# 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 ${\displaystyle C}$ and measured in unit Farad ${\displaystyle F}$

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

Capacitor can be made from 2 parallel plates

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

From above

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

## Electricity response of capacitor

### Capacitor and DC electricity

Electric charge

${\displaystyle Q=CV}$

Capacitance

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

Voltage

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

### Capacitor and AC electricity

Voltage

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

Current

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

Power

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

Impedance

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

Reactance

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

Phase angle

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

Time constant

${\displaystyle T=RC}$