I strongly suspect that one or more of the diodes inside the alternator
failed shorted and the alternator needs replacing.
Sorry in advance for boring you with some details :)
In simple terms, think of diodes as one way valves when it comes to current:
they allow current to only flow in one direction. On alternators, diodes
"make" DC from the AC that the alternator generates. When boosting, they
also make sure that the current being supplied by the booster cables is not
allowed to flow through the alternator as it isn't designed to do that.
On your alternator, the shorted (bad) diodes conduct in both directions so
current from the booster cables is not stopped, causing current to go
through it when boosting. This is a lot more current than the alternator can
handle so it smokes - it may have damaged more than the diodes now.
Try to get the car running again and measure the voltage across the battery
while running. You can buy a cheap multimeter at radio shack or sears(if you
are in the US), if you don't have one. Make sure you understand how to read
DC voltage before you use it.
It should be about 14.5 volts DC (the normal charging voltage).
If you don't see 14.5V DC, you could switch to AC out of curiousity and most
likely measure several volts AC, indicating that the diodes are blown. If
you don't see a charging voltage, I'd replace the alternator. On some
Honda/Accura alternators one can just put new diodes in, so it may pay to
check with the dealer on the replacement parts.
If anything else, just report back here.
After thinking about it just a little longer, perhaps don't try to start the
car: Since your alternator is smoking, you don't want to do more damage to
it in case you can fix it by justs replacing the diodes (it might save you
Instead, disconnect the fat wire from the alternator and measure from it to
the body. If diodes in the starter are bad, you will see a very low
resistance (a couple of ohms) regardless wheter you switch the black and red
wire on your multimeter.
Btw, you didn't mention it, but when you rechanged your battery did it just
go flat all by itself after a little time? If so, another indication that
the alternator has bad diodes.
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