Using Kirchoff's Laws to solve a circuit

  • Thread starter lylos
  • Start date
  • #1
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Homework Statement



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

problem.jpg



Homework Equations



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


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?
 

Answers and Replies

  • #2
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Following the path with just the resistor and the capacitor can I reduce the current to the equation: i2 = (V/r)e^(-t/rC)
 
  • #3
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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.
 
  • #4
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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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