Electronics Handbook/Components/Resistors

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Resistor[edit]

Resistors.jpg

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

Resistor.gif

Characteristics[edit]

Resistance[edit]

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[edit]

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[edit]

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[edit]

Resistor are availble in two main types

Fixed Resistor[edit]

Resistor of a fixed value

Resistors.jpg

Variable Resistor[edit]

Resistor of a variable value

PCB variable resistors.jpg

Colored Band Coded Value[edit]

4-Band Resistor.svg
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[edit]

Series Configuration[edit]

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

Resistors in Series.svg
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[edit]

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[edit]

Configuration \frac {V_o}{V_i}
PotentialDivider.png \frac {V_o}{V_i} = \frac{R_2}{R_2 + R_1}
Superposition Example.svg \frac {V_2}{V_1} = \frac{R_3 + R_1}{R_2 + R_1}
  • Mạch Chia Điện
Voltage divider.svg

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
Superposition Example.svg

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
Resistorscombo.png
R_{EQ} = (R_1 \| R_2) + R_3 = {R_1R_2 \over R_1 + R_2} +R_3
  • Delta-Star Transformation

Delta-Star Transformation.svg

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}} </math>
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[edit]

Component Resistor
Construction Resistor is made from straight line conductor with the following dimension Length l , Area A , Conductivity \rho
Symbol Resistor.gif
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 4-Band Resistor.svg

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

References[edit]