Capacitors

A capacitor is formed when ever two conductors are placed near each other, but separated by an insulator. Many different materials and construction techniques are used in practical capacitors depending on the application.

Capacitors can be used to block DC currents, because of the insulating layer, but allow AC currents to pass due to capacitor action. They are also used to store charge as in a smoothing capacitor in a power supply.

The equation for a capacitor is:

C = Q / V

If a constant current is used to charge (or discharge) a capacitor then the voltage across it will vary in accordance with:

dV/dt = I / C

And the energy stored on the capacitor at any time is given by:

E = 0.5 V2 C

Because an ideal capacitor prevents DC current flow but allows AC current flow it has an “AC resistance”. This property is more correctly called capacitive reactance or reactive impedance. This value varies with frequency and can be calculated by the following formula:

Xc = 1 / ( j w C ) = - j / wC

Symbol
 
Units
C
Capacitance in Farads
F
Q
Charge in Coulombs
C
V
Voltage in Volts
V
dV/dt
The rate of change of voltage with time
V / s
I
Current in Amps
A
E
Energy in Joules
J
Xc
Capacitive Reactance in Ohms
W
j
The imaginary number
Ö -1
w
Angular frequency = 2 p f
rad / s
f
Frequency in Hertz
Hz

 

Component values are usually shown as text, eg 10pF or 10p indicates 10 pico-farads. The decimal point is often replaced with the scaling symbol as in 0u1 which indicates 0.1 micro farads (this might also be written as 100n). On physically small parts including surface mount components the above value would be shown as 104 where the last digit is a multiplier and is the number of zeros to be added to the first two digits to make the value in pico farads.

Some capacitors have a polarity marking which must be observed. Generally these are large value parts that use specific construction techniques. Such devices are called electrolytic and tantalum. If these are operated with the polarity reversed they can explode or emit noxious fumes.


Series connection


1/CTOT = 1/C1 + 1/C2 + … + 1/Cn

Parallel connection


CTOT = C1 + C2 + … + Cn


A typical use for capacitors is in timing circuits

Charging


Vc = Vs ( 1 - e -t / R C )
I = ( Vs / R ) e -t / R C

Discharging


Vc = Vstart e -t / R C
I = ( Vstart / R ) e -t / R C

 

 
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