Well, I have a 12v 5ah @ 20 hrs Sealed Pure Lead battery hooked up to a DC Aux socket. In the socket, I have a USB car charger.
I am going to be charging my iPhone 6 from it.
The iPhone requires 5v and 1 amp. I have a total of 5 ah so would that give me 5 hours of charging. 5ah/1amp=5
It does notseem right to me so I converted to watt hours.
12v x 5ah =60 watt hours for the battery and the iPhone uses 5 watts to charge.
60 watt hours / 5 watt = 12 hours of charging?
Would anyone be able to help me out with the math on this one?

Thanks!

 

Ok. I am a bit fuzzy on these stuff, but... you forgot that the charging is not going to be constant. An empty iphone battery will take as much current as the charger can give it, 1 Ampere. But... as the iphone battery gets closer to full, it will take less current. Remember that batteries are elector-chemical devices, so pure electrical laws/rules do not explain everything.

 

Your second pass is the right thinking. Amp-hours can be used to compare sources and loads only at the same voltage. The true measure is watt-hours, which includes the effect of voltage in its calculation. But three things:

1. You have to add in (or subtract) charger circuit efficiency.
2. The charger output rating is no necessarily what the phone is drawing.
3. The phone's internal charging circuit may not draw a colstant power level throughout the charge cycle.

#1 reduces the total possible charging time below the theoretical max (12 hours in your case), while #2 and #3 increase it. Also, one of the tricks internal charging circuits use to shorten the charge cycle is to fiddle with the terminal voltage so the battery charge rate is almost constant.

ak

 

Thanks for both replies!

I guess i'm thrown off more by the math then anything.

For instance and this is on paper and not taking into account any inefficiencies. If I have a battery that's 12 v 6.9 ah and have a dc motor that's 12 v 1.5 amp and I wanna figure out how ling I can run that motor, the the math works.
6.9 v / 1.5 v = 4.6 hours
also, when I do the math for watt hours, 6.9 v x 12 v = 82.9 watts. 12 v *1.5 v = 18 watts. 82.9 / 18 = 4.6 watt hours.

yet if I do that math for the phone and my battery, the amp hours = 5 and the watt hours = 12?

 

You can't compare amp-hours to watt-hours, because amps do not equal watts. Although related, they are quantities of very different things. In your example, both the motor and the battery are 12 V so things look one way. But the phone is 5 V while the battery still is 12 V, so things ollk another way. The mistake that is leading to your error is that while the phone charger draws 1 A at 5 V, that does not equate to 1 A at 12 V. With a theoretical 100% efficient buck regulator, the phone would draw only 0.4167 A from a 12 V battery, and 0.4167 x 12 = ???

ak