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Physics capacitor time unknown

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data
    A 100 micro F capacitor is discharged through a resistor of resistance 470K Ohms. Determine the 'half-life' of this circuit. The half life being the time it takes for the initial voltage to decrease by 50%.


    2. Relevant equations
    Is my answer correct? If not, what have I done wrong?


    3. The attempt at a solution
    Here's what I've done:

    Using V = V(Initial)e^-(t/RC)
    Since the initial V is double V, divide both sides by V which will result in, 0.5 = e^-(t/RC).
    RC (time constant) = 47 seconds

    Taking natural logs of both sides and re-arranging gives:

    47*ln(0.5) = - t
    so t = 32.6 seconds
     
  2. jcsd
  3. Feb 8, 2013 #2

    CWatters

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    Science Advisor
    Homework Helper

    Looks ok to me.

    As a check... the time constant of an RC circuit is very roughly = R * C

    In this case R * C = 47 seconds which isn't a million miles away from 32 seconds.

    See also..

    http://en.wikipedia.org/wiki/RC_time_constant

    PS: Large real world capacitors typically have a large manufacturing tollerance (20 to 80%) so somerimes R*C is as accurate as you need to get. It's a different matter for small capacitors which can be accurate to a few percent.
     
    Last edited: Feb 8, 2013
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