Electronics Handbook/Components/Capacitors

Capacitor

A capacitor is an electronic component made from two conducting plates separated by a non conducting dielectric of the dimension :

Length l
Area A
Dielectric Constant $\epsilon$

The Capacitance of the Capacitor can be calculated by the formual below

$C = \epsilon \frac{A}{l}$

The electronics symbol of a capacitor is shown below

DC Characteristics

When connecting a resistor with a DC voltage source in a closed loop circuit

Charge

$Q = C V$

Voltage

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

Capacitance

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

AC Characteristics

When connecting a resistor with an AC voltage source in a closed loop circuit

Voltage

$v = C \frac{dv}{dt}$

Current

$i = \frac{1}{C} \int v dt$

Reactance

$X_C = \frac{1}{\omega C} \angle -90^0$
$X_C = \frac{1}{j\omega C}$
$X_C = \frac{1}{sC}$

Impedance

$Z_C = R_C + X_C$
$X_C = R \angle 0 + \frac{1}{\omega C} \angle -90^0$
$Z_C = R + \frac{1}{j\omega C}$
$Z_C = R + \frac{1}{sC}$

Frequency Response

$\omega$ $X_C$ $Z_C$
$\omega = 0$ $X_C = oo$ $Z_C = oo$
$\omega = \frac{1}{C}$ $X_C = 1$ $Z_C = \sqrt{2}R$
$\omega = 00$ $X_C = 0$ $Z_C = R$

Phase Angle Difference

$Tan\theta = \frac{1}{\omega CR} = \frac{1}{2 \pi f CR} = \frac{1}{2 \pi} \frac{t}{T}$
T = CR

Capacitor Types

There are two main types of Capacitors

Fixed Capacitor

Capacitor that has a fixed value

Variable Capacitor

Capacitor that has a variable value adjusted by a dial

Capacitor Configuarations

Series Connection

Two or more capacitors can be connected in series to decrese the total capacitance

$C_t = C_1 + C_2 + .... + C_n$

Parallel Connection

$\frac{1}{C_t} = \frac{1}{C_1} + \frac{1}{C_2} + .... + \frac{1}{C_n}$

Summary

Component Capacitor
Construction Capacitor is made from two conducting plates separated by a dielectric of dimension Length l, Diện Tích A , Dielectric Strength
Symbol
Capacitance $C = \frac{Q}{V} = \rho \frac{A}{l}$
Voltage $V = \frac{Q}{C}$
Electric Charge Q = V C
Voltage $V = \frac{1}{C} \int I dt$
Current $I = C \frac{dV}{dt}$
Energy $P = \frac{1}{2} C V^2$
Reactance $X_L = \frac{V_L}{I_L}$
$X_L = \frac{1}{\omega C} \angle -90$
$X_C = \frac{1}{j\omega C}$
$X_C = \frac{1}{s C}$
Impedance $Z_C = R + X_C$
$Z_C = R \angle 0 + \frac{1}{\omega C} \angle 90 = \sqrt{R^2 + (\frac{1}{\omega C})^2} \angle Tan^-1 \omega \frac{L}{R}$
$Z_C = R + \frac{1}{j\omega C} = \frac{1}{R}(1 + j\omega T)$
$Z_C = R + \frac{1}{sC} = \frac{1}{R} (1 + sT)$
Frequency Response