In an electric circuit, the component which the main purpose is to difficult the flow of electrical currents is called electrical resistance or resistor.

Important definitions:

- Electrical resistance \((R)\) :
- A resistive element of a circuit is said to be a ohmic resistance if it does not depend on the voltage applied, neither it depends on the direction or intensity of the current (Ohm's Law). For these elements, the electrical resistance is a constant ratio between the potential difference \(\mathbb{V}\) between the conductor terminals and the current intensity \(i\) passing through it, so $$ R = \frac{\mathbb{V}}{i}.$$ The electrical resistance of a solid depends on two factors:
- The number of free electrons in its structure;
- The mobility of free electrons through the solid molecules network.

- Ohmmeter:
- It is the instrument used to measure the electrical resistance.

A conductor obeys Ohm's law if the value of its resistance is independent of the potential difference and current \(i\) applied. That is, the potential drop \(\mathbb{V}\), on an ohmic resistance \(R\), which is traversed by a current \(i\), is given by: $$\mathbb{V} = R i.$$ Ohm's law is an empirical law and is valid for some materials. In general, metal conductors are ohmic, but others may not be, as gases or liquids, and other electronic devices such as transistors and diodes. For the latter, the variation of the \(\mathbb{V}\) with the current intensity is not linear. These are called non-ohmic or non-linear conductors. However, we can state that for small variations of \(\mathbb{V}\), almost all conductors of nature obey Ohm 's Law.

For a conductor cylinder, made of a material with resistivity \(\rho\) , its electrical resistance is directly proportional to its length \(L\) and inversely proportional to the area \(A\) of its cross-section, such that: $$ R = \rho \frac{L}{A}.$$

The unit of resistivity in \(IS\) is Ohm \(\times\) meter, \([\rho]=\Omega m\) .Other quantities related to resistivity are:

- Conductance \((G)\)
- It is the inverse of the electrical resistance $$G = \frac{1}{R}.$$ The electrical conductance unit is the Siemens, \([G]= S = \frac{1}{\Omega}\) .
- Conductivity \((\sigma)\)
- It is the inverse of resistivity, $$ \sigma = \frac{1}{\rho}.$$

- as heat generators (electric irons, ovens);
- to limiting electrical current;
- as voltage dividers.

Color | 1 alg | 2nd alg | Multip | Tolerance |
---|---|---|---|---|

None | - | - | - | 20% |

Silver | - | - | \(10^{-2}\) | 10% |

Gold | - | - | \(10^{-1}\) | 5% |

Black | - | 0 | \(10^{0}\) | - |

Brown | 1 | 1 | \(10^{1}\) | 1% |

Red | 2 | 2 | \(10^{2}\) | 2% |

Orange | 3 | 3 | \(10^{3}\) | - |

Yellow | 4 | 4 | \(10^{4}\) | - |

Green | 5 | 5 | \(10^{5}\) | 0.5% |

Blue | 6 | 6 | \(10^{6}\) | |

Violet | 7 | 7 | \(10^{7}\) | |

Grey | 8 | 8 | \(10^{8}\) | |

White | 9 | 9 | \(10^{9}\) |

In addition to the resistor of constant resistence, there are resistors with variable resistance, known as rheostats. There are rheostats that can change continuously between certain resistance limits, and there are others whose resistance can only assume discrete values.

For a conductor to obey Ohm's law will depend on how its resistance changes with temperature. Once there is an increase in temperature the vibration of the molecules of the material increases, and will be greater the number of collisions between the moving charges and vibrating molecules. With this, resistance increases since the current has more dificult to flow.

A resistive material \(R_0\) at a temperature \(T_0\) have a higher resistance \(R\) when undergoing a temperature change \(T - T_0\) . For many materials, the relationship between temperature and resistance is given by the equation $$R=R_0[1+\alpha(T-T_0)],$$ where \(\alpha\) is the thermal coefficient of variation of resistance.