Circuit Ready: What is a Capacitor (C)..?

What is capacitor

Capacitor is an electronic component that stores electric charge. The capacitor is made of 2 close conductors (usually plates) that are separated by a dielectric material. The plates accumulate electric charge when connected to power source. One plate accumulates positive charge and the other plate accumulates negative charge.

The capacitance is the amount of electric charge that is stored in the capacitor at voltage of 1 Volt.

The capacitance is measured in units of Farad (F).

The capacitor disconnects current in direct current (DC) circuits and short circuit in alternating current (AC) circuits.

Capacitor symbols

Capacitor
Polarized capacitor
Variable capacitor

Capacitance

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

$C=\frac{Q}{V}$

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):

$C=\varepsilon \times \frac{A}{d}$

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,.. :

$\frac{1}{C_{Total}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}+...$

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):

$i_c(t)=C\frac{dv_c(t)}{dt}$

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:

$v_c(t)=v_c(0)+\frac{1}{C}\int_{0}^{t}i_c(\tau)d\tau$

Energy of capacitor

The capacitor's stored energy E_C in joules (J) is equal to the capacitance C in farad (F)

times the square capacitor's voltage V_C in volts (V) divided by 2:

E_C = C × V_C²/ 2

AC circuits

Angular frequency

ω = 2π f

ω - angular velocity measured in radians per second (rad/s)

f - frequency measured in hertz (Hz).

Capacitor's reactance

$X_C = -\frac{1}{\omega C}$

Capacitor's impedance

Cartesian form:

$Z_C = jX_C = -j\frac{1}{\omega C}$

Polar form:

Z_C = X_C∟-90º

Capacitor types

Variable capacitor	Variable capacitor has changeable capacitance
Electrolytic capacitor	Electrolytic capacitors are used when high capacitance is needed. Most of the electrolytic capacitors are polarized
Spherical capacitor	Spherical capacitor has a sphere shape
Power capacitor	Power capacitors are used in high voltage power systems.
Ceramic capacitor	Ceramic capacitor has ceramic dielectric material. Has high voltage functionality.
Tantalum capacitor	Tantalum oxide dielectric material. Has high capacitance.
Mica capacitor	High accuracy capacitors.
Paper capacitor	Paper dielectric material.