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RC Circuit ; why RC=(VT/2 delta V)

  1. Aug 2, 2012 #1
    1. The problem statement, all variables and given/known data
    I need to prove that RC=(VT/2 delta V)


    Select the circle components of Charging and discharging of a capacitor
    Measure the resistance of resistor with a multimeter
    When you run a different frequency the cycle time change
    run different frequency that T<<tao, T=tao, T>>tao
    Choose components So that T<<tao,
    V - the voltage of Function Generator
    delta V= Voltage amplitude


    2. Relevant equations

    when -T/2<t<0
    Q(a)=-cv+Ae^(-t/tao)

    when T/2>t>0
    Q(b)=cv+Be^(-t/tao)

    A=(2cv)/(e^(T/2tao)+1)
    B=(-2cv)/(e^(-T/2tao)+1)

    3. The attempt at a solution

    Q=VC

    Va=Qa/C

    Vb=Qb/C

    delta V= Vb-Va

    RC=tao

    I place Vb-Va on RC=(VT/2 delta V) and I played with the equation

    but I didn't get RC=(VT/2 delta V)
     
    Last edited by a moderator: Aug 2, 2012
  2. jcsd
  3. Aug 3, 2012 #2
    I tried another solution but I got stuck:

    Va=Qa/C

    I used Va:

    delta V= V(0)-V(-T/2)

    VT/2 delta V

    e^(T/2tao)=1+T/2tao -- taylor

    and I get RC+T/4

    what wrong?
     
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