# Fundamental Physics/Electronics/Resistors

## Resistor

A resistor ( ${\displaystyle R}$ ) is an electronic component that resists, restricts, or opposes the flow of electrical current.

### Resistor Construction

The electrical resistance of a given object depends primarily on two factors:

• What material is it made?
• what is shape?

therefore, can be computed as:

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

where ${\displaystyle l}$ 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 ${\displaystyle \rho ,{l},{A}}$ are constant,therefore ${\displaystyle R}$ already is constant.

### Resistor's 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

${\displaystyle V=IR}$

Therefore,

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

## Resistor in DC circuit

### Resistance

Ohm law ${\displaystyle V=IR}$

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


where:

R is resistance (ohms, Ω),
V is voltage (volts, V),
I is current (amperes, A).

### Conductance

Conductance (G) is defined as the inverse of resistance, calculated as:

${\displaystyle G={\frac {1}{R}}}$

where:

G is conductance (siemens, S).

### Voltage

Voltage is calculated as:

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

### Current

Current is calculated as:

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

### Power

Power is calculated as:

${\displaystyle P=I\cdot V\;\;\;\;\;\;\ and\;\;\;\;\;\;\ I={\frac {V}{R}}\;\;\;\;\;\;\ and\;\;\;\;\;\;\ V=R\cdot I}$
${\displaystyle P=I^{2}R\;\;\;\;\;\;\ P={\frac {V^{2}}{R}}}$

## Resistor in AC circuit

### Voltage

${\displaystyle v=iR}$

### Current

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

### Power

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

### Reactance

${\displaystyle X_{R}={\frac {v}{i}}=0}$

### Impedance

${\displaystyle Z_{R}=X_{R}+R=R}$

### Phase

v and i are in phase

## Resistor Configuration

### Resistors in Series

For n resitors connected adjacent to each other as shown

The total resistance

${\displaystyle R_{1}+R_{2}+...+R_{n}}$

For 2 series resistor of same value

${\displaystyle R_{t}=R_{1}+R_{2}=R+R=2R}$

### Resistors in parallel

For n resitors connected facing each other as shown

The total resistance

${\displaystyle {\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+...+{\frac {1}{R_{n}}}}$

For 2 parallel resistor of same value

${\displaystyle {\frac {1}{R_{t}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}={\frac {R_{1}+R_{2}}{R_{1}R_{2}}}={\frac {R+R}{RR}}={\frac {2R}{RR}}={\frac {2}{R}}}$
${\displaystyle R_{t}={\frac {1}{2}}R}$

### Resistors in 2 port network

2 resistor to form 2 port network as shown

${\displaystyle v_{o}={\frac {v_{i}}{R_{1}+R_{2}}}R_{2}}$
${\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {R_{1}+R_{2}}{R}}_{2}}$

3 resistor connected in T configuration

${\displaystyle v=v_{i}{\frac {R_{2}}{R_{1}+R_{2}}}}$
${\displaystyle v=v_{o}{\frac {R_{2}}{R_{3}+R_{2}}}}$
${\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {R_{3}+R_{2}}{R_{1}+R_{2}}}}$

3 resistor connected in Π configuration

${\displaystyle i_{1}={\frac {v_{i}}{R_{1}}}}$
${\displaystyle i_{3}={\frac {v_{o}-v_{i}}{R_{2}}}}$
${\displaystyle i_{3}={\frac {v_{o}}{R_{3}}}}$
${\displaystyle i_{1}=i_{2}+i_{3}}$
${\displaystyle {\frac {v_{i}}{R_{1}}}={\frac {v_{o}-v_{i}}{R_{2}}}+{\frac {v_{o}}{R_{3}}}}$
${\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {Y_{3}+Y_{2}}{Y_{1}+Y_{2}}}}$

## 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.
2. For more information, see EN 60062.
3. Yellow and Gray are used in high-voltage resistors to avoid metal particles in the lacquer.

Resistors found in electronic kits and hobby projects have up to four bars indicating the color code. The first two bars represent the first and second significant digit, the third represents the exponent or decimal multiplier, and the fourth represents the tolerance. The chart to the right shows information about the color coding on resistors.