RLC Parallel Circuit Calculator

Analyze parallel RLC circuits: resonant frequency, impedance, phase, quality factor, bandwidth, and branch currents. Interactive graph and detailed formulas for engineers and students.

Parallel RLC admitance: Y = 1/R + j(ωC - 1/(ωL))    |Z| = 1/|Y|,   φ = -atan2(ωC - 1/(ωL), 1/R)

Resonance: ω₀ = 1/√(LC),   f₀ = 1/(2π√(LC))

R=1kΩ, L=0.1H, C=1µF
R=100Ω, L=50mH, C=10µF
R=10kΩ, L=0.2H, C=100pF
R=50Ω, L=1mH, C=100nF
Computing...

Understanding Parallel RLC Circuits

A parallel RLC circuit consists of a resistor (R), inductor (L), and capacitor (C) connected in parallel across an AC source. It exhibits resonance and frequency-dependent impedance, making it fundamental in filters, oscillators, and impedance matching networks.

Key Formulas:

Admittance: Y = G + jB = 1/R + j(ωC – 1/(ωL))

Impedance magnitude: |Z| = 1 / √( (1/R)² + (ωC – 1/(ωL))² )

Phase: φ = –atan2( (ωC – 1/(ωL)) , 1/R )

Resonant frequency: f₀ = 1 / (2π√(LC))

Quality factor: Q = R · √(C/L)   (parallel RLC)

Bandwidth: BW = f₀ / Q

Frequency Response Characteristics

Region Impedance Behavior Phase
f << f₀ Inductive dominance, |Z| increases with f Negative (current lags)
f = f₀ Maximum impedance (resistive) |Z| = R Zero (in phase)
f >> f₀ Capacitive dominance, |Z| decreases with f Positive (current leads)

Applications

  • Band-stop / notch filters – high impedance at resonance blocks signal.
  • Oscillator tanks – determine frequency of oscillation.
  • Impedance matching – transform impedances at resonance.
  • Inductor/capacitor selection – Q factor defines selectivity.

Calculator Features:

  • Real‑time calculation of all relevant AC parameters.
  • Interactive impedance vs. frequency graph (logarithmic frequency axis).
  • Preset examples for quick testing.
  • Formulas and theory integrated for learning.

Frequently Asked Questions

Resonant frequency f₀ = 1/(2π√(LC)). At this frequency, the inductive and capacitive susceptances cancel, leaving a purely resistive impedance equal to R.

Q = R √(C/L). It indicates sharpness of resonance: higher Q means narrower bandwidth and more selective filtering.

Impedance reaches its maximum value = R (for ideal components). The circuit acts as a pure resistor.

To clearly show impedance variation over several decades, especially the symmetrical response around resonance.