Discharging Capacitor: Differential Equation in terms of Vs, C, R

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Discussion Overview

The discussion revolves around the formulation of a differential equation for a discharging capacitor in an electrical circuit, specifically focusing on the voltage across the capacitor and the assumptions regarding the source voltage (Vs) at different time intervals. The scope includes theoretical aspects of circuit analysis and differential equations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that the voltage across the capacitor is 10V when t<0 and questions whether Vs is 0 or 10V at that time.
  • Another participant suggests that assuming Vs=0 at t<0 is reasonable, but clarifies that it may refer to the voltage at the negative end of Vs being zero, which is a common practice in circuit analysis.
  • A third participant questions the initial statement about the voltage across the capacitor, asking for precise wording to confirm the interpretation.
  • Another participant emphasizes the need to specify the polarity of the 10V across the capacitor before proceeding, noting that the source voltage should be assumed to remain at +10V throughout the analysis.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding the source voltage (Vs) and the polarity of the voltage across the capacitor. There is no consensus on these points, and the discussion remains unresolved.

Contextual Notes

Participants highlight the importance of defining the reference point for voltage and the polarity of the voltage across the capacitor, which may affect the formulation of the differential equation. There are also uncertainties regarding the interpretation of the problem statement.

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Homework Statement



The voltage across the capacitor is 10V when t<0
The switch is closed at t=0

I have to find the diff eq. in terms of Vs, C, R by balancing the current at node Vc(t). But i am not sure whether the Vs is 0 or 10V at t<0

The Attempt at a Solution



I am assuming Vs = 0 at t<0 since the voltage across capacitor is 10V. Also, I am not sure what current balance at the node means...I mean when the switch is closed the current through the capacitor is the same as current through the resistor. So,

iR = iC
(Vc/R) = C (dVc/dt)

How do i write this in term of Vs? Isn't the current through the resistor Vc/R since Vs is 0 at the beginning?
 

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I'm not sure what you mean when you say "I am assuming Vs=0...". I think you mean that you are assuming that the voltage at the negative end of Vs is zero - which would be a fine assumption. It doesn't really matter what point you take as your "ground" or zero voltage level.

If you take Vs- as zero, then obviously Vs+ will be "Vs" and Vc(0) will be at (Vs-10v). Or, perhaps, (Vs+10V), since the polarity of the voltage across the capacitor is not explicitly specified.
 
The voltage across the capacitor is 10V when t<0
Are you sure this is what it says--"across the capacitor"? Can you quote precisely the wording of the question?
 
You have to specify the polarity of the 10V across C before proceeding with the problem. It could be +10V or -10V.

Since the source is not mentioned in the problem statement you should asume it stays at +10V for all time -infinity to +infinity.
 

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