RLC Parallel Circuit Impedance Calculator
Calculate total impedance, phase angle, resonant frequency, and quality factor for a parallel RLC circuit at any operating frequency.
🔀 What is a Parallel RLC Circuit's Impedance?
A parallel RLC circuit combines a resistor (R), an inductor (L), and a capacitor (C) all connected across the same two nodes, so they share the same voltage while their currents add. Because the three branch currents combine differently than in a series circuit, a parallel RLC circuit's total impedance behaves in the opposite way to a series circuit as frequency changes: it reaches a maximum at resonance instead of a minimum, since the inductive and capacitive branch currents cancel out at that point, leaving only the resistor's current flowing from the source.
This circuit topology appears throughout real electronics design. Tank circuits in oscillators use a parallel LC combination (with parasitic or intentional R) to select a single resonant frequency for feedback. Parallel resonant filters reject a narrow band of frequencies around f0 by presenting very high impedance there. Antenna matching networks and tuned RF amplifier loads both rely on the sharp impedance peak a high-Q parallel RLC circuit produces at its resonant frequency.
A common point of confusion is expecting parallel RLC circuits to behave like series RLC circuits with the impedance formula just plugged in directly. They do not: because the branches share voltage and add current, the natural starting point is admittance Y = 1/R + j(ωC − 1/(ωL)), not impedance. Total impedance Z is then the reciprocal, |Z| = 1/|Y|, which is exactly why impedance behaves oppositely at resonance compared to a series circuit.
This calculator takes your resistance, inductance, capacitance, and operating frequency, and returns the total impedance magnitude, the phase angle, the resonant frequency, the quality factor, and a chart showing how impedance rises to a peak at resonance and falls away on either side.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Near Resonance, Peak Impedance
R = 1,000 Ω, L = 100 mH, C = 1 µF, evaluated at 500 Hz
Example 2 — Well Above Resonance, Capacitive
Same R = 1,000 Ω, L = 100 mH, C = 1 µF, evaluated at 2,000 Hz
Example 3 — Well Below Resonance, Inductive
Same R = 1,000 Ω, L = 100 mH, C = 1 µF, evaluated at 150 Hz
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the impedance of a parallel RLC circuit?
Total impedance magnitude is |Z| = 1/sqrt((1/R)^2 + (wC - 1/(wL))^2), derived from the admittance Y = 1/R + j(wC - 1/(wL)) since Z = 1/Y. For R = 1000 ohms, L = 100 mH, C = 1 microfarad at 500 Hz, |Z| is approximately 999.14 ohms.
Why does impedance peak at resonance in a parallel RLC circuit?
At resonance, the inductive susceptance 1/(wL) exactly equals the capacitive susceptance wC, so they cancel in the admittance sum, leaving only the conductance 1/R. Since impedance is the reciprocal of admittance, a minimum admittance produces a maximum impedance, exactly the opposite of a series RLC circuit.
What is the phase angle in a parallel RLC circuit?
The phase angle theta = -atan2(wC - 1/(wL), 1/R) tells you how far the circuit's overall current leads or lags the source voltage. A positive angle means inductive behavior (current lags), a negative angle means capacitive behavior (current leads), and zero means purely resistive at resonance.
What is the quality factor of a parallel RLC circuit?
Q = R x sqrt(C/L) for a parallel RLC circuit. This is the inverse relationship compared to a series RLC circuit, where Q = (1/R) x sqrt(L/C), so a larger resistance R gives a higher Q and a sharper resonance peak in a parallel circuit.
How is parallel RLC resonant frequency calculated?
The resonant frequency f0 = 1/(2 x pi x sqrt(LC)) is the same formula used for a series RLC circuit, since resonance is defined by where the reactive (or susceptive) terms cancel, and that condition depends only on L and C, not on how R is connected.
What units does this calculator use for L and C?
Inductance is entered in millihenries (mH) and internally converted to henries by dividing by 1,000. Capacitance is entered in microfarads (uF) and internally converted to farads by dividing by 1,000,000. Resistance is in ohms and frequency is in hertz.
How is a parallel RLC circuit different from a series RLC circuit?
In a series RLC circuit, impedance is minimum at resonance and rises away from it. In a parallel RLC circuit, impedance is maximum at resonance and falls away from it. Both share the same resonant frequency formula f0 = 1/(2*pi*sqrt(LC)), but their impedance-versus-frequency behavior is opposite.
Why does the calculator use admittance instead of impedance directly?
In a parallel circuit, the branch currents add, which means the branch admittances (1/R, 1/XL, 1/XC as susceptances) add directly, making Y = 1/R + j(wC - 1/(wL)) the natural quantity to compute first. Impedance Z is then simply the reciprocal, |Z| = 1/|Y|.
Can total impedance ever exceed R in a parallel RLC circuit?
No. Since |Z| = 1/sqrt((1/R)^2 + B^2) where B is the net susceptance, adding any nonzero B can only increase the denominator, so |Z| is always less than or equal to R, with equality exactly at resonance where B = 0.
What does it mean if the phase angle is close to zero but not exactly zero?
A phase angle near zero means your chosen operating frequency is close to, but not exactly at, the resonant frequency f0 = 1/(2*pi*sqrt(LC)) for your L and C values. Check the resonant frequency result to see exactly how far off you are.
Does resistance affect the resonant frequency of a parallel RLC circuit?
No. The resonant frequency f0 = 1/(2*pi*sqrt(LC)) depends only on inductance and capacitance, exactly as in the series case. Resistance R does not shift the resonance point, but it does control the peak impedance value and the sharpness (Q) of the resonance.