I have this clarification, battery voltage is the same as alternator voltage or is it different? what i exactly mean is if the batteries are at different State of charge their terminal voltage will be different if the engine is running or vehicle is running condition? The batteries are Lead acid.
The alternator voltage is a slightly higher voltage than that of the battery, this is to charge the battery. For most normal cars, the battery is 12V and the alternator outputs just above 14V. Whenever the car is running and the alternator is at sufficient speed the voltage on the terminals would be slightly above 14.? volts.
Most modern car alternator regulators will bulk up to 14.2-14.5 vdc right after car is started. The length of time at the bulk (absorb) voltage is dependent on battery voltage rise time to the bulk (absorb) voltage after car was started or battery charge current drop off at bulk (absorb) voltage. After bulk time period the regulator drops to 13.2 - 13.7 vdc. Normally the bulk period only last for a few seconds to a minute after car is started.