1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the time in which a potential drop is equal to 3V

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Capacitor, C1, is initially charged so that it has a potential difference of 12V. At time t=0, switch S1 is closed allowing the capacitor to discharge through resistor R1. At t=5, the potential across the capacitor has fallen to 6V. At what time will the potential across the capacitor reach 3V?


    2. Relevant equations
    V=Voe^(-t/RC)


    3. The attempt at a solution
    6=12e^(-5/RC)
    The RC is confusing to me. I'm not sure how what I'm supposed to do with it.
     
  2. jcsd
  3. Dec 4, 2012 #2

    Mute

    User Avatar
    Homework Helper

    If 6=12e^(-5/RC), what does RC have to be to make that equation true?
     
  4. Dec 4, 2012 #3
    It would equal 5ln(2), but I don't know how to use that for the answer. If I plug it in, there are lots of natural logs.
     
  5. Dec 4, 2012 #4

    Mute

    User Avatar
    Homework Helper

    Not quite - you made a division error. Double-check the time again. Also, you should keep track of the units.

    Once you've found RC, it may involve a natural log, but sometimes things just involve natural logs. At any rate, it's just a number, so you can now solve for the time at which V = 3 volts, and then you can plug in the number for RC to get a numerical answer for the time at which V = 3 V. Does that make sense?
     
  6. Dec 4, 2012 #5
    I went from
    6=12e^-5(RC)
    ln(1/2)=-5/RC
    RC=7.21

    Is that correct?
     
  7. Dec 4, 2012 #6

    Mute

    User Avatar
    Homework Helper

    Yes, that is correct. Note that that is 5/ln(2), whereas before you wrote 5*ln(2).

    So RC = 7.21... what? What are the units? (Did your problem tell you the units? You didn't list any in your problem statement).

    Anywho, now that you have RC = 7.21, can you solve for the time at which V = 3 volts?
     
    Last edited: Dec 4, 2012
  8. Dec 4, 2012 #7
    RC is in s.
    So then it would just be
    3=12e^(-t/7.21)
    t=10s
     
  9. Dec 4, 2012 #8

    Mute

    User Avatar
    Homework Helper

    Yep, looks good.
     
  10. Dec 4, 2012 #9
    Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook