Electrical resistance

The electrical resistance of an electrical conductor is a measure of the difficulty of passing an electric current through a substance. It explains the relationship between voltage (amount of electrical pressure) and the current (flow of electricity). With more resistance in a circuit, less electricity will flow through the circuit. The inverse of resistance is conductance, a measure not much used.

Resistance, discovered by Georg Simon Ohm in 1827, is the ratio between voltage and current. Ohm's law said that the voltage between any two points in a conductor changes directly as the current between the two points, given the temperature remains the same. He described it with the equation:

<math>R = \frac{V}{I}</math>

which models the ratio, where:

<math display="inline">R</math> is the resistance of the object, measured in ohms (Ω)
<math display="inline">V</math> is the voltage across the object, measured in volts (V)
<math display="inline">I</math> is the current going through the object, measured in amperes (A)

Calculating resistance

The resistance of a wire increases as it becomes longer and decreases as it becomes wider. (A simple analogy is a road - the more lanes there are, the less traffic there is.) The resistance R of a wire with a constant width, therefore, can be calculated as:

<math>R = \rho\frac{\ell}{A}, \,</math>

where <math>\ell</math> is the length of the conductor, measured in meters [m], <math display="inline">A</math> is the cross-sectional area of the conductor measured in square meters [m²], and ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-meters (Ω m).

Example: Calculate the resistance of copper wire with a radius of 2mm and a length of 5 meters.

Solution:

The resistivity (<math>\rho\,</math>) of copper is <math>1.68*10^{-8} \,</math> Ω m.
The cross sectional area (<math>A\,</math>) is <math>\pi r^2=\pi *(2*10^{-3})^2=4\pi *10^{-6}\,</math> square meters
The length (<math>\ell\,</math>) is <math>5\,</math> meters

Because: <math>R = \rho\frac{\ell}{A}, \,</math>

<math>R = 1.68*10^{-8} \frac{5}{4\pi *10^{-6}}\thickapprox 6.685*10^{-3}\Omega \,</math>

Applications

Resistors are used in electrical circuits to provide electrical resistance.