Energy Supplied by a Battery

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Homework Statement


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



Homework Equations


P=IV


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?
 

Answers and Replies

  • #2
ehild
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Check your graph.

ehild
 
  • #3
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Ok when I tried to find the area using the graph i only took the area of the triangle.
 
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