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

$C=ϵ\frac{A}{l}$

From above

$C=\frac{Q}{V}=ϵ\frac{A}{l}$

$ϵ=\frac{Q}{V}\frac{l}{A}$

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

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

Impedance

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

Reactance

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

Phase angle

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

Time constant

$T=RC$