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).
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.