I just replaced both the battery and alternator on my 92 accord wagon because the alternator went. Still after replacing them, my interior lights are dim and my battery light dims in and out. I got the alternator tested at Advance Auto and they said the alternator reads a 11.3 which the guy told me that fine?! Is they any idea what the problem could possibly be?

 

Yes.
In prep for this comment I just went out and measured the voltage from my static '92 car battery
(been 90 minutes since being driven) and battery voltage is 12.76 volts.
So any alternator needs to be delivering >12.9 volts to charge the battery.

You bought a cheap **** alternator from a **** store staffed by minimum wage + $0.75 employees.
You could demand that the **** store replace their product under warranty - or - what I would do is go to local
NAPA store and get an alternator; and just call this $45 car part episode one of life's many lessons.

My experience: I won't buy from Autozone or O'Reilly's (Advance isn't in my town) other than oil and filters in new boxes.
If I want some component to work on my car I go to the dealer or NAPA.

I don't intend to go into history here, but listen up:
Reliable Parts = dealer, or NAPA.

 

Does sound like a faulty replacement alternator.

 

A problem that occasionally occurs and is devishly difficult to diagnose, is worn harmonic balancer/ crankshaft pulley. The rubber bushing between outer pulley and inner drive can begin to slip. Symptoms will mimic faulty alternator (low battery voltage due to lack of charge), but no Alt light (not sure why).

Diagnostic procedure is to mark a radial line (center bolt-pulley) across the rubber sandwich. If this radial mark separates, you have worn rubber sandwich.

Fix requires a new harmonic balance/crankshaft pulley.

good luck

 

If the store tested it and said 11.3 volts is fine, then they are wrong.
The alternator should put out approx. 13.5 to 14.5 volts.
Talk to the store manager. Ask them to pull another one off the shelf and test that one and see what it puts out. Then kindly ask the manager to educate his employees, so they don't mislead other customers.

 

Bought a new alternator from napa and now the battery light doesn't come on but the car only runs for a min or two then turns off

 

Do the instrument panel lights (Alt, Check Engine, Oil Pressure) come on when car shuts down or is panel dark?

Have you checked that battery is charged enough to run car? What is voltage?

good luck