Thermal limiting current density simply explained using copper

Different properties of copper

• For example, when it comes to whether a cable should be made of copper or aluminum, various properties of the substances are compared.
• Aluminum is lighter than copper, so it can make sense to make a wire out of aluminum if weight is a concern.
• But aluminum has a higher resistance, for this reason a larger cross-section must be selected, which can cancel out the weight advantage.
• When heated, aluminum expands more, which must also be taken into account when making a decision.
• The thermal limiting current density of copper is 154 A / mm², while that of aluminum 102 A / mm² amounts to.


Resistance of copper wire - what you should know about its specific resistance

Ever since electricity became a household name, we have known the special ...

The latter value in particular is of great importance when it comes to calculating the required cable cross-section.

Importance of the thermal limiting current density

• When you pass current through a wire, the wire will heat up. This heating increases the higher the current strength and the longer you expose the wire to this current.
• If no cooling takes place, it applies that P = I² R and Q = P t. So Q = I² R t. So you can assume that the temperature depends linearly on the time and squared on the current strength.
• If you let a certain current flow through the wire for exactly one second, the wire will heat up to a certain temperature. A sudden increase in temperature is therefore not to be expected.
• Because of the Brownian molecular motion, which increases with increasing temperature, it becomes more and more difficult for the electrons to flow through the wire. So the resistance R is not constant because a warm wire has a higher resistance.
• As soon as you have exceeded a certain current strength, there will be a sudden increase in resistance and thus in heat. That is what is meant by thermal limiting current density.
• According to the definition, this is achieved when the current has a cable cross-section of 1 mm² causes a temperature increase of 200 K in one second.

So if you want to send 1,000 A through a cable without this temperature increase occurring, the copper cable must have a cross-section of more than 1000 A: 154 A / mm² = 6.5 mm² to have. For example, if you made the line out of aluminum, it would have to be 1000 A: 102 A / mm² = 9.8 mm² to have.