# Total energy

## Homework Statement

A 12 V battery is rated at 200 Ah (Amps hours). How much total energy can it supply?

P=IV

## The Attempt at a Solution

First I did E = 1/2 C V^2. (Got 4,320,000 J, although I'm not sure if that is correct). But now I need to convert it to kwh so my question is can I use P = IV in this manner:
P = 200 Ah * 12 V
P = 2400 Wh = 2.4 kWh
or do I need to manipulate my original energy finding?

4,320,000 J != 2.4 kWh so one must be wrong

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Huh? amp hours? That's a new one.. You plugged in 200 Ah for I..meaning that Ah is a measurement of current? According to Wikipedia, Ah is a measurement of electrical charge..

Where did 1/2 C V^2 come from? What did you use for C, and why?

P has units of power, not energy - to get energy you have to multiply by a time, which is what you did, though this might have been accidental since amp-hours are units of charge, not current.

Also, 2400 Wh is not equal to 24 kWh.

Alright, using P=IV was the wrong approach

Heres how I calculated Capacitance:
First 200 Ah * 60 min/h * 60 s/min = 720,000 Coulombs.
CV = q
C*12 = 720,000 C
C = 60,000 F (which seems really high)

1/2 * 60,000 F * 12^2 = 4,320,000 J which is equal to 1.2 kWh ( i think )

Am I calculating the correct amount of charge?

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CV = q ??
the C refers to capacitance. do you have a capacitor in the circuit?
Hint: what do you have to do to the equation P = IV to get units of energy on the left hand side?

Heh, whoops, wasn't thinking about actually needing a capacitor in it.

Anyway, now I got it, thanks all.