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Homework Help: Using Kirchoff's Laws to solve a circuit

  1. Feb 25, 2007 #1
    1. The problem statement, all variables and given/known data

    Find i, i1, i2 in terms of V, r, R, c, and t on the following circuit:

    problem.jpg


    2. Relevant equations

    I suppose I would use Kirchoff's law for this...


    3. The attempt at a solution

    i = i1 + i2
    -ir + V – i1R = 0
    -ir + V – Vc = 0

    Vc = V – ir = q/c
    i1R = -ir + V

    Where do I go from here?
     
  2. jcsd
  3. Feb 25, 2007 #2
    Following the path with just the resistor and the capacitor can I reduce the current to the equation: i2 = (V/r)e^(-t/rC)
     
  4. Feb 25, 2007 #3

    Mentz114

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    Gold Member

    After the transient current that charges the capacitor has gone, you have 2 resistors in series so

    V = i ( r + R)

    You can get the transient by calculating the voltage across R.
     
  5. Feb 25, 2007 #4
    This is what I'm currently thinking...

    i= [V/(r+R)](1-e^-(t/rC))+(V/r)e^-(t/rC)
    i1= [V/(r+R)](1-e^-(t/rC))
    i2= (V/r)e^-(t/rC)
     
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