Electronics Bible/Capacitor

Capacitor is an electronics device made from a 2 parallel plates conductor that can store energy as Electric field

Capacitance

Capacitance represents capacitor's capability to store energy as Electric field . Capacitor has a symbol $C$ and measured in unit Farad $F$

$C={\frac {Q}{V}}$

Capacitor can be made from 2 parallel plates

$C=\epsilon {\frac {A}{l}}$

From above

$C={\frac {Q}{V}}=\epsilon {\frac {A}{l}}$

$\epsilon ={\frac {Q}{V}}{\frac {l}{A}}$

Electricity response of capacitor

Capacitor and DC electricity

Electric charge

$Q=CV$

Capacitance

$C={\frac {Q}{V}}$

Voltage

$V={\frac {Q}{C}}$

Capacitor and AC electricity

Voltage

$v(t)={\frac {1}{C}}\int i(t)dt$

Current

$i(t)=C{\frac {d}{dt}}i(t)$

Power

$p(t)={\frac {1}{2}}Cv^{2}(t)$

Impedance

$Z={\frac {v(t)}{i(t)}}=R_{C}+X_{C}=R+{\frac {1}{\omega C}}\angle -90=R+{\frac {1}{j\omega C}}=R+{\frac {1}{sC}}$

Reactance

$X_{C}={\frac {1}{\omega C}}\angle -90={\frac {1}{j\omega C}}={\frac {1}{sC}}$

Phase angle

$Tan\theta ={\frac {1}{\omega T}}$

Time constant

$T=RC$