitance (C)

µF

Frequency

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Impedance Components

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Resonance

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Frequently Asked Questions

How do you calculate RLC impedance?▼

Series: Z = √(R² + (XL−XC)²). XL = 2πfL, XC = 1/(2πfC). Phase θ = arctan((XL−XC)/R). If XL>XC: inductive. If XC>XL: capacitive. At resonance: Z = R.

What is resonant frequency?▼

f₀ = 1/(2π√(LC)) — where XL = XC. Impedance is minimum (= R) in series, maximum in parallel. Example: 10mH + 1µF → f₀ = 1,591.5 Hz.

What is impedance vs resistance?▼

Resistance opposes DC+AC equally (real number). Impedance is total AC opposition including reactance (complex: Z = R + jX). Impedance varies with frequency; resistance doesn't.

What is Q factor?▼

Q = f₀/bandwidth = (1/R)√(L/C). Higher Q = sharper resonance. Crystal Q=10,000+, LC circuits Q=10-100. Q determines filter selectivity and oscillator stability.

What is the impedance triangle?▼

R horizontal, X=(XL−XC) vertical, Z hypotenuse. Z=√(R²+X²), θ=arctan(X/R). Positive X = inductive (current lags), negative = capacitive (current leads), zero = resonance.

Series vs parallel impedance?▼

Series: Z adds, impedance minimum at resonance (bandpass filter). Parallel: reciprocal, impedance maximum at resonance (tank circuit/notch). Same resonant frequency f₀=1/(2π√LC).

How to match impedance?▼

Maximum power when source Z = load Z (conjugate match). Use L-networks, transformers, or transmission line stubs. Common: 50Ω systems (RF), 75Ω (video/cable TV), 8Ω (speakers).