# Calculating electrical energy over time

1. Apr 12, 2013

### anj16

Hello,

Let's say I am generating 5 amp at a constant 1 volt and storing it in a battery without any loss of energy. The question is what am I adding to the battery? Am I adding power as a function of time or is it something else? So say if I were to calculate how much energy has accumulated after 5 hours how would I do that?

Thank you.

Last edited: Apr 12, 2013
2. Apr 12, 2013

### Staff: Mentor

P=VI
E=PT

Power is energy added per unit time.

3. Apr 13, 2013

### anj16

Ah I see, thank you.

4. Apr 13, 2013

### technician

Amp means coulomb per second. Volt means Joule per coulomb.
therefor V x I means Joules per second = power.
power x time = energy in Joules

5. Apr 13, 2013

### anj16

What if my voltage isn't constant? Doesn't that mean that my power isn't constant either? And doesn't E=PT rely on constant power?

6. Apr 13, 2013

### technician

you would then find yourself talking about 'instantaneous power'. If the voltage changes presumably the current also changes.
An interesting example is in AC circuits where V and I are changing and can be out of step.

7. Apr 13, 2013

### anj16

what do you mean by instantaneous power? Wait do you mean to take the integral of the power function with respect to time?

8. Apr 13, 2013

### milesyoung

Sure.

You're right again. $E(t) = \int_{t0}^t P(\tau) \mathrm{d}\tau$ is true in general.