Current battery problem with i(t) = −25 mA sin(ωt)e^(−t/τ) (see description)?
The current through a 12 V battery is i(t) = −25 mA sin(ωt)e^(−t/τ) where τ = 1 ms and
ω = 2πf , where f = 1 MHz. Find the net charge and net energy supplied by the
battery from t = 0 to t = ∞.
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Hmm,
Charge is :
Integral of current*dt from 0 to infinity.
That integral doesn't look very nice....:(
WIkipedia's integral table has something under the (composed function) category that looks adequate: http://en.wikipedia.org/wiki/Lists_of_integrals
Energy is:
Integral of Power*dt
where power = V*current
I wonder if i did something wrong but, it look like the answer from calculating charge can simply be multiplied by the volts (since volts appears to be constant) in order to get power.
My word, there must be away around that integral. The wikipedia link again..same section http://en.wikipedia.org/wiki/Lists_of_integrals