Parallel Rlc Calculator

Parallel RLC Circuit Calculator

Analyze the behavior of a parallel RLC circuit by calculating its key electrical properties. Enter the component values and frequency below. Ensure you use base units (Hertz, Ohms, Henries, Farads).

Circuit Parameters
Frequency (f): Hz
Resistance (R): Ω (Ohms)
Inductance (L): H (Henries)
Capacitance (C): F (Farads)
Note: For Farads, 1µF = 1e-6 F, 1nF = 1e-9 F, 1pF = 1e-12 F. For Henries, 1mH = 1e-3 H.

Understanding Parallel RLC Circuits

A parallel RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel. When an AC voltage source is applied, the circuit’s behavior is frequency-dependent due to the reactances of the inductor and capacitor.

Key Parameters:

  • Inductive Reactance (XL): The opposition offered by an inductor to alternating current. It increases with frequency.
    XL = 2πfL
  • Capacitive Reactance (XC): The opposition offered by a capacitor to alternating current. It decreases with frequency.
    XC = 1 / (2πfC)
  • Impedance (Z): The total opposition to current flow in an AC circuit. For a parallel RLC circuit, it’s calculated using admittances (reciprocal of impedance).
    Conductance (G) = 1/R
    Inductive Susceptance (BL) = 1/XL
    Capacitive Susceptance (BC) = 1/XC
    Total Admittance (Y) = √(G2 + (BC – BL)2)
    Total Impedance (Z) = 1/Y
    Phase Angle (θ) = arctan((BC – BL)/G) for Admittance Y. The impedance phase angle is -θ.
  • Resonant Frequency (fr): The frequency at which XL = XC. In a parallel RLC circuit, impedance is maximum at resonance.
    fr = 1 / (2π√(LC))
  • Quality Factor (Q): A measure of how underdamped an oscillator or resonator is. For a parallel RLC circuit at resonance, it relates the energy stored to the energy dissipated per cycle. A higher Q factor indicates a sharper resonance peak (narrower bandwidth).
    Q = R√(C/L) or Q = R / XL(resonant) = R / XC(resonant)
  • Bandwidth (BW): The range of frequencies for which the circuit’s power is at least half its maximum power (at resonance).
    BW = fr / Q

At resonance, the reactive components (BL and BC) cancel each other out, and the circuit appears purely resistive (impedance is maximum and equal to R if it’s an ideal parallel tank driven by a current source, or more complex if driven by a voltage source with series resistance). Below resonance, the circuit is predominantly inductive. Above resonance, it’s predominantly capacitive.

Electronics Resources Parallel R-L-C Circuits (AllAboutCircuits) RLC Circuit – Parallel (Wikipedia) Parallel RLC Circuit (HyperPhysics)

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