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Equation for RLC circuit

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Figure_P08.44.jpg
    In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA and R=1250 ohms

    Find vC(t) for t≥0.
    Express your answer in terms of t, where t is in milliseconds.

    2. Relevant equations

    i=c*dv/dt
    3. The attempt at a solution
    the only part of this problem i am not getting is solving for the constants with the given initial conditions... the 2 roots to the differential equation are -5000. so:
    v(t)=C_1*e^(-5000t)+C_2*t*e^(-5000t)
    and
    dv/dt [at t=0+]=-5000*C_1+C_2=i/c=(6*10^-3)A/(320*10^-9 F)=18750 volts/s
    v(0)=C_1=15V
    so C_2 -5000*15=18750...C_2=93750
    but apparently C_2 is actually equal to 56250....If the equation was C_2-5000*15=-18750, then i would get 56250...where am i going wrong???
     
  2. jcsd
  3. Oct 20, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    As the charge flows away from the capacitor, I=-dQ/dt= - C dV/dt.

    ehild
     
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