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Capacitor discharge

  1. Jul 11, 2011 #1
    1. The problem statement, all variables and given/known data
    Determine how long it takes the capacitor to discharge to a value of 3v
    C=1.5E-6F
    R=1E3ohms
    Vi=25v
    Vf=3v


    2. Relevant equations
    T=RC
    v=Vi*e^(t/T)



    3. The attempt at a solution
    T=1000*1.5E-6
    T=1.5E-3s

    Vf(3v) is 12% of the initial 25v

    Im having trouble solving for time with this equation v=Vi*e^(t/T)

    many thanks in advance
     
  2. jcsd
  3. Jul 11, 2011 #2
    Should I be solving for t or using a normalised universal timeconstant(RC) curve to estimate time?
     
  4. Jul 11, 2011 #3

    jambaugh

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    Science Advisor
    Gold Member

    Firstly [itex] V = V_i e^{-t/T}[/itex] there's a negative sign reflecting the decay of the voltage... it doesn't grow!

    Secondly solving this for t is basic algebra, apply inverse operations until you isolate t.
    [itex] A = B e^{t/C}[/itex]
    [itex]A/B = e^{t/C}[/itex]
    [itex]\ln(A/B) = t/C[/itex]
    [itex]C\ln(A/B) = t[/itex]
     
  5. Jul 11, 2011 #4
    Thanking you jambaugh
     
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