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Scholar
Karma Points: 246
(Clemson University)
Respect (100%):
Date Posted: 6/17/2008 9:57:07 PM  Status: Live
completely lost
Course Textbook Chapter Problem
Calculus Based Physics N/A N/A N/A
Question Details:
The current supplied by a battery slowly decreases as the battery runs down. Suppose that the current as a function of time is I= ( 0.860 A) e^{- t /6 hr} .
What is the total number of electrons transported from the positive electrode to the negative electrode by the charge escalator from the time the battery is first used until it is completely dead?
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Answers:

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Oracle
Karma Points: 58,609
(NIMBLE - the National Institute of Monkey Business and Learning)
Date Posted: 6/18/2008 12:18:09 AM  Status: Live
Asker's Rating: Lifesaver   
Response:
total charge  =  integral of  I dt  =
 
                   integral of  (0.860 e-t/21600 )           note:  21600 sec  =  6 hours
 
              =    0.860 * (-21600)  e-t/21600    eval from t = 0  to  t = infinity   you get
 
total charge  =  0.860 * (-21600) ( e-∞  -  e0 )  =  0.860 * (-21600) * (-1)  =
 
                 =     18576 Coulomb of charge
 
number of electrons?  convert...
 
     18576 C  *   1 electron / 1.60 x 10-19 C  =     1.161 x 1023 electrons
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