To judge the problem for an alternator, there are few steps you can try
Run your car and unplug the positive connection of the battery, if the car stops then it is more likely there is a problem with the alternator
Another way of checking alternator is by checking interior lights, usually an alternator charges your car battery when the car is on. If the interior lights come on brightly and fades away slowly, it indicates that the alternator cannot keep a charge when the car is running. It means there is a problem with the alternator.
You can also check by racing your car with headlights on, if the light brighten up when you race the car and lose power when you slow it down, indicates a problem with the alternator