RC Circuit, Need help forming equation.

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Homework Help Overview

The discussion revolves around an RC circuit problem where the switch has been in one position for an extended period before being moved to another position at time t=0. Participants are tasked with finding the initial current i(0) for t>0, utilizing Kirchhoff's Voltage Law (KVL) and first-order differential equations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to analyze the circuit before and after the switch is moved, noting that the circuit is open at t<0, leading to an initial current of zero. They express confusion regarding their result compared to the expected answer provided by the teacher. Other participants question the nature of the voltage source in the circuit and its relationship to the current.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into the circuit's components and questioning the original poster's approach. There is a recognition of potential sign errors in the KVL application, and further clarification is sought regarding the correct sign conventions. No consensus has been reached yet, but there is a productive exchange of ideas and corrections.

Contextual Notes

Participants are navigating through the complexities of the circuit setup, including the role of the dependent voltage source and the implications of the switch's position. There is an emphasis on ensuring the correct application of KVL and the associated sign conventions, which remains a point of contention in the discussion.

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Homework Statement


The switch has been in position 1 for a long time before moving to position 2 at t=0. Find i(0) for t>0.

Image of circuit:
http://img215.imageshack.us/img215/9200/circuit3.png


Homework Equations


KVL
First Order Diff Eq


The Attempt at a Solution


So to start the problem what I did was look at the circuit at t<0. I got a current for i(0) to be 0 because the circuit is open at t<0. When I switched it to position two I did KVL to form a first order linear equation. For my answer I got i(0)=Ce^(-1000t)
My teacher gave us the answer to work too and I cannot get it. He said the answer should be .3125e^(-500t)mA. Can anyone help me?
 
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That diamond shaped thing is a voltage generator ?
It's voltage is [tex]20.000 i_0[/tex] ?
 
Quinzio said:
That diamond shaped thing is a voltage generator ?
It's voltage is [tex]20.000 i_0[/tex] ?

the voltage is a dependent source. and yes it is 20,000i_0
 
For my answer I got i(0)=Ce^(-1000t)

I checked your teacher answer an it is correct (no wonder).
That circuit is very simple for who (like me) works in the electornic field.

What steps did you do to get your answer ?
 
Last edited:
Quinzio said:
I checked your teacher answer an it is correct (no wonder).
That circuit is very simple for who (like me) works in the electornic field.

What steps did you do to get your answer ?

I looked at the circuit at t< 0 and said that the capacitor makes an open circuit. So the dependent voltage source goes away and you are left with an open circuit and the voltage source and resistor. Since its an open circuit I said there is no current for t < 0.

For t > 0 you have only part of the circuit do to the switch so you are left with: The 60k ohm resistor, the dependent source, and the capacitor. I did KVL and ot 60ki(0) - (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0

From that I got an differtial of 1000i(0) a di/dt = 0 and got i(0)=Ce^-1000t
 
60ki(0) - (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0

There are/is mistakes with signs.
Run the looop in the direction of i(0), and pay attention to signs.
 
Quinzio said:
60ki(0) - (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0

There are/is mistakes with signs.
Run the looop in the direction of i(0), and pay attention to signs.

I am not sure then, I thought I was using one of the sign conventions. My professor has told us that you can do it two ways and you will get the same answer. I change it to what I believe will be the proper sign convention. Otherwise I am stuck. If you are able to please explain more it will be really helpful.

60ki(0) + (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0
 

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