A capacitor is a passive two-terminal electrical component used to store energy electrostatically in an electric field. The capacitors contains two electrical conductors (plates) separated by a dielectric (i.e. insulator). The "nonconducting" dielectric acts to increase the capacitor's charge capacity. A dielectric can be glass, ceramic, plastic film, air, vacuum, paper, mica, oxide layer etc.
Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.
When there is a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge +Q to collect on one plate and negative charge −Q to collect on the other plate.
If a battery (i.e. dc supply) has been attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if a time-varying voltage (i.e. ac supply) is applied across the leads of the capacitor, a displacement current can flow.
An ideal capacitor is characterized by a single constant value for its capacitance (C).
Capacitance
Capacitance is expressed as the ratio of the electric charge Q on each conductor to the potential difference V between them.
C = Q / V
The SI unit of capacitance is the farad (F), which is equal to one coulomb per volt (1 C/V). Typical capacitance values range from about 1 pF (10−12 F) to about 1 mF (10−3 F).
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 = ε * A / D Farad (F)
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).
Electronic Symbol
Typical schematic diagram symbols are as follows;
Capacitors in Parallel
Capacitors in a parallel configuration each have the same applied voltage. Their capacitances add up. Using the schematic diagram to visualize parallel plates, it is apparent that each capacitor contributes to the total surface area.
Ceq
= C1 + C2 + . . . + Cn
Capacitors in Series
The total capacitance of capacitors in series, C1, C2, . . ., Cn
1/Ceq = 1/C1 + 1/C2 + . . . + 1/Cn
Capacitor Current
The capacitor's momentary current I(t) is equal to the capacitance of the capacitor times the derivative of the momentary capacitor's voltage V(t):
Capacitor Voltage
The capacitor's momentary voltage V(t) is equal to the initial voltage of the capacitor plus 1/C times the integral of the momentary capacitor's current I(t) over time t:
Energy Stored by a Capacitor
The capacitor's stored energy EC in joules (J) is equal to the capacitance C in farad (F) times the square capacitor's voltage VC in volts (V) divided by 2:
AC circuits
Angular frequency
ω - angular velocity measured in radians per second (rad/s)
f - frequency measured in hertz (Hz).
Capacitor's reactance
The capacitive reactance is defined as the opposition offered by a pure capacitor to the flow of alternating current.
Capacitor's impedance
Rectangular/Cartesian form:
Polar Form:
ZC = XC∟-90º
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