I have a 12v 6AH battery, connected the terminals to my car charger to obtain nominal charging voltage for my phone..if the battery's initial capacity was 12v 6AH what would be the current capacity at 5v..how much Ah

 

how much Ah

6Ah. Actually a good bit less, because the Ah rating is the optimistic figure supplied by the manufacturer for the battery discharging under very specific conditions. Or are you asking about how much current (Amps, not Ampere-hours) will be drawn by a 12V-to-5V converter?

 

I have a 12v 6AH battery, connected the terminals to my car charger to obtain nominal charging voltage for my phone..i

Typically most phone chargers for automotive use take the 12 to 14 volts from the automotive system and run it through a simple voltage regulator like a LM7805 and provide 5 volts to the phone. The phone handles the rate of charge for its internal battery. The current draw is generally very little depending on the charger, typically a few hundred mA.

The discharge rate on the battery (how long will the battery last) is dependent on the battery as Alec-t mentioned. This means a 12 Volt 6.0 Amp SLA (Sealed Lead Acid) battery will not necessarily deliver 12 Amps for 30 min, 3 Amps for 2 hours or 1 Amp for 6 hours. The mentioned LM7805 is just a single example of a voltage regulator, any of several are used for automotive cell phone chargers but I don't know of any which actually use a DC / DC Converter.

Ron

 

The Ah rating of a lead-acid batter is usually for a current draw of no more that 1/10th of its Ah rating or 0.6A for a 6Ah battery.
Above that current the Ah capacity will decrease.