Parallel wires

[skylink]

I have a question. If you have two parallel runs and one wire is significantly larger than the other will the small wire overheat? Example: You have a 6awg wire in parallel with a 18awg wire connected to a 50amp load @ 240V. What happens? (I would never do this, I'm just curious when It comes to electrical theory)

 

[d0nut]

Yes, the current will divide between your two conductors based on the resistance of each conductor.

 

[EC Dan]

Using the formula for a current divider, for your example you'd get 47 A through the 6 AWG and 3 A through the 18 AWG wires, which are both below the minimum (non-corrected and non-adjusted) ampacities of those wires.

 

[synchro]

As EC Dan mentions, the current will divide such that neither conductor will be overloaded. An issue to consider is that if the 6 AWG gets disconnected, then the 18 AWG will conduct the entire 50A (at least until it burns out).

 

[LarryFine]

Using the formula for a current divider, for your example you'd get 47 A through the 6 AWG and 3 A through the 18 AWG wires, which are both below the minimum (non-corrected and non-adjusted) ampacities of those wires.

What's keeping the current so low in the 18g wire in your theory?

 

[synchro]

What's keeping the current so low in the 18g wire in your theory?

It has about 16 times the resistance of the 6 AWG wire, but they both have the same voltage across them.

The current divider formula for parallel resistors R1 and R2 is that when a current I is applied to them, the current though R1 will be I x R2/(R1+R2), and the current through R2 will be I x R1/(R1+R2).

 

[wwhitney]

As EC Dan mentions, the current will divide such that neither conductor will be overloaded.

Conductance (1/R) is proportional to the area of the conductor, and in the current divider, the current will divide in proportion to the conductances.

So if ampacity were proportional to area, then you could parallel two equal length wires of different sizes, apply a current equal to the sum of their ampacities, and expect the current to divide with each wire carrying its ampacity.

Since ampacity isn't proportional to area in general (for large sizes the ampacity increases less than proportionally as the area increases), that won't work in general.

Of course in the example, the current applied is 50A, less than the sum of the ampacities.

Cheers, Wayne

 

[skylink]

It has about 16 times the resistance of the 6 AWG wire, but they both have the same voltage across them.

The current divider formula for parallel resistors R1 and R2 is that when a current I is applied to them, the current though R1 will be I x R2/(R1+R2), and the current through R2 will be I x R1/(R1+R2).

Okay, so the smaller wire is limiting the current, but can it overheat?

 

[winnie]

My hunch is that in an unequal size parallel installation the _larger_ conductor will be the one to overheat.

But this is not as simple as just comparing the cross section of the wires because in addition to the resistance effects you will also have various induction and proximity effects, so I'd call this a rough guess not a solid analysis.

Consider a #8 Cu in parallel with a #3 Cu.

The #8 has a 75C ampacity of 50A, the #3 100A.
The #8 has a cross section of 8.37mm^2, the #3 26.7

Push 150A through this parallel set, and I'd expect about 36A in the #8 and 114A in the #3.

-Jon

 

[Dsg319]

Where you at Gar?

This would be a great bench test to complete.

 

[EC Dan]

My hunch is that in an unequal size parallel installation the _larger_ conductor will be the one to overheat.

But this is not as simple as just comparing the cross section of the wires because in addition to the resistance effects you will also have various induction and proximity effects, so I'd call this a rough guess not a solid analysis.

Consider a #8 Cu in parallel with a #3 Cu.

The #8 has a 75C ampacity of 50A, the #3 100A.
The #8 has a cross section of 8.37mm^2, the #3 26.7

Push 150A through this parallel set, and I'd expect about 36A in the #8 and 114A in the #3.

-Jon

To further your hunch, I actually don't think there's any combination of two unequal wire sizes (but same insulation) in which the larger size can safely carry it's share of the current while the smaller wire overheats on it's share of the current. If that's the case then his question on whether the smaller wire will overheat can actually be answered generally as "no". I haven't fleshed out this idea so someone may prove that wrong.

 

[skylink]

My hunch is that in an unequal size parallel installation the _larger_ conductor will be the one to overheat.

But this is not as simple as just comparing the cross section of the wires because in addition to the resistance effects you will also have various induction and proximity effects, so I'd call this a rough guess not a solid analysis.

Consider a #8 Cu in parallel with a #3 Cu.

The #8 has a 75C ampacity of 50A, the #3 100A.
The #8 has a cross section of 8.37mm^2, the #3 26.7

Push 150A through this parallel set, and I'd expect about 36A in the #8 and 114A in the #3.

-Jon

Ughh...I thought this would be a simple answer. How did u come up with that answer?

