Parallel RLC Impedance Calculator

Parallel RLC impedance

Wire a resistor, an inductor and a capacitor in parallel and they all see the same voltage. What differs is the current, which divides among the three branches. To get the total impedance magnitude you use Z = 1 / sqrt((1/R)^2 + (1/Xc - 1/Xl)^2), with Xl = 2πfL and Xc = 1/(2πfC). Plug in R = 100 Ω, L = 10 mH, C = 1 µF and f = 1 kHz and the calculator gives Z ≈ 97.6 Ω with a slightly inductive phase, because at that frequency Xl comes out smaller than Xc.

At the resonance frequency f₀ = 1/(2π√(LC)) the two reactive branches cancel out and the parallel impedance peaks. If you ignore losses it is purely resistive and equal to R. Move away from f₀ in either direction and the impedance falls off. That behavior is why a parallel RLC tank acts like a band-pass filter if you look at the current, and a band-reject filter if you look at the voltage.

Applications

You will meet parallel RLC analysis in any AC circuits course (Sedra/Smith, Boylestad, Irwin). It shows up in radio frequency tank circuits, in the load networks of oscillators, in power factor correction banks designed around IEEE 519 and IEC 61000-3-2, in EMC filters at the AC input of equipment, and in antenna impedance matching. When the topic is harmonics mitigation, ABNT NBR 5410 and IEC 60364 bring up parallel capacitor banks too.

FAQ

How does the impedance compare to the series case? They are dual circuits, so the answer flips. Series impedance bottoms out at resonance, while parallel impedance hits its maximum there.

What happens far above resonance? Xc drops low, so the capacitor branch takes over and the parallel impedance ends up small and mostly capacitive.

Does R always lower the impedance? Yes. A smaller R shunts more current at resonance, which pulls down both the peak impedance and the Q factor.