Hi! In Voltage regulator like 7805cv, Since the difference in input and output voltage will just turn into heat, does it mean a higher voltage battery will last just the same as lower voltage battery if they have same capacity?
Yep, basically it's so many amps for so many hours ie AH
You better of using either a DC-DC converter. There are nice compact ones in the market. or use a simple buck converter. Both make more effective use of your battery capacity
nicoverduin:
You better of using either a DC-DC converter. There are nice compact ones in the market. or use a simple buck converter. Both make more effective use of your battery capacity
I agree, but it doesn't answer the question
jackrae, you answered the question, nicoverduin offered advice.
7805
Be a 12v or 9v if they both have the same Amp/hour rating eg 5ah 9v or 5ah 12v the regulator will chew through the same power.
Thanks for the replies! 
im making a phone charger, its overheating on 12V. 9V is fine
Pololu.com has some cheap DC-DC converters premade.
The MC34063 makes a great 12V to 5V switching buck regulator. Cheap, too. Just about every cigarette lighter plug USB adapter I've taken apart has that chip in it.
An online calculator to determine part values:
http://dics.voicecontrol.ro/tutorials/mc34063/
If using batteries to charge your phone, with a linear regulator you'll burn up the same Ah with 9V or 12V, if they have the same Ah capacity. But with a switching regulator, you'll get more charge time out of 12V.