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Time constant question

  1. May 30, 2009 #1
    i understood every thing except at the last 30 seconds

    he says "after 5 time constants t=rc" current will be 0
    i cant understand by what mathematical equation he got this number 5
    ??
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. May 30, 2009 #2
    intuitively i know that after the capacitor will be filled with charge
    it will stop being a conductor

    but how he came up with the "5"
    ??
     
  4. May 30, 2009 #3

    Hao

    User Avatar

    The 5 he choose is an example of a 'magic number'.

    We know that current decays as [tex]I = I_{initial} e^{-\frac{t}{R C}}[/tex].

    Hence, as time passes, I gets smaller and smaller.

    After 1 time constant,
    [tex]\frac{I}{I_{initial}} = e^{-1} = 0.368[/tex]
    After 2 time constants,
    [tex]\frac{I}{I_{initial}} = e^{-2} = 0.135[/tex]
    After 3 time constants,
    [tex]\frac{I}{I_{initial}} = e^{-3} = 0.050[/tex]
    After 4 time constants,
    [tex]\frac{I}{I_{initial}} = e^{-4} = 0.018[/tex]
    After 5 time constants,
    [tex]\frac{I}{I_{initial}} = e^{-5} = 0.007[/tex]

    So a more accurate statement is, "After 5 time constants, the current is approximately 0."

    He could have easily said 4 or 6 or 100. They key point is that after about 3-5 time constants, the current is effectively 0.

    Edit: Formatting error, sorry,
     
    Last edited: May 30, 2009
  5. May 30, 2009 #4
    xyzt
     
  6. May 30, 2009 #5
    thanks
     
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