# Electronics Handbook/Components/Resistors

## Resistor

Resistor is an electronic component made from straight wire conductor of the dimension

Length l,
Area A, that has a
Conductivity $\rho$

Resistor has Electronic Symbol shown below

## Characteristics

### Resistance

The characteristic of the Resistor is defined by its Resistance R which measures the resistance of the Resistor to the current flow

$R = \frac{1}{\rho}\frac{A}{l}$

### DC Characteristics

When connect Resistor with a DC voltage source in a closed loop circuit

Voltage

$V = I \times R$

Current

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

Resistance

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

Energy Supplied

$E_V = V I$

Energy Dissipated as heat or Energy Loss as Heat into the surrounding

$E_R = \frac{V^2}{R} = I^2 R$

Energy Transfer

$E = E_V - V_R = I ( V - IR ) = V ( I - \frac{V}{R} )$

The Efficiency of Energy transfer

$n = \frac{E}{E_V} = \frac{V - IR}{V} = \frac{I - \frac{V}{R}}{I}$

### AC Characteristics

When connect Resistor with a AC voltage sourse in a closed loop circuit

Voltage

$v = i \times R$

Current

$i = \frac{v}{R}$

Power

$p = \frac{v^2}{R} = i^2 R$

Impedance

$Z_R = \frac{v}{i}$

## Resistor Types

Resistor are availble in two main types

### Fixed Resistor

Resistor of a fixed value

### Variable Resistor

Resistor of a variable value

## Colored Band Coded Value

 Đen (Black) Nâu(Brown) Đỏ (Red) Cam (Orange) Vàng (Yellow) Xanh Lá Cây (Green) Xanh Da trời(Blue) (Tím (Violet) Xám (Grey) Trắng (White) 0 1 2 3 4 5 6 7 8 9

## Resistor Configurations

### Series Configuration

Two or more resistor can be connected in series to increase the total resistance . The Total Resistance is equal to the sum of all the resistor's resistance . The total resistance In Series connected circuit Current and voltage will be reduced

$R_{eq}=R_1+R_2+R_3+...+R_n \,$

When connect two reistors of the same resistance the total resistance is doubled

R + R = 2R

### Parallel Configuration

Two or more resistor can be connected in parallel to decrease the total resistance .

$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$

### 2 Port Network Configurations

Configuration $\frac {V_o}{V_i}$
$\frac {V_o}{V_i} = \frac{R_2}{R_2 + R_1}$
$\frac {V_2}{V_1} = \frac{R_3 + R_1}{R_2 + R_1}$
• Mạch Chia Điện

Mạch Điện của hai điện trở mắc nối theo hình trên

$I = \frac{V}{R_2 + R_1}$
$V_o = I R_2 = V \frac{R_2}{R_2 + R_1}$
$\frac{V_o}{V_i} = \frac{R_2}{R_2 + R_1}$
• Mạch T

Nếu điện thế trên R2 bằng V

$V = V_2 \frac{R_1}{R_1 + R_3} = V_1 \frac{R_1}{R_2 + R_1}$
$\frac{V_1}{V_2} = \frac{R_1 + R_2}{R_1 + R_3}$
• Mạch π

Mạch điện với 3 Điện Trở bắt theo dạng hình π . Với R1 tại cổng nhập, Với R3 tại cổng xuất

IR1 = IR2 + IR3
$\frac{v_i}{R_1} = \frac{v_i - v_o}{R_2} + \frac{v_o}{R_3}$
$\frac{v_i}{v_o}= ( \frac{R_3}{R_1} ) ( \frac{R_2 - R_1}{R_2 - R_3} )$
$\frac{v_o}{v_i}= ( \frac{R_3}{R_1} ) ( \frac{R_2 - R_1}{R_2 - R_3} )$
• Mạch Nối Tiếp Song Song
$R_{EQ} = (R_1 \| R_2) + R_3 = {R_1R_2 \over R_1 + R_2} +R_3$
• Delta-Star Transformation

$R_1 = \frac{R_\mathrm{a}R_\mathrm{b}}{R_\mathrm{a} + R_\mathrm{b} + R_\mathrm{c}}$
<mathrm{b}R_\mathrm{c}}{R_\mathrm{a} + R_\mathrm{b} + R_\mathrm{c}} [/itex]
$R_3 = \frac{R_\mathrm{c}R_\mathrm{a}}{R_\mathrm{a} + R_\mathrm{b} + R_\mathrm{c}}$

• Y - Δ Hoán Chuyển
$R_\mathrm{a} = \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_2}$
$R_\mathrm{b} = \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_3}$
$R_\mathrm{c} = \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1}$

## Summary

Component Resistor
Construction Resistor is made from straight line conductor with the following dimension Length l , Area A , Conductivity \rho
Symbol
Reistance $R = \frac{V}{I} = \frac{1}{\rho} \frac{A}{l}$
Voltage V = I R
Current $I = \frac{V}{R}$
Resistance & Temperature $R = R_0 + NT$ for Conductor
$R = R_0 e^NT$ for Non Conductor
Energy loss as heat & Resistance $P_R = VI = I^2 R = \frac{V^2}{R}$
Energy supplied PV = VI
Energy transmitted P = PV - PR
$P = V - IR$
$P = I - \frac{V}{R}$
Energy Efficiency $n = \frac{P_V Cos\theta}{P_V} = Cos\theta$
$n = \frac{V - IR}{V}$
$n = \frac{I - \frac{V}{R}}{V}$
Resistance $Z_R = R$ /_ 0
$Z_R = R$
$Z_R = R$
Coded Color

Hệ Thống Vạch Màu giá trị của điện trở

 Đen (Black) Nâu(Brown) Đỏ (Red) Cam (Orange) Vàng (Yellow) Xanh Lá Cây (Green) Xanh Da trời(Blue) (Tím (Violet) Xám (Grey) Trắng (White) 0 1 2 3 4 5 6 7 8 9