Basics of the Electrical Capacitor

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Capacitors are electrical devices manufactured to possess capacitance. Capacitors oppose changes in voltage over time by creating a current. This behavior makes capacitors useful for stabilizing voltage in DC circuits. One way to think of a capacitor in a DC circuit is as a temporary voltage source, always “wanting” to maintain voltage across its terminals at the same value. A typical capacitor is made up of two parallel conductive plates separated by an insulator called a dielectric as shown below:
Parallel plate Capacitor
Capacitors have voltage ratings as well as capacitance ratings. The various symbols used to represent capacitors in circuit diagrams are shown below:
Capacitor Symbols
Capacitance of a Capacitor
Electrically, the capacitance of a capacitor is its ability to store electrical charge. The bigger the capacitance, the more the electrical charge stored. The capacitance of a parallel plate capacitor is given by:
C = ЄA/d
Where:
C = capacitance of capacitor in faradays (F). Units could be microfards (μF) or picofarads (pF)
Є = electric permittivity of the dielectric material
A = Area of capacitor plates
d = Separation of the plates

The capacitance output of the capacitor will increase if a higher dielectric material is used or if the area of the plates is increased or if the distance of separation between the plates is decreased.

Flow of DC Current through a capacitor:

The relationship between a voltage and current in a capacitor is given by:
I = CdV/dt.
When a capacitor that is initially uncharged is connected to a DC Voltage source, it tends to draw a large current. During the charging process, the capacitor voltage rises and charging current decreases. After the capacitor has received sufficient charge the capacitor voltage equals the applied voltage and the current flow ceases. After the capacitor has charged, it looks like an open circuit in a DC circuit.

Energy Stored in a Capacitor
The energy stored in a capacitor is given by:
E = ½ CV2 = 1/2QV 

Capacitors in Series & Parallel
Capacitance adds when capacitors are connected in parallel. It diminishes when capacitors are connected in series:
C(parallel) = C1+C2+…+Cn
C(series) = 1/[1/C1 + 1/C2+ ….+1/Cn]

Flow of AC current through a Capacitor
If an AC voltage is applied to a pure capacitor, the current is at maximum when the voltage begins to rise from zero, and the current is zero when the voltage across the capacitor is at maximum. The current leads the applied voltage by 90°as indicated by the waveform below:
Voltage-Current phasor of Capacitor with AC current through it.

Capacitive Reactance
This is the opposition to AC current flow in a purely capacitive circuit, measured in ohms. Capacitive reactance is given by the formula:
Xc = 1/2πfC

Where:
Xc = capacitive reactance
f  =  frequency
C = capacitance