CAPACITORS AND INDUCTORS

Capacitor: 
In both digital and analog electronic circuits a capacitor is a fundamental element. It 
enables the filtering of signals and it provides a fundamental memory element. 
The capacitor is an element that stores energy in an electric field. 
The circuit symbol and associated electrical variables for the capacitor is shown on 
Figure 1. 

The capacitor may be modeled as two conducting plates separated by a dielectric as 
shown on Figure 2. 

When a voltage v is applied across the plates, a charge +q accumulates on one plate and a 
charge –q on the other. 

Capacitance

The capacitance (C) of the capacitor is equal to the electric charge (Q) divided by the voltage (V):

C is the capacitance in farad (F)

Q is the electric charge  in coulombs (C), that is stored on the capacitor

V is the voltage between the capacitor's plates in volts (V)

Capacitance of plates capacitor

The capacitance (C) of the plates capacitor is equal to the permittivity (ε) times the plate area (A) divided by the gap or distance between the plates (d):

C is the capacitance of the capacitor, in farad (F).

ε is the permittivity of the capacitor's dialectic material, in farad per meter (F/m).

A is the area of the capacitor's plate in square meters (m²].

d is the distance between the capacitor's plates, in meters (m).

Capacitors in series

 

The total capacitance of capacitors in series, C1,C2,C3,.. :

Capacitors in parallel

The total capacitance of capacitors in parallel, C1,C2,C3,.. :

C_Total = C₁+C₂+C₃+...

Capacitor's current

The capacitor's momentary current i_c(t) is equal to the capacitance of the capacitor,

times the derivative of the momentary capacitor's voltage v_c(t):

Capacitor's voltage

The capacitor's momentary voltage v_c(t) is equal to the initial voltage of the capacitor,

plus 1/C times the integral of the momentary capacitor's current i_c(t) over time t: