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.
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.