Electronics Handbook/Components/Capacitors

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Capacitor[edit]

Capacitors.JPG

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

Capacitor.gif

DC Characteristics[edit]

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

Charge[edit]

Q = C V

Voltage[edit]

V = \frac{Q}{C}

Capacitance[edit]

R = \frac{Q}{V}

AC Characteristics[edit]

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

Voltage[edit]

v = C \frac{dv}{dt}

Current[edit]

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

Reactance[edit]

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

Impedance[edit]

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[edit]

\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[edit]

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

Capacitor Types[edit]

There are two main types of Capacitors

Fixed Capacitor[edit]

Capacitor that has a fixed value
Capacitors box.jpg Capacitors dipped.jpg Tantalum capacitor.JPG

Variable Capacitor[edit]

Variable capacitors.jpg
Capacitor that has a variable value adjusted by a dial

Capacitor Configuarations[edit]

Series Connection[edit]

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

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

Parallel Connection[edit]

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

2 Port Connection[edit]

  1. 2 Port Connection

Summary[edit]

Component Capacitor
Construction Capacitor is made from two conducting plates separated by a dielectric of dimension Length l, Diện Tích A , Dielectric Strength
Symbol Capacitor.gif
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