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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. 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. 


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! 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:
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. 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. 
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