# The thickness of the copper wire is important

## Specific resistance copper - information and calculation

### What is the resistivity?

The specific resistance indicates the resistance a certain material has to the flow of electrical current. To put it simply and practically: How well can a wire made of this material conduct electrical energy? The reciprocal of the specific resistance is the conductivity. The specific resistance depends on the density of the atoms and the number of free electrons in this material. The lower the specific resistance, the faster the electrons can flow through this material. The specific electrical resistance is a material constant that is influenced by temperature. This means that a certain material has a certain resistance value at a certain temperature. The symbol is the Greek letter Rho (ρ).

### What is the conductivity of copper compared to other metals?

Copper has a specific resistance of 0.0171 Ohm mm² / m. Compared to other metals, copper has a very high conductivity: only silver has a slightly better conductivity of 0.016 Ohm mm² / m, but is ruled out for mass use due to its high price. With aluminum, the specific resistance of 0.028 ohm mm² / m is significantly higher, with iron it is many times worse with 0.1 ohm mm² / m. This is why copper is the preferred conductor material in electrical engineering and electronics.

### What role do the length and cross-section of a cable play?

The conductivity of a wire or cable is related to its cross-section (calculated in square millimeters) and its length. The shorter and the thicker the cable, the lower its resistance. On the other hand, a long and thick cable can have the same resistance as a short and thin cable. In order to be able to calculate the resistance of a wire or a coil, one has to know the cross-sectional area of the wire. The cross-section (A) of a round wire can be calculated from the diameter (d) using the number Pi (π):

### What role does temperature play?

The resistance of a certain substance depends on its temperature. Metals have a positive temperature coefficient, so they conduct better at low temperatures: the warmer the material, the greater the resistance, while the lower the temperature, the better the conductivity. This is due to physics: In metals, more charge carriers are released at lower temperatures (it is the other way around with semiconductors, which means that they conduct better at higher temperatures).

The factor with which the resistance changes depending on the temperature is the temperature coefficient. With pure metals (i.e. not with alloys) this coefficient is largely constant over a wide temperature range. With the help of the temperature coefficient, the difference in conductivity at a certain temperature in deviation from the conductivity at the reference temperature (for copper this is 20 degrees Celsius) can be calculated. On this basis, the resistance can also be used to measure the temperature: Resistance thermometers use the largely constant temperature coefficient of metals to measure the temperature via the change in resistance.

### How do I calculate the resistance of a conductor?

The specific resistance is the resistance of a conductor one meter long and a square millimeter cross-section at 20 degrees Celsius. It is given in ohms per square millimeter divided by meters (ohms mm² / m) and is 0.0171 ohms mm² / m for copper. That means: A copper wire with an average area of one square millimeter (this corresponds to a diameter of about 1.12838 millimeters) and one meter in length has a resistance of 0.0171 ohms.

So, in order to calculate the resistance (R) of a cable or a coil, you need to consider the diameter and length of the wire. These two values are included with the following formula:

ρ is the specific resistance of copper, which is always the same at 0.0171. Therefore the formula can be simplified as follows:

In this formula, the following characters represent these values:

- R: Resistance of the wire or coil in ohms
- ρ: Specific electrical resistance of the material in ohms mm² / m
- l: length of the conductor in meters
- A: Cross-sectional area in square millimeters

### How is the cross-sectional area calculated?

The cross-sectional area of a wire is calculated using the number Pi (π), which represents the relation between the diameter (d) and the area of a circle. The formula then looks like this:

### What is the standard temperature?

These formulas calculate the resistance without taking the variable temperature factor into account and, for the sake of simplicity, assume a standard temperature of 20 degrees Celsius. To calculate the resistance of a conductor at a different temperature, you have to include the temperature coefficient in the formula.

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