why does the alternator light stay on after cranking on 1990 Toyota 4Runner

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i installed a new alternator and it still stays on
(3) Answers
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Just to add if the alternator is not charging on that cat the brake light and battery light will stay on (even if the brake fluid level is OK and hand brake is off.)
The required voltage at the batery is a minimum of 13.5 volts and a maxium of 14.5. At idle with lights, A/C and wipers on it has to mantain 13.5 volts. You need to have the battery check and clean your terminals good.
Have you checked the voltage at battery positive and negative terminals while engine running.
Reading should be between 13.2-14.4 voltage. Either lower or higher reading indicates bad battery; bad connection(to ground)
or shorting in wiring.