Sinusoidal Steady State and Resonance

Syllabus: Sinusoidal steady state analysis: phasors, complex power, maximum power transfer.

11 hand-picked visual resources on this topic, 5 of them little-known gems — under each card, look for See it. Every link is checked against the live site before it ships.

Phasors and impedance

Replace derivatives with $j\omega$ and the circuit becomes algebra. The sign of the reactance tells you whether current leads or lags.

$Z_R=R,\quad Z_L=j\omega L,\quad Z_C=\frac{1}{j\omega C}$
$Z=R+jX$
$X>0$ inductive, current lags; $X<0$ capacitive, current leads
$\sin(\omega t+\phi)=\cos(\omega t+\phi-90^\circ)$
put every source in cosine form before adding phasors

See it

Complex power

Only the real part is consumed; reactive power sloshes back and forth. Use RMS values throughout.

$S=VI^{*}=P+jQ$
$V,I$

Resonance and Q

At resonance the reactances cancel and the impedance is purely real. $Q$ measures sharpness — and the formula flips between series and parallel.

$\omega_0=\frac{1}{\sqrt{LC}}$

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Sinusoidal Steady State and Resonance

Syllabus: Sinusoidal steady state analysis: phasors, complex power, maximum power transfer.

11 hand-picked visual resources on this topic, 5 of them little-known gems — under each card, look for See it. Every link is checked against the live site before it ships.