ELC-03

Series RLC resonance

ω0 = 1/√(LC), Q = (1/R)√(L/C).

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AC circuitsThomsonIEC 60318

Governing equation

\omega_0=\dfrac{1}{\sqrt{LC}},\quad Q=\dfrac{1}{R}\sqrt{\dfrac{L}{C}}

where

L: Inductance (mH)
C: Capacitance (µF)
R: Resistance (Ω)
f_0: Resonant frequency (Hz)
Q: Quality factor (—)

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-03 — Series RLC resonance) is the form associated with Thomson · IEC 60318. Working symbols: $L$ , $C$ , $R$ $\rightarrow$ $f_0$ , $Q$ . The imaginary part of series impedance vanishes when ωL = 1/(ωC), defining Thomson's resonant frequency.

Purpose

Purpose: compute

f_0

Q

from

L

C

R

in Electrical via

\omega_0=\dfrac{1}{\sqrt{LC}},\quad Q=\dfrac{1}{R}\sqrt{\dfrac{L}{C}}

ω0 = 1/√(LC), Q = (1/R)√(L/C). Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

L = 10.000\,\mathrm{mH}

C = 1.000\,\mathrm{\mu F}

R = 8.000\,\mathrm{Ω}

, the governing relation

\omega_0=\dfrac{1}{\sqrt{LC}},\quad Q=\dfrac{1}{R}\sqrt{\dfrac{L}{C}}

yields

f_0 = 1591.549\,\mathrm{Hz}

Q = 12.500\,\mathrm{—}

. Series RLC, high-Q approximation for bandwidth. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Inductance L10 mHCapacitance C1 µFResistance R8 Ω

Outputs

Resonant frequency f_01591.549 Hz
Quality factor Q12.500 —

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Narration of this film

Series RLC, high-Q approximation for bandwidth.

The imaginary part of series impedance vanishes when ωL = 1/(ωC), defining Thomson's resonant frequency.

Reading speed

Watch on YouTube