A battery provides a continuous current of 9mA (.009A) for 40hrs (144,000sec). During that time the voltage drops from 1.5 to 1.0. Assume the drop is linear with time. How much energy does the battery deliver during this 40hr interval
The Attempt at a Solution
First I found an equation for voltage as a function of time (s) V(t)=1.5-3.472x10^-6t.
Then I figured power as a function of time P(t)=IxV(t)=.009(1.5-3.472x10^-6t)
P(t)=.0135-3.1x10^-8t. To find the energy delivered, I integrated P(t) so that E=.0135t-3.1x10^8t^2/2. The limits were from 0 to 144,000. I ended up with 1944-321.408=1622.6J
My problem is that when I just made a graph of power vs time and found the area under it from 0 to 144,000 I got 324J. Could I please get some guidance as to what I'm doing wrong?