Using Kirchoff's Laws to solve a circuit

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Homework Help Overview

The discussion revolves around applying Kirchhoff's laws to analyze a circuit involving resistors and a capacitor. Participants are tasked with finding the currents i, i1, and i2 in terms of voltage (V), resistance (r, R), capacitance (c), and time (t).

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to set up equations based on Kirchhoff's law but questions the next steps in their reasoning. Other participants explore the behavior of the circuit over time, particularly focusing on the transient response of the capacitor and the series configuration of resistors.

Discussion Status

Participants are actively engaging with the problem, offering various equations and interpretations of the circuit's behavior. Some have proposed specific equations for the currents, while others are still questioning the assumptions and setup of the problem.

Contextual Notes

There is an implicit assumption regarding the initial conditions of the circuit and the behavior of the capacitor over time, which may not be fully defined in the original post.

lylos
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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?
 
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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)
 
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.
 
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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