I would never wire something up like this, but I'm just trying to understand the theory behind a real-world application. Although paralleling different size connectors would never be done. The thought occurred to me what if? I have not studied electrical theory in so long that I couldn't make sense of it.

Exactly. We are only trying to anticipate what would happen in theory.
In practice, you have to try it and see.

I suspect 18AWG copper wire will survive 50A continuous.

As I said, there are no ill effects of paralleling 6AWG with 18AWG. The smaller wire does not get any hotter that the larger wire.
Think in terms of cross-sectional area of the copper conductor. All you are doing is adding additional paths for current to flow by adding more cross-sectional area.

As long as the resistivity of the conductor is the same, the current flux in the two wires is the same, i.e. amps per unit area is equal in both wires.

 

Exactly. We are only trying to anticipate what would happen in theory.
In practice, you have to try it and see.

I suspect 18AWG copper wire will survive 50A continuous.

As I said, there are no ill effects of paralleling 6AWG with 18AWG. The smaller wire does not get any hotter that the larger wire.
Think in terms of cross-sectional area of the copper conductor. All you are doing is adding additional paths for current to flow by adding more cross-sectional area.

As long as the resistivity of the conductor is the same, the current flux in the two wires is the same, i.e. amps per unit area is equal in both wires.

To explain it another way it doesn't get any hotter, because it's sharing the load? The two together are providing a less resistive path together then the two would by themselves?

 

To explain it another way it doesn't get any hotter, because it's sharing the load? The two together are providing a less resistive path together then the two would by themselves?

My thinking here is where I went with my first post. The resistivity of AWG 6 wire is about 0.3951 Ohms per 1,000 feet and AWG 18 wire is about 6.385 Ohms per 1,000 feet. Keep in mind round trip as in distance to and back from the load. In this case you have a 240 Volt 50 Amp load. A 240 volt 50 amp load would be about 240 / 50 = 4.8 Ohms so a 4.8 Ohm load. The current leaving the source will split Kirchoff's voltage and current laws apply). Additionally the load will not actually see 240 volts but a little less because of the I * R drop of the cables. The AWG 6 cable will carry the larger of the two conductors since the current is not going to split equally.

Ron

 

Let's do the math.

Cross-sectional area
#6 AWG wire is 26251 CM (circular mils)
#18 AWG wire is 1624.3 CM

#6 AWG wire has 16.16 times more cross-sectional area than #18 AWG wire.

Resistance
#6 AWG is 0.3951Ω per 1000 ft.
#18 AWG is 6.385Ω per 1000 ft.

#18 AWG wire is 16.16 times more resistive that #6 AWG wire for the same length of wire.

We know this from theory because the resistance of a length of wire can be determined as

R = ρ x L / A

where,
R = resistance
ρ = resistivity
L = length
A = cross-sectional area

Thus, if you parallel #18 AWG wire with #6 AWG wire, the #6 AWG wire will take 16 times more current than the #18 AWG wire.

50A load
#6 AWG wire will conduct 16/17 of 50A = 47A
#18 AWG will conduct 1/17 of 50A = 3A

 

Thus, if you parallel #18 AWG wire with #6 AWG wire, the #6 AWG wire will take 16 times more current than the #18 AWG wire.

Ratio and proportion.

Ron

 

Under the conditions,

The 6 AWG will run hotter.

Resistance of the 18 AWG will be 16.2 times the 6 AWG. => The power dissipated in the 6 AWG will be 16.2 times more.
The surface area of the 6 AWG is 4 times more than that of the 18 AWG.

In the long term when the temperatures have stabilized, the 6 AWG whic has a power dissipation 16 times the 18 AWG, but with a surface area (for heat dissipation) only 4 times , the temperature is bound to be higher.

 

One useful application of paralleled wires has been for current measurement purposes. Putting several identical wires in parallel has been used to allow reading higher currents on a clamp-on ammeter probe and it worked very well. The small probe was suffering saturation and would not read the current accurately.
In addition, I once owned a car that used a parallel wire setup to display battery charge/discharge current. That was a Chrysler idea quite a few years ago, their last ammeter hardware offering, I think.

 

To explain it another way it doesn't get any hotter, because it's sharing the load? The two together are providing a less resistive path together then the two would by themselves?

@nd!ru7

you are suffering the effect of lots of experts trying to all be helpful,
and then we drill down into ever increasing levels of minutia

There are many correct answers here,

Bottom line, to a first degree,
two wires in parallel,
current is split between the conductors proportional to the resistance,

Heating is different,
the power dissipated in each wire is Watts = volts times amps,
as volts across the two wires in parallel is the same, the watts are proportional to the current,

the temperature of the wire, as well as the power dissipated,
is dependent upon upon physical properties, such as
coating on wire,
other heating sources
mounting
air flow
et all

These we can not know,
so the minutia of the question about temperature is "un knowable"

As an advice,
there are various tables on line, for various wire sizes , in given situations,
for instance

https://www.engineeringtoolbox.com/wire-gauges-d_419.html

I hope this clarifies thigns,

 

In my neighborhood there are two highways running north and south. One of them has 10 lanes, the other has only two. The 10 lane highway (6 AWG) can carry more traffic (current) than the two lane can. In theory both wires should see the same amount of heating.

BTW: Your drawing cleared it up nicely.

 

I thought that I already said it.

The #6 AWG wire has 16 times more cross-sectional area than the #18 AWG wire.
The #6 AWG wire has 1/16 the resistance of the #18 AWG wire.
The #6 AWG wire will conduct 16 times more current than the #18 AWG wire.

Current flux = current / cross-sectional area is the same in both wires.

There is no appreciable difference in heating effect in the two wires.