AC circuit opposition
What is AC impedance?
AC impedance is the total opposition a circuit presents to alternating current. It combines resistance with the net effect of inductive and capacitive reactance.
Unlike resistance alone, impedance accounts for energy storage in inductors and capacitors as well as energy dissipation in resistors.
Series RLC formula
AC impedance formula
Series circuit impedanceZ = √(R² + (Xₗ − Xc)²)
- Z is total impedance in ohms.
- R is resistance in ohms.
- Xₗ is inductive reactance in ohms.
- Xc is capacitive reactance in ohms.
Worked example
Calculate series AC impedance
Suppose a series RLC circuit has resistance of 30 Ω, inductive reactance of 50 Ω, and capacitive reactance of 10 Ω.
- Find net reactance: Xₗ − Xc = 50 − 10 = 40 Ω.
- Square resistance and net reactance.
- Z = √(30² + 40²).
- Z = √2500 = 50 Ω.
Balanced reactance
Impedance at series resonance
Series resonance occurs when inductive reactance equals capacitive reactance. Their effects cancel, so net reactance becomes zero.
Under the ideal model, impedance then equals resistance and circuit current reaches its maximum value for a fixed supply voltage.
Circuit behavior
Inductive and capacitive dominance
- When Xₗ is greater than Xc, the circuit is inductive-dominant.
- When Xc is greater than Xₗ, the circuit is capacitive-dominant.
- When Xₗ equals Xc, the circuit is at resonance.
Inverse calculations
Solving for individual reactance
Because the reactance difference is squared, solving the impedance equation backward can produce two mathematical branches.
This calculator uses the inductive-dominant branch when solving for Xₗ and the capacitive-dominant branch when solving for Xc.
Unit guidance
Impedance and reactance units
- Impedance: ohms (Ω).
- Resistance: ohms (Ω).
- Inductive reactance: ohms (Ω).
- Capacitive reactance: ohms (Ω).
- All entered values must use compatible units.
Practical applications
Where AC impedance matters
- Series RLC circuit analysis.
- AC current calculations.
- Filter and resonant circuits.
- Power-factor analysis.
- Audio crossover networks.
- Electrical and electronics laboratory work.
Model limitations
Assumptions and limitations
- The circuit is treated as a series RLC circuit.
- Components are assumed ideal.
- Parasitic effects are ignored.
- Component values are assumed constant.
- Frequency-dependent losses are not included.
- Phase angle and complex impedance are not calculated directly.
Common questions
AC impedance calculator FAQ
What formula does the AC impedance calculator use?
It uses Z = √(R² + (Xₗ − Xc)²) for a series RLC circuit, where Z is impedance, R is resistance, Xₗ is inductive reactance, and Xc is capacitive reactance.
What is the unit of AC impedance?
AC impedance is measured in ohms, represented by the symbol Ω.
What happens when inductive and capacitive reactance are equal?
When Xₗ equals Xc, the net reactance is zero and the circuit impedance equals its resistance. This condition is called series resonance.
Can impedance be smaller than resistance?
No. In this ideal series RLC model, impedance is always equal to or greater than resistance.
Why can solving for reactance produce two mathematical answers?
The squared reactance difference removes its sign. This calculator uses the inductive-dominant branch when solving for Xₗ and the capacitive-dominant branch when solving for Xc.