For residential work , I would normally use a 100 amp CB for # 4 copper . Not a 125 amp CB .

Wyr
God bless

I only run copper around here because the inspectors take an extra close look at any aluminum wiring that runs inside finished walls. They get out their box and start doing calculations and stuff.
If they saw 4ga on a 125 amp breaker they may not even bother to question it.

This is for a dedicated welder circuit.
NEC 630.11 I think is the one.
Because welders are intermittent variable loads, depending on the welding machines I could as much as double the breaker size over what's normally installed on a given wire size.
I could go as little as 6 gauge on a 100 amp breaker.
But I run my welding circuits to be at least 50% duty cycle for the wire size. Running my miller model 250 which is about out the size of an apartment refrigerator and weighs 360lb, at full power draws about 100 amps. 100 amps on 4 gauge wire is about a 80 or 90% duty cycle. My welder is rated for a 40% duty cycle at full power. If some how I ran the full 125 amps on that 4 gauge line it would be good for about a 60% duty cycle.
A welding machine that would draw 125 amps at a 60% duty cycle would be a machine about 2 class sizes bigger than what I have now. Those welding machines are typically used to build bridges, skyscrapers, power plants, ships, oil rigs.

When I move I will pull the 125 amp breaker off that welder circuit and put in an 80 or 90 amp breaker and relabel it "electric vehicle charger ".

When I installed our electric vehicle charger for our Nissan Leaf ( that we had before it got run into and totaled ) , I ran # 6 copper & put it on am 2 pole 40 amp CB . It was fused , internally , with 40 amp fuses .

We run only copper .

Wyr
God bless

My hard wired charger will likely be 8 gauge ran on a 40 amp breaker also. I have the slow charging 2011 leaf, it will only draw 16 amps max with my after market 3.8kw charger. That 40 amp circuit will be incase I upgrade to a vehicle and charger that can do 6.6kw charging.
My other EVSE is the original 12 amp nissan brick charger converted to 240v by me.

I could have used # 8 Romex , but I had # 6 left over from another job .

I installed the GE Wattstation . It was just about the cheapest " full power " level 2 device I could find .

Ours was a 2012 Leaf . Still with the 3.8 kw charging rate , also .

Wyr
God bless

Did you ever amp clamp that 2012 leaf while charging?

I do not think so . At least I can not remember doing so .

Wyr
God bless

What size / amperage circuit breaker ?

Wyr
God bless

My main charging circuits at home are two seperate 20 amp, 12/3 with ground romex cables going to 6-20 amd 5-20 combination duplex receptacles. That way when I'm not charging I can use them for any normal 120v activity.
Then I have 30 and 50 amp RV circuits at my away locations. They are dedicated circuits that run outside to an RV box with a L14-30, 10/3 with ground and a 30 amp breaker.
The one 14-50 is wired on 50 amp with 6 gauge, so my buddy can use his little stick welder.

Then if 20 amp circuits become too small my welding circuit at home is ran on 4 gauge so it can handle anything.
I could charge like 6 cars at my house if most of them used 12 or 16 amp evse chargers.