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How to calculate the initial rate of dischrage of a capacitor.

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data

    A) A DMM with its 10M(ohms symbol) internal resistance is connected to a 9.9 microF capacitor that has been charged to 10 V. Calculate the intial rate of discharge of the capacitor through the DMM in micro-Coulombs per second. Hint: You do not need exponentials for this calculations.

    B) Assuming this initial rate of discharge in the question above is maintained for 3 seconds, by what percentage would the capacitor be discharged?


    2. Relevant equations

    How do I calculate the initial rate of discharge? My lab did not go over it but I Found this formula online but it only goes over time.

    T = ( C * V ) / I


    3. The attempt at a solution

    I = V/R
    = (10 / 10
    = 1

    T = ( C * V ) / I
    = (3.9 * 10) / 1
    = 39 seconds

    So the rate is .1 microF a second?
    And if it were discharged for 3 seconds it would be .3 which is 7.6% of the charge discharged.


    I am lost! Any help is greatly appreciated, thanks!
     
  2. jcsd
  3. Mar 8, 2010 #2

    berkeman

    User Avatar

    Staff: Mentor

    You are close when you say I = 10V / 10Meg Ohms (you wrote 10 Ohms, BTW).

    After fixing the missing "Meg", you would get I = 1uA

    Now you need to convert that into coulombs per second. What is the relationship between Amps and Coulombs per second?
     
  4. Mar 8, 2010 #3

    The relationship between coulombs per second and amps is that one Amp is one coulomb per second. I think I need this equation:

    Q= I * t

    t = Q / I also I = Q/t

    So to find Q

    C = Q/V so we get Q = CV

    Q = ( 3.9 * 10^-6 * 10 V ) I = 10/10*10^6
    = 3.9*10^-5 couloumbs = 1*10^-6

    t = Q / I
    = 3.9*10^-5 couloumbs / 1 * 10^-6 couloumbs/second
    = 39 seconds

    I just realized that what I just did is pretty much the same as above.
     
  5. Mar 9, 2010 #4

    berkeman

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    Staff: Mentor

    Better is [tex]I = \frac{dQ}{dt}[/tex]
     
  6. Mar 11, 2010 #5
    thanks. i think i got it. turned it in yesterday.
     
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