 

[wwhitney]

To further your hunch, I actually don't think there's any combination of two unequal wire sizes (but same insulation) in which the larger size can safely carry it's share of the current while the smaller wire overheats on it's share of the current. If that's the case then his question on whether the smaller wire will overheat can actually be answered generally as "no". I haven't fleshed out this idea so someone may prove that wrong.

I imported NEC Chapter 9 Table 8 and (2017) Table 310.15(B)(16) into a spreadsheet, and I checked that "ampacity/kcmil" is strictly a decreasing function of kcmil, for both aluminum and copper, and for all 3 insulation temperatures. I thought that due to rounding to the nearest 5 amps, there was a chance that wouldn't be true for some of the small sizes, but it didn't happen.

So under the approximation "impedance/length is proportional to 1/kcmil," then the above is true. Is that approximation really going to be off by more than a couple percent in this context?

Cheers, Wayne

 

[electrofelon]

My hunch is that in an unequal size parallel installation the _larger_ conductor will be the one to overheat.

But this is not as simple as just comparing the cross section of the wires because in addition to the resistance effects you will also have various induction and proximity effects, so I'd call this a rough guess not a solid analysis.

Consider a #8 Cu in parallel with a #3 Cu.

The #8 has a 75C ampacity of 50A, the #3 100A.
The #8 has a cross section of 8.37mm^2, the #3 26.7

Push 150A through this parallel set, and I'd expect about 36A in the #8 and 114A in the #3.

-Jon

interesting discussion. My quick knee jerk answer would be that the smaller conductor would overheat, but when you do the math it tells a different story.

 

[winnie]

Responding to my calculation

Ughh...I thought this would be a simple answer. How did u come up with that answer?

The two wires are two resistors in parallel.

You just use Ohm's law, V = I * R, and note that since the wires are connected at both ends, V must be the same.

So I1 * R1 = I2 * R2

Resistance is inversely proportional to cross section (approximately, ignoring things like 'skin effect')

So I1/A1 = I2 / A2

Look up the cross section of the two wires in question. For #8 A1 = 8.37. For #3 A2 = 26.7

Total current is I1 + I2, and to make up the problem I just added the 75C ampacity of the conductors (150A total), but you could pick any value.

This gives two equations:
I1 / 8.37 = I2 / 26.7
I1 + I2 = 150

Then it is just simple algebra.

-Jon

 

[GoldDigger]

What has been left out so far is that the temperature of the wire will depend on both the power converted to heat in the wire and the thermal resistance between the wire and the environment. The surface area of a length of wire goes up only as the first power of the diameter, so it seems to me that the larger conductor is more likely to overheat.

 

[Arester]

Interesting … I think initially the current will be divided as already suggested according to resistance. Later on though since the power released in wire grows with square of current and dissipation ability per kcmil increase only proportionally with diameter. The larger wire resistance will grow faster forcing the smaller wire to take on more than it’s initial (fair) share of current

When the total current is substantially smaller than the assembly total ampacity some equilibrium may be reached if there is adequate cooling. Typically however the smaller wire will burn.

Maybe that is why our ancestors that put NEC together insisted that identical wires be used for parallel feeders and if that was not enough they asked to make sure that their length is also identical.

The pandemic left me with some spare time to ponder the issue of wire operating temperature at certain loads and ambient temperatures that I never had time to analyse before. The result is a voltage drop calculator that takes all of this in to account and actually shows wire resistance at different temperatures. Take a look – it may allow verification of the above – without causing smoke. It works without registration up to # 6 AWG.

https://mc-group.ca/voltage_drop_calculator.htm

 

[Sea Nile]

As the small wire heats up, it's resistance will increase resulting in more current traveling in the larger wire.

Copper and electricity. Resistance and heating.

An interactive on-line booklet for post 16 physics students about copper and electricity, questions and interactive diagrams.

resources.schoolscience.co.uk

excerpt from website: "As the wire gets hotter, the ions vibrate more vigorously. This makes it more difficult for electrons to pass along the wire. Hence the resistance increases."

 

[tallgirl]

However, as the large wire warms, increases it's resistance, shifting more current to the smaller wire, the smaller wire will also warm up, increasing ITS resistance, and shifting load back to the larger wire.

 

[GoldDigger]

I do not think that the effect of conductor heating is significant enough to seriously affect current distribution and heating.
Just note that the ampacity of the pair of non-identical wires will probably be less than the sum of the two independent ampacities because of the difference ratios between resistance and heat dissipation.
Anything other than equal current distribution over equal conductors will end up with the current distribution NOT matching the relative ampacities. No opinion on which conductor will be more stressed at this point. Have to think more about it. Probably the larger one.