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Homework Statement
The power absorbed by the box is ##p(t) = 2.5e^{-4t}W##. Compute the charge and energy delivered to the box for ##0 < t < 250ms##.
An image of the problem: http://gyazo.com/7cb5858f681c3c9db33e20b434c2b782
Homework Equations
##i = \frac{dq}{dt}##
##q = \int_{-∞}^{t} i dx##
Note that energy over time is the same as work over time.
##\frac{dE}{dt} = p = vi##
##E = \int_{t_1}^{t_2} p dt = \int_{t_1}^{t_2} iv dt##
##v = 50e^{-t}V##
##p = 2.5e^{-4t}W##
##0 < t < 250ms##
The Attempt at a Solution
The question asks to compute the charge and energy delivered for ##0 < t < 250ms##.
I don't have any current to work with, but I do have power and voltage.
Wouldn't I just integrate ##p(t)## from 0 to 250? That would give me energy.
Integrating ##p(t)/v(t)## from 0 to 250 would give me charge wouldn't it?
Something doesn't feel right. The answers are different.
The answer for the energy is listed as: 395.1mJ
The answer for the charge is listed as: 8.8mC
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