ELC-46

LC resonance

Natural LC frequency.

Reading speed

CircuitsLC resonance

Governing equation

f_0=1/(2\pi\sqrt{LC})

$C \in \left[0.1, 200\right]$

where

L: L (mH)
C: C (µF)
f_0: Frequency (Hz)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

f_0=1/(2\pi\sqrt{LC})

$C \in \left[0.1, 200\right]$

$C = 0.1$ $f_0 = 5032.9$

Along the curve

②

Domain of the variable — blue

C_{\min} = 0.1,\quad C_{\max} = 200

$C \in \left[0.1, 200\right]$

$C = 0.1$ $C = 0.1$

Along the curve

③

Response curve — green

f_0=1/(2\pi\sqrt{LC})

$C \in \left[0.1, 200\right]$

$C = 0.1$ $f_0 = 5032.9$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}f_0}{\mathrm{d}C}

$C \in \left[0.1, 200\right]$

$C = 1.357$ $f_0^{\prime} = -1610.1$

Along the curve

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-46 — LC resonance) is the form associated with LC resonance. Working symbols: $L$ , $C$ $\rightarrow$ $f_0$ . Natural LC frequency. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

f_0

from

L

C

in Electrical via

f_0=1/(2\pi\sqrt{LC})

Natural LC frequency. 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 = 10.000\,\mathrm{\mu F}

, the governing relation

f_0=1/(2\pi\sqrt{LC})

yields

f_0 = 503.29\,\mathrm{Hz}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

L L10 mHC C10 µF

Outputs

Frequency f_0503.29 Hz

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Natural LC frequency. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube