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LCR series circuit
Intermediate
Impedance combines R and net reactance.
Z = √(R²+(X_L−X_C)²)Impedance Z = √(R² + (X_L − X_C)²) and I = V/Z. The phase angle is tanφ = (X_L − X_C)/R.
R = 30 Ω, X_L = 80, X_C = 40: Z = 50 Ω.
Subtract the reactances before squaring.
In more detail
In a series LCR circuit, resistance, inductive reactance and capacitive reactance combine to give impedance Z = sqrt(R² + (XL − XC)²). The current and voltage differ in phase by an angle set by the reactances.
Real-world uses
- Radio tuners use LCR circuits to select stations.
- Filters in audio equipment are built from LCR networks.
- Radio engineers design LCR circuits to select one station by setting the impedance to a minimum at the right frequency.
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Frequently asked questions
How is impedance found?
By adding resistance and net reactance as vectors, using Pythagoras.
What is the phase angle?
The angle whose tangent is the net reactance divided by resistance.
What is impedance?
The total opposition to AC current, combining resistance and reactance.
Related topics in AC Circuits & EM Waves
Resistor in AC · Inductor in AC · Capacitor in AC · Phase angle · Series resonance · Quality factor in LCR