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Homework Help: Calculating time constant in RC Circuit

  1. Feb 25, 2008 #1
    1. The problem statement, all variables and given/known data

    You see this trace on your oscilloscope for an RC circuit. The vertical scale is 5volt/square and the horizontal scale is 50ms/square. What is the time constant of the RC circuit?

    2. Relevant equations

    Vc(t) = Vo(e^(-t/RC)
    Vr(t) = -Vo * e^(-t/RC)
    t halftime = Tln(2) = .69T

    3. The attempt at a solution

    So when the voltage is at its peak (15 V), that's Vo. and if I take that as V(t), it's V at 20 ms (approximately). Substituting this:

    15 V = 15V(e^(.02/RC))
    1 = e^-.02/RC
    ln(1) = -.02/RC
    0 = -.02/RC

    Cross multiplying to solve here doesn't help me. Is there another formula I can use?
     

    Attached Files:

  2. jcsd
  3. Feb 25, 2008 #2

    kdv

    User Avatar

    The left side of the equation is V(t) so you need to read off the value of V at 20 ms. For example, if it's 13 volts, then you will solve
    [tex] 13 = 15 e^{-0.02 s/RC} [/tex]
     
  4. Feb 25, 2008 #3
    Yeah, that's what I did..I said that the V at 20 ms was 15 (the peak). Should I just pick another arbitrary time?
     
  5. Feb 26, 2008 #4

    kdv

    User Avatar

    But V cannot be equal to 15 volts at 0 second AND at 20 ms!!

    V_0 is the voltage at t=0

    I think your mistake is that you did not reset t=0 at the point where the decreasing exponential starts. If you measure V_0 at the peak, you must set t=0 at that point.
     
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