AC Impedance Calculator – RLC

Calculate impedance, current, power factor, and resonance for series and parallel RLC circuits.

50Hz=EU, 60Hz=US
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Impedance in a Series or Parallel RLC Circuit

AC impedance extends resistance to circuits where inductors and capacitors make current depend on frequency and phase. A resistor contributes a real opposition R. An inductor has reactance XL=ωL that increases with frequency, while a capacitor has reactance XC=1/(ωC) that decreases with frequency. Their opposite phase effects are why an RLC circuit can pass through resonance as frequency changes.

For a series RLC circuit, the net reactance is X=XL−XC, so |Z|=√(R2+X2). Below resonance the circuit is net capacitive, above resonance it is net inductive, and at the ideal resonance XL=XC, leaving Z=R and power factor equal to 1. Parallel RLC circuits are better analyzed with admittance because branch currents add.

XL=2πfL,   XC=1/(2πfC),   f0=1/[2π√(LC)]
SymbolMeaningWhy it appears / units
RResistanceΩ; dissipates real power.
XLInductive reactanceΩ; grows linearly with f.
XCCapacitive reactanceΩ; falls as 1/f.
ZImpedance magnitudeΩ; determines current magnitude V/|Z|.
φVoltage-current phase angleDegrees or radians; its cosine is the power factor for a sinusoidal circuit.

Reactance is not energy loss by itself. Ideal inductors and capacitors alternately store and return energy, whereas resistance converts electrical energy into heat. Real components also have winding resistance, dielectric loss, parasitic capacitance, and frequency-dependent behavior, so the ideal RLC equations are a first model rather than a complete high-frequency component model.

Worked Examples

Example 1: Series RLC: R=100Ω, L=50mH, C=10μF, f=50Hz
XL=15.7Ω, XC=318Ω, Z=√(100²+302²)
Result: Z≈318.7Ω, PF≈0.314
Capacitive circuit at 50Hz
Example 2: At resonance: f=f₀=1/(2π√LC)
X_L=X_C, Z=R minimum
Result: Max current, PF=1
Pure resistive at resonance
Example 3: Series RLC almost at resonance
R=50Ω, L=0.10H, C=100µF, f=50Hz → XL=31.42Ω, XC=31.83Ω
Result: |Z|≈50.00Ω, PF≈1.000
The resonance frequency is about 50.33Hz, so the reactive terms nearly cancel at 50Hz.
Example 4: Same circuit below resonance
R=50Ω, L=0.10H, C=100µF, f=20Hz → XL=12.57Ω, XC=79.58Ω
Result: |Z|≈83.61Ω, φ≈−53.3°
Because XC>XL, the series circuit is net capacitive and current leads the source voltage.

Common Mistakes

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Subtracting reactances without considering the circuit topology

XL−XC belongs to a series RLC impedance. Parallel branches are naturally combined through admittance, not by copying the series formula.

⚠️
Using millihenries or microfarads as SI base units

Convert mH to H and µF to F before evaluating 2πfL or 1/(2πfC).

⚠️
Calling reactance a power loss

Ideal reactance changes phase and current magnitude but does not consume average real power. Resistance is the term that dissipates energy in the ideal model.

Frequently Asked Questions

Series vs parallel resonance?
Series: minimum impedance (maximum current) at resonance. Parallel: maximum impedance (minimum current) at resonance. Series for current amplification (filters); parallel for voltage amplification (tank circuits).
Power factor improvement?
Low PF means large reactive current. Add capacitors in parallel to inductive loads to improve PF. Target PF>0.95 to reduce I²R losses and avoid utility PF penalties.
Why does inductive reactance increase with frequency?
An inductor's voltage is proportional to the rate of change of current, v=Ldi/dt. Faster sinusoidal variation means a larger rate of change for the same current amplitude, which appears in phasor form as XL=ωL. Therefore inductors oppose high-frequency current more strongly.
Why does capacitive reactance decrease with frequency?
A capacitor current is i=Cdv/dt. At higher frequency, a given voltage amplitude changes more rapidly and drives more current. The voltage-to-current ratio therefore becomes smaller, giving XC=1/(ωC).
What does a negative phase angle mean in a series RLC circuit?
With the common convention φ=angle(Z), a negative value means the net reactance is capacitive. Current leads source voltage. A positive angle means net inductive behavior and current lags the voltage. At ideal series resonance, the angle is zero.
Does resonance frequency depend on resistance?
The ideal reactance-cancellation frequency 1/[2π√(LC)] does not contain R. However, resistance affects damping, bandwidth, Q factor, and the exact frequency at which some measured response quantities peak. Real component losses and parasitics can also shift observed resonance.

Formula Explorer connections

Interpretation: This engineering-physics relationship connects load, material property, geometry, deformation or system response. Assumption: Confirm material linearity, geometry, support conditions and safety convention. Small deformation, elastic behavior and ideal loading are common assumptions.

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