# Fundamental Physics/Electronics/Resistors

## Resistor

A resistor ( $R$ ) is an electronic component that resists, restricts, or opposes the flow of electrical current. Symbol of resistor Construction of resistor $R=\rho {\frac {l}{A}}$ where $l$ is the length of the conductor, measured in metres [m], A is the cross-section area of the conductor measured in square metres [m²] and ρ (rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-metres (Ω·m).

In This formula $\rho ,{l},{A}$ are constant,therefore $R$ already is constant.

## Resistance Resistance is the resistor's characteristic to resist the current flow and reduces the voltage. Resistance has symbol R measured in ohm Ω can be calculated from Ohm's law

Ohm's law

$V=IR$ Therefore,

$R={\frac {V}{I}}$ ## Electricity response

 passive electrical component Picture Electric response Resitor DC response $V=IR$ $I={\frac {V}{R}}$ $P_{V}=IV$ $R={\frac {V}{I}}={\frac {1}{G}}=\rho {\frac {l}{A}}$ $G={\frac {I}{V}}={\frac {1}{R}}=\sigma {\frac {A}{l}}$ $B=IL=I{\frac {\mu }{2\pi r}}$ $P_{R}=I^{2}R(T)$ $R(T)=R_{o}+nT$ $R(T)=R_{o}e^{nT}$ $P=P_{V}-P_{R}$ AC response $v_{R}(t)=i(t)Z_{R}$ $i_{R}(t)={\frac {v(t)}{Z_{R}}}$ $P_{R}(t)=i(t)^{2}Z_{R}={\frac {v^{2}(t)}{Z_{R}}}$ $Z_{R}={\frac {v_{R}(t)}{i_{R}(t)}}=R+X_{R}=R\angle 0=R$ $X_{R}=0$ ## Resistor Configuration

### Resistors in Series

For n resitors connected adjacent to each other as shown

The total resistance

$R_{1}+R_{2}+...+R_{n}$ For 2 series resistor of same value

$R_{t}=R_{1}+R_{2}=R+R=2R$ ### Resistors in parallel

For n resitors connected facing each other as shown

The total resistance

${\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+...+{\frac {1}{R_{n}}}$ For 2 parallel resistor of same value

${\frac {1}{R_{t}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}={\frac {R_{1}+R_{2}}{R_{1}R_{2}}}={\frac {R+R}{RR}}={\frac {2R}{RR}}={\frac {2}{R}}$ $R_{t}={\frac {1}{2}}R$ ### Resistors in 2 port network

2 resistor to form 2 port network as shown

$v_{o}={\frac {v_{i}}{R_{1}+R_{2}}}R_{2}$ ${\frac {v_{o}}{v_{i}}}={\frac {R_{1}+R_{2}}{R}}_{2}$ 3 resistor connected in T configuration

$v=v_{i}{\frac {R_{2}}{R_{1}+R_{2}}}$ $v=v_{o}{\frac {R_{2}}{R_{3}+R_{2}}}$ ${\frac {v_{o}}{v_{i}}}={\frac {R_{3}+R_{2}}{R_{1}+R_{2}}}$ 3 resistor connected in Π configuration

$i_{1}={\frac {v_{i}}{R_{1}}}$ $i_{3}={\frac {v_{o}-v_{i}}{R_{2}}}$ $i_{3}={\frac {v_{o}}{R_{3}}}$ $i_{1}=i_{2}+i_{3}$ ${\frac {v_{i}}{R_{1}}}={\frac {v_{o}-v_{i}}{R_{2}}}+{\frac {v_{o}}{R_{3}}}$ ${\frac {v_{o}}{v_{i}}}={\frac {Y_{3}+Y_{2}}{Y_{1}+Y_{2}}}$ ## Resistor color code

Color Significant
figures
Multiplier Tolerance Temp. Coefficient (ppm/K)
Black 0 ×100 250 U
Brown 1 ×101 ±1% F 100 S
Red 2 ×102 ±2% G 50 R
Orange 3 ×103 15 P
Yellow 4 ×104 (±5%) 25 Q
Green 5 ×105 ±0.5% D 20 Z
Blue 6 ×106 ±0.25% C 10 Z
Violet 7 ×107 ±0.1% B 5 M
Gray 8 ×108 ±0.05% (±10%) A 1 K
White 9 ×109
Gold ×10-1 ±5% J
Silver ×10-2 ±10% K
None ±20% M
1. Any temperature coefficent not assigned its own letter shall be marked "Z", and the coefficient found in other documentation.