RLC Parallel Calculator

Output

Degree


 

An RLC parallel circuit consists of resistance (R), inductance (L), and capacitance (C) connected in parallel. Understanding RLC parallel circuit analysis is fundamental for RF engineers, filter designers, and circuit analysts working with frequency-selective networks and resonant systems. The calculator accepts input values for capacitance, inductance, resistance, and operating frequency to compute the circuit's impedance characteristics. 

resonant frequency of parallel rlc circuit formula

 

The impedance of an RLC parallel circuit is denoted as Z and is calculated using the following formula:

 

Parallel RLC resonant frequency Calculator

Where R is resistance, L is inductance, C is capacitance, and ω is the Angular frequency ω=2πf

The phase difference is the angle by which the voltage applied to an RLC circuit delays or leads the resulting current. And it can be calculated using:

impedance of parallel rlc circuit

 

Example of Impedance of a Parallel RLC Circuit

Find the impedance of a parallel RLC circuit at resonance with R = 1kΩ, L = 10mH, and C = 100nF.
First, the resonant frequency of a parallel RLC circuit formula:
f₀ = 1/(2π√(LC)) = 1/(2π√(10×10⁻³ × 100×10⁻⁹))
f₀ = 5.03 kHz

At resonance, XL = XC, so:
Z = R = 1kΩ
φ = 0° (purely resistive)
 

Calculate impedance at 10 kHz for R = 470Ω, L = 5mH, C = 220nF.

ω = 2πf = 2π × 10,000 = 62,832 rad/s

XL = ωL = 62,832 × 5×10⁻³ = 314.16Ω
XC = 1/(ωC) = 1/(62,832 × 220×10⁻⁹) = 72.34Ω

1/Z = √[(1/R)² + (1/XL - 1/XC)²]
1/Z = √[(1/470)² + (1/314.16 - 1/72.34)²]
1/Z = √[0.00000452 + 0.0000836]
Z = 106.8Ω

Phase angle:
φ = arctan[R(1/XL - 1/XC)]
φ = arctan[470 × (-0.0106)]
φ = -78.3° (capacitive)

Here are more examples of our projects featuring RLC Circuits, Speaker with Equivalent RLC Circuit. For more information, you can dive into our tutorials. 

 

Frequently Asked Questions on RLC Parallel Calculator

⇥ What happens at resonance in a parallel RLC circuit?
At resonance, the inductive and capacitive reactances cancel out, leaving only the resistance. The impedance is maximum (equal to R), and the circuit appears purely resistive with zero phase shift.

⇥ How does a parallel RLC differ from a series RLC? 
Key differences:

  • Parallel: Maximum impedance at resonance, current divides among components
  • Series: Minimum impedance at resonance, voltage divides among components
  • Parallel is used for bandstop filters, series for bandpass filters

⇥ What is the quality factor (Q)? 
Q factor indicates the sharpness of resonance. Higher Q means narrower bandwidth and more selective frequency response. Q = R/X at resonance, where X is the reactance of L or C.

⇥ What causes losses in RLC circuits? 
Real components have parasitic elements:

  • Inductor: Series resistance (DCR), parallel capacitance
  • Capacitor: Equivalent series resistance (ESR), leakage
  • PCB traces add inductance and resistance. These reduce Q and shift the resonant frequency.

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