# Calculate the temperature rise in a wire due to current

An insulated wire, if I pass a current at a given voltage, what will the temperature rise be.

Below is what I think I understand so far ...

I'm assuming the insulated wire is a 5 m long single conductor in free air ambient air at 20°C, with no active cooling. A typical 20 AWG stranded wire is 0.62 mm2 CSA and has a resistance of 32.4 Ω/km.

A device draws a constant 10 amps at 12 V through the wire.
There would be a volt drop over the 5 m wire.

10 A x (5 m x 0.0324) = 1.62 V

Total power passing into the wire is P = IV 120 W and power lost in the wire is 1.62 V X 10 A = 16.2 W

This power 'loss' will try to heat the wire. The natural cooling effect around the wire will tend to cool the wire towards ambient.
The difference between these two factors should result in the temp rise of the wire.

But how would I calculate the Temp rise in degrees C? I am aware that the insulation has an absolute upper operational limit of 105°C.
I appreciate that the insulation will have a big effect this, are there ball park values for PVC or other ways to estimate this value?

• This cannot be computed without insulation cable specs. But it will be hot. Aug 16, 2021 at 14:54
• Calculating/simulating is hard. Looking it up is easier. Insulation rating is something you can specify- I've seen as low as 60°C and as high as 200°C or more. It makes a big difference whether you have wires bundled or not, the altitude and other factors. Aug 16, 2021 at 14:54
• Ball park = use a current table. Otherwise this is a question for Physics SE question and brush up on your calculus, specifically differential equations because that's the equation you will need to solve ala en.wikipedia.org/wiki/Heat_equation Aug 16, 2021 at 15:08
• I remember seeing years ago somewhere a preview for a book about cables and such, and one page (and the next few) had a detailed mathematical analysis for the temperature in a conductor. It involved heavy mathematical formulas, very impressive, only to have something along the lines of: "this is the theory, in practice it can vary depending on ...", at the end. I guess that makes the conclusion. Either that or FEMM & co. Aug 16, 2021 at 15:22
• You also need to consider heat loss through the connections at each end of the wire. Although the area of these is much smaller than the insulated surface of the wire the thermal conductance is likely much, much higher. Aug 16, 2021 at 15:37