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Mobile charger amperage limit

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So the device can take up to 32A. Essentially what I'm getting is that I will not risk the device getting ruined again running on 13A, so the tesla rep who brought me the replacement charger was wrong. Is it normal that when charging on 13A the voltage (as seen on the screen) occasionally changes to between 226-231 volts? Or is it a sign that the electricity line is having trouble to supply 13A. I will say again, the plug was never too hot to the touch, even after 8+ hours of charging.
That is completely normal.

It is normal in the US for the voltage coming in from the utility to vary. I see my normal 240 volt service vary from about 233 to 244 volts. But the standard is plus or minus 10%, which is 216 to 264 volts. The usual cause of the variance is the load both on the grid and on a particular service.

Depending on the length of the wire from the utility transformer to your premises, and the length of the wire from your breaker / fuse panel to the receptacle in which the TMC is plugged in to, you might see the voltage drop a bit when the car begins charging. Then, whilst the car is steadily drawing 13, or 32 or whatever amps, when the voltage varies that is either other heavy loads coming on / going off at your premises, or the general condition of your grid as the loading varies over time.

Don't overthink this. The TMC is designed for use up to 32 amps, and many people use it at 32 amps for years without problems.

It is a good idea to check the plug and receptacle from time to time. If it is warm that is OK, but if it feels hot, that usually indicates a problem. What makes charging an EV different from almost any other residential load is that it is on for hours. When I charge my Model X from 10% to 100% at 24 amps (240 volts) this can take better than 15 hours.
 
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What I would suggest is letting it charge at 13a for an hour, at least. Stop the charge, immediately unplug the mobile connector and carefully feel the prongs and body of the plug and the face of the receptacle. If they seem too hot (like you can't keep your hand on it) then it might be worthwhile to dial the rate down.
I charged on 12A for two hours. The pins are a little bit warm to the touch but nothing substantial. Does it make sense to stop the charge and "let the charger rest" after x hours charging at 12A? Once again, my max charge is 13A, but for now I max it at 12A.
 
I charged on 12A for two hours. The pins are a little bit warm to the touch but nothing substantial. Does it make sense to stop the charge and "let the charger rest" after x hours charging at 12A? Once again, my max charge is 13A, but for now I max it at 12A.
No, definitely not. Way too much thought is going into this. The first UMC was simply defective. Pins would have to be untouchably hot before you should become at all concerned.
 
I charged on 12A for two hours. The pins are a little bit warm to the touch but nothing substantial. Does it make sense to stop the charge and "let the charger rest" after x hours charging at 12A? Once again, my max charge is 13A, but for now I max it at 12A.
After an hour or so, you're at full temperature. "A little bit warm" is what I'd expect. To me that says you should be fine leaving it at 13a and no need to lower it, or let it rest.
 
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Just to add that the breakers for household power circuits in Israel are 16A, so the 13A is already lower than the limit of the circuit. The 80% rule does not exist outside of North America, but Tesla chose to be extra safe. If you don't want issues with plugs, use a hardwired EVSE which is inherently safer. You will be able to charge at 11kW on a three-phase 16A circuit.
 
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