Calculus of A Discharging Capacitor

Discussion in 'Homework Help' started by Larry Makanza, Nov 29, 2010.

  1. Larry Makanza

    Thread Starter New Member

    Nov 19, 2010
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    How much time does it take a fully charged 500 microfarad capacitor, connected in series with a 20K ohm resistor across a 15v supply, to discharge its current to 0.5 milliamps? I have tried to solve this problem for quite a few days and have come to realize there is basic principle operation of capacitors in dc circuits which I am simply not getting. So far my best effort answer is 18.97 sec. Is this correct?
     
  2. beenthere

    Retired Moderator

    Apr 20, 2004
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  3. mik3

    Senior Member

    Feb 4, 2008
    4,846
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    Use this equation:

    ic=(Vo/R)*exp(-t/(RC))

    where:

    ic=instantaneous capacitor current (A)
    Vo=initial voltage of the capacitor (V)
    R=resistance of the resistor (Ω)
    C=capacitance (F)

    This equation can be derived by using the basic equation ic=C*dv/dt and first order differential equations.
     
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