Finding IA After a Long-Closed Switch: A Homework Problem

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Discussion Overview

The discussion revolves around a homework problem involving an electrical circuit with a switch that has been closed for a long time and then opens at t=0. Participants are tasked with finding the current IA for all time, considering the behavior of capacitors and resistors in the circuit before and after the switch opens.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • The initial poster presents their understanding of the problem and proposes equations for current, including i(t)=Ioe^(-t/(CReq)) and i(t)=(Q/P)+Ae^(-Pt), while questioning how to find the equivalent resistance (Req) due to the configuration of the circuit.
  • Some participants suggest that to find Req, the voltage source can be removed in the diagram for t>0, leading to a configuration of parallel and series resistors.
  • There is a discussion about the behavior of the capacitor at t=0, where it acts as a short circuit, and how this affects the voltage across the resistors and the calculation of IA initial and final.
  • One participant notes that eventually the capacitor will act as an open circuit, which influences the final current through the resistors.
  • There are suggestions on how to approach finding the initial and final currents, emphasizing the importance of understanding the capacitor's behavior at the moment the switch opens.

Areas of Agreement / Disagreement

Participants generally agree on the approach to finding Req and the behavior of the capacitor at t=0. However, there are differing views on the specifics of calculating the initial current and the implications of the circuit configuration, indicating that the discussion remains unresolved.

Contextual Notes

Participants express uncertainty regarding the exact values for Req and the initial current IA, highlighting the need for clarity on the circuit's configuration and assumptions made in the analysis.

Who May Find This Useful

This discussion may be useful for students studying electrical circuits, particularly those dealing with transient analysis involving capacitors and resistors in series and parallel configurations.

ChillFreeze
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Homework Statement


The problem is:
After being closed for along time, the switch shown in figure 1 opens at t=0. Find IA for all time.


Homework Equations


I believe it would be i(t)=Ioe^(-t/(CReq)) or i(t)=(Q/P)+Ae^(-Pt)
Q/p=Vo/r and 1/p is time constant or t/(CReq)


The Attempt at a Solution


I find that if i label the inductor as Vc i find the voltage as 0 at time 0 because the capacitor becomes a short over a long period of time. I get what is in t<0 and when t>0 . I believe i need to find Req but the problem is how do i find that with the wire between the two resistors? Or is it just the 1k ohms anyway? After finding Req i know that I=if+in and in=Ke^(t/(CReq). t>0 and if=10/2000=1/200 so i=(1/200)+Ke^(t/(CReq) t>0 now i think i need to find out the current so that i can have whatever current i get say B so B=1/200 + K the K = B-1/200
so that it means i=(1/200)+(K)e^(t/CReq) Then using B (current) for all t i=B+B(1-e^(-t/CReq)u(t)

So how do i find what i called B and how do i find the original Req?
Thanks to whoever can help me. Also i placed the original diagram, the t>0 and t<0 diagrams as well. Thanks again
 

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well the t<0 t>0 are my own...so that is what i think is right.
 
Well, you can simply remove the voltage source in your tgreater diagram to find Req. It's just two parallel resistors in series with a third. This and the cap value will give you your time constant. From there you just need Ia initial and Ia final. You know that eventually the cap is going to be an open circuit, so all of the 10v will be traveling through the left two resistors. What does this tell you about Ia final?

Ia initial is a tad trickier, but not bad. You know that the cap was an open circuit at t=0- and that it's set across a short circuit with no voltage drop. So what does this tell you about the cap's voltage? At time t=0+ the cap acts as a short circuit, so it should be a simple task to find the voltage across the 3k resistor and the corresponding current. With these values in hand, you should be able to answer this question.

Hope it helps.

I wouldn't put your diagrams in a zip next time. You'll probably get more and faster help.
 
Thanks, i will keep that in mind for next time, they were to big so i just put them in a zip to make them fit. Thanks again
 

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