ELC-47

Series RLC Q

Sharpness of series resonance.

Reading speed

CircuitsSeries RLC Q

Governing equation

Q=\omega_0 L/R

$R \in \left[0.1, 40\right]$

where

omega_0: w0 (rad/s)
L: L (H)
R: R (Ω)
Q: Q (—)

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

Q=\omega_0 L/R

$R \in \left[0.1, 40\right]$

$R = 0.1$ $Q = 100$

Along the curve

②

Domain of the variable — blue

R_{\min} = 0.1,\quad R_{\max} = 40

$R \in \left[0.1, 40\right]$

$R = 0.1$ $R = 0.1$

Along the curve

③

Response curve — green

Q=\omega_0 L/R

$R \in \left[0.1, 40\right]$

$R = 0.1$ $Q = 100$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}R}

$R \in \left[0.1, 40\right]$

$R = 0.351$ $Q^{\prime} = -166.1$

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-47 — Series RLC Q) is the form associated with Series RLC Q. Working symbols: $omega_0$ , $L$ , $R$ $\rightarrow$ $Q$ . Sharpness of series resonance. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

Q

from

omega_0

L

R

in Electrical via

Q=\omega_0 L/R

Sharpness of series resonance. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

omega_0 = 1000.000\,\mathrm{rad/s}

L = 0.010\,\mathrm{H}

R = 2.000\,\mathrm{Ω}

, the governing relation

Q=\omega_0 L/R

yields

Q = 5.00\,\mathrm{—}

. 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

w0 omega_01000 rad/sL L0.01 HR R2 Ω

Outputs

Q Q5.00 —

Reading speed

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Narration of this film

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

Sharpness of series resonance. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube