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Current, voltage drop and heat

If a current is sent through a copper wire, this causes a voltage drop at the connected device as well as generation of heat in the wire itself.
Depending on the specific application and the ambiant temperature, this will lead to a certain minimal wire size (square diameter i.e. mm² ) of the wire to meet specifications and demands.

As a rule of thumb you could determine if in a certain application the bottleneck will be either voltage drop or heat generation in the cable. To calculate both, you see a formula for voltage drop and graphs for determining the generation of heat.

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Voltage drop

Regularly, a voltage drop of 5% is taken in account as acceptible for most applications. Check your specific application to find out if this is acceptable!
At a 12 Volt application that would mean a voltage drop of 0.6 Volt.

As in a higher Voltage application a certain percentage would mean a higher voltage drop, this leads to a lower acceptable wire size compared to a lower voltage application if the current is equal! Unless, as stated above, not the voltage drop but the generated heat is the limitation in the design!

 

Calculating the required minimal wire size when the maximal voltage drop and maximal current are known:

Wire size (mm2) =

 wire length (m) x 2 x current (A) x 0,0175
Acceptable voltage drop (Volt)

 

Heat generation

When a current flows through a copper wire, a voltage drop will occur at the end of the wire. So the wire itself dissipates power and thus generates heat.
This leads to a temperature rise. How much depends on many parameters: the wire insulation, and the possibility to transfer heat to the environment of the wire (is it a single wire with air flowing around it, or is it a part of a cable or bundle of wires, in which there are other wires possibly generating heat?).

For a good estimation of the temperature rise in wires in a range of wire sizes (mm²) you can use the below graph. Higher currents and/or multi wire applications lead to higher temperature rises compared to lower currents and/or single wire applications.

Add the ambiant temperate to the temperature rise and you are able to estimate the temperature your wire will rise to. This enables you to choose the temperature your wire must be specified to and/or the wire size in mm² (or that you have to improve the heat flow from the wire to the environment!).

 Copper wire temperature versus current curves

Short circuit or other peak situations: in some cases these situations are taken in account in the design. Meaning that wire sizes are calculated for situations that would normally not occur.
Tip: This is not always necessary in this way. Some of our wires have a much higher peak temperature rating than the maximum continuous temperature.
For example the SPEC44 wire had a temperature specification of 150°C, but can temporarily withstand 300°C as the insulation is unmeltable. Enabling to calculate with the 150° for normal use, and with 300°C for short circuit situations often enables a smaller and thus lighter and cheaper wire size! For as long as temperature is the bottleneck instead of voltage drop ...

 

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