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

Capacitor and DC electricity
Electric charge
 * $$Q = C V$$

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

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
 * $$T=RC$$