What is the voltage across a capacitor?

Discussion in 'Homework Help' started by charmcaster, Jan 28, 2015.

  1. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    What is the voltage across a capacitor after being charged from a 100 V source for a period of one time constant?
     
  2. wmodavis

    Well-Known Member

    Oct 23, 2010
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    There is a formula for that. Do you know what it is?

    A key piece of information that will help you is the definition of Time Constant.
     
  3. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    I google n get, after the first interval, the capacitor voltage equals 63.2% of the battery voltage. so answer I got is 63.2. Is it right?
     
  4. wmodavis

    Well-Known Member

    Oct 23, 2010
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    Yup.
     
  5. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    Thanks!
     
  6. MrChips

    Moderator

    Oct 2, 2009
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    Next question.

    How long would it take for the capacitor to charge to the battery voltage?
     
  7. wmodavis

    Well-Known Member

    Oct 23, 2010
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    Very long time. Or I should ask how close to the battery voltage do you mean?
     
  8. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    Time constant. For RC circuit its RC.
     
  9. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    capacitor fully charged after five time constants have elapsed.
     
  10. MrChips

    Moderator

    Oct 2, 2009
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    Five time constants is not the correct answer (but is a good answer if you supply an error criteria). See the answer given by wmodavis.

    As an exercise, calculate the percent error from fully charged for n time constants (for n = 1 to 10).

    What is the error for n = 5 and n= 6?
     
  11. MrAl

    Well-Known Member

    Jun 17, 2014
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    Hi,

    It is interesting how this changed a little over the years. Way back when, 5 time constants was a good enough approximation because it came in very close to the full supply voltage (cap charging through resistor powered by voltage source). But today with the never ending question for resolution and accuracy, that may not be good enough. Back then most measuring instruments could not detect a 0.7 percent difference, or at least it didnt matter that much. These days with high resolution ADC units we probably want 0.5 percent or better, usually better, and with an RC filter somewhere in the input circuit the time we have to wait before we get a good reading (acquisition time) has to be increased.
     
  12. crutschow

    Expert

    Mar 14, 2008
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    I would think the capacitor can be considered effectively fully charged when it is within the capacitor's intrinsic thermal noise level (√kT/C) of the charging voltage. :rolleyes:
     
  13. MrChips

    Moderator

    Oct 2, 2009
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    Agreed. When the error is within the noise level we can say it is fully charged.
     
  14. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    Thanks! error for n=5 is 99.3%
     
  15. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    Thank you all!
     
  16. MrChips

    Moderator

    Oct 2, 2009
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    You are very welcome.

    Note that the error at n = 5 is 100 - 99.3 = 0.7%

    n = 6, error = 0.2%
    n = 7, error = 0.1%
     
    charmcaster likes this.
  17. charmcaster

    Thread Starter New Member

    Jan 13, 2015
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    :)
     
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