Rlccircuit Impedance Calculator
Calculate rlccircuit impedance accurately for your build. Get material quantities, waste allowances, and project cost breakdowns.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Z = sqrt(R^2 + (XL - XC)^2); XL = 2*pi*f*L; XC = 1/(2*pi*f*C)
Where Z is impedance in ohms, R is resistance, XL is inductive reactance (proportional to frequency), XC is capacitive reactance (inversely proportional to frequency), f is frequency in Hz, L is inductance in henries, and C is capacitance in farads. Resonant frequency f0 = 1/(2*pi*sqrt(LC)).
Worked Examples
Example 1: Audio Bandpass Filter Design
Problem:A series RLC circuit has R = 100 ohm, L = 10 mH, C = 100 uF, driven at 1000 Hz with 12V. Calculate the impedance, current, and resonant frequency.
Solution:XL = 2*pi*1000*0.01 = 62.83 ohm\nXC = 1/(2*pi*1000*0.0001) = 1.59 ohm\nNet reactance = 62.83 - 1.59 = 61.24 ohm (inductive)\nZ = sqrt(100^2 + 61.24^2) = 117.26 ohm\nCurrent = 12 / 117.26 = 0.1023 A = 102.3 mA\nPhase = arctan(61.24/100) = 31.47 degrees\nResonant freq = 1/(2*pi*sqrt(0.01*0.0001)) = 159.15 Hz
Result:Z: 117.26 ohm | I: 102.3 mA | Phase: 31.47 deg | f0: 159.15 Hz
Example 2: Resonance Analysis
Problem:Find the resonant frequency and Q factor for a series RLC with R = 50 ohm, L = 5 mH, C = 10 uF. What is the impedance at resonance?
Solution:f0 = 1/(2*pi*sqrt(0.005*0.00001)) = 711.8 Hz\nXL at resonance = 2*pi*711.8*0.005 = 22.36 ohm\nQ = XL/R = 22.36/50 = 0.447\nBandwidth = f0/Q = 711.8/0.447 = 1592 Hz\nAt resonance: Z = R = 50 ohm (XL = XC, they cancel)\nCurrent at resonance = V/R (maximum)
Result:f0: 711.8 Hz | Q: 0.447 | BW: 1592 Hz | Z at resonance: 50 ohm (purely resistive)
Frequently Asked Questions
What is impedance in an RLC circuit and how is it calculated?
Impedance is the total opposition to alternating current flow in a circuit containing resistance, inductance, and capacitance. Unlike simple DC resistance, impedance is a complex quantity that accounts for both energy dissipation through resistance and energy storage through reactive components. For a series RLC circuit, the impedance magnitude is calculated as Z equals the square root of R squared plus the quantity XL minus XC squared, where XL is the inductive reactance equal to 2 times pi times frequency times inductance, and XC is the capacitive reactance equal to 1 divided by 2 times pi times frequency times capacitance. The phase angle between voltage and current is the arctangent of the net reactance divided by the resistance. Impedance is measured in ohms and varies with frequency, reaching a minimum at the resonant frequency in series circuits.
What is impedance and how does it differ from resistance?
Resistance opposes DC current and is purely real. Impedance opposes AC current and includes resistance plus reactance (from capacitors and inductors). Impedance is a complex number: Z = R + jX, measured in ohms. Capacitive reactance decreases with frequency while inductive reactance increases with frequency.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy