Finding the function of the cap.

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Discussion Overview

The discussion revolves around finding the voltage across a capacitor, Vc(t), in a circuit involving a switch and an initially charged capacitor. Participants explore the application of Thevenin's theorem and the behavior of the circuit over time, particularly after the switch is manipulated. The focus includes theoretical reasoning and mathematical expressions related to capacitor discharge.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes using Thevenin's equivalent to analyze the circuit and derives the expression Vc(t) = final + (initial - final) e^(t/RC).
  • Another participant questions the initial approach, suggesting that the capacitor disappears from the circuit after the switch is opened, indicating a misunderstanding of the circuit configuration.
  • A later post requests clarification on the circuit diagram and the role of a current source, indicating potential errors in the original setup.
  • One participant attempts to find the Thevenin equivalent and calculates a time constant of 1.67x10^-7, leading to a proposed expression for Vc(t) that suggests exponential behavior.
  • Another participant challenges the calculated Thevenin resistance, stating they found an indeterminate result and expressing concern that the proposed Vc(t) would increase without limit, which contradicts expected physical behavior.
  • One participant describes their method for determining the Thevenin equivalent and corrects a sign error in their expression for Vc(t), presenting a different exponential decay model.

Areas of Agreement / Disagreement

Participants express differing views on the circuit configuration and the validity of the proposed mathematical models. There is no consensus on the correct approach or the behavior of Vc(t) over time, indicating ongoing debate and uncertainty.

Contextual Notes

Participants mention potential drawing errors and the need for accurate circuit representation. There are unresolved questions regarding the Thevenin equivalent and the implications of the derived expressions for Vc(t).

johndoe
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3113203781_233b4fbdd4_o.jpg


This is one of the questions I got in my finals, and I couldn't do it back then. I want to find Vc(t) , given the cap is initially charged up to 10V, the switch is then opened. My approach is to find the thevein eq of the circuit, which I would came up with a resistor in parallel with the cap, and then find the function using the expression Vc(t) = final + (initial - final) e^(t/RC).
sounds good?
 
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johndoe said:
3113203781_233b4fbdd4_o.jpg


This is one of the questions I got in my finals, and I couldn't do it back then. I want to find Vc(t) , given the cap is initially charged up to 10V, the switch is then opened. My approach is to find the thevein eq of the circuit, which I would came up with a resistor in parallel with the cap, and then find the function using the expression Vc(t) = final + (initial - final) e^(t/RC).
sounds good?

After the switch is opened, the cap disappears from the circuit, no?
 
berkeman said:
After the switch is opened, the cap disappears from the circuit, no?

ops the switch should be opened initially and then closed(drawing error)
 
What is the source on the right? It can't be a current source of value 5ix, since there is only one ix flowing through the resistor before the switch is closed...

I think you need to re-draw the circuit correctly, and then show us your work on the solution. Then we may be able to offer some help.
 
Question:
Finding the function of the 0.1uF cap Vc(t) when the switch is closed at t=0 given that the cap is initial charged up to 10V.

3117971925_4c2bc42cf6_o.jpg


ok my attempt at this I find the thevenin eq of the right hand side circuit and come up with :
3117972721_0e2f97c1db_o.jpg


Vc(infinite) = 0, Vc(0)=10 , time constant = RC = 1.67x10^-7

Vc(t) = 0 + ( 10-0) e^(t/(1.67x10^-7 ))

Appreciate if u could have a look at it.
 
How did you get 1.67 ohms for your thevenin equivalent circuit? I got an indeterminate answer for the thevenin equivalent circuit. You could do it without that. Furthermore, your final answer doesn't make much physical sense; Vc(t) would increase exponentially without limit as time passes.
 
Defennder said:
How did you get 1.67 ohms for your thevenin equivalent circuit? I got an indeterminate answer for the thevenin equivalent circuit. You could do it without that. Furthermore, your final answer doesn't make much physical sense; Vc(t) would increase exponentially without limit as time passes.

This is what I did :
3120459633_644b262141_o.jpg


I hook up a 1V source and solve for I1 and thus the Rth.

And I left out a - sign in my final answer
Vc(t) = 10e^-t/RC
 

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