Laplace Transform on RC circuit

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Discussion Overview

The discussion revolves around applying the Laplace Transform to analyze an RC circuit, specifically focusing on finding the voltage across the capacitor over time. Participants are addressing the challenges of setting up the problem for partial fraction expansion and dealing with initial conditions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how to format the equation for partial fraction expansion and questions the treatment of the initial voltage V(0').
  • Another participant asks for clarification on the problem statement and raises a question about the initial charge on the capacitor when the switch was open.
  • A participant clarifies that the goal is to find v(t) for t>0 in a series RC circuit with a voltage source E, resistor R, and capacitor C.
  • There is a suggestion that it is reasonable to assume V(0') is equal to 0, although the problem statement lacks explicit information about it.
  • Participants discuss the need to refer to inverse Laplace transform tables and propose a method for setting up the equation to solve for coefficients A and B in the partial fraction expansion.
  • A link is provided for additional resources on partial fraction expansion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial condition for V(0') and express differing levels of understanding regarding the setup of the problem for partial fraction expansion. The discussion remains unresolved with multiple competing views on how to proceed.

Contextual Notes

There are limitations regarding the clarity of the problem statement and the assumptions about initial conditions, which are not fully defined in the discussion.

CoolDude420
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Homework Statement


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Homework Equations

The Attempt at a Solution


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I'm kind of lost now, how do I go about getting this into the right form for partial fraction exapnsion. And also what do I do with the V(0'). There was no information given about it.
 

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What is the problem statement? It is not clear from what you supplied. Also, why do you have an initial charge on the capacitor when the switch was initially open?
 
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The problem is to find v(t) for t>0. The diagram is a series combination of a voltage source E, resistor R and capcitance C. Where v(t) is the voltage across the capacitor. The step function diagram is for E not v(t)
 

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CoolDude420 said:
I'm kind of lost now, how do I go about getting this into the right form for partial fraction exapnsion.
Algebra.
And also what do I do with the V(0'). There was no information given about it.
It's reasonable to assume it's equal to 0, though the problem statement really should have included information about it.
 
vela said:
Algebra.

It's reasonable to assume it's equal to 0, though the problem statement really should have included information about it.

Any idea on what next "algebra" step to take?
 
take a look at any inverse laplace table. You need to find a way to get your system into one of those forms.
So...

E/C / [ S * (Rs+1/C) ] = A1 + [A2 / S] + [A3 / (Rs+1/C)]

Solve for A and B. How do you do that. Try setting s=0 and s= -1/(RC), which will cancel out the values
 

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