First Order RC Circuit Analysis: Homework Equations and Attempted Solution

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Discussion Overview

The discussion revolves around the analysis of a first-order RC circuit, focusing on the application of relevant equations and the interpretation of time constants in relation to step functions. Participants are addressing a homework problem that involves understanding the behavior of the circuit over time.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant presents the equation for voltage in a driven RC circuit and expresses uncertainty about their interpretation of the step function and the time constant.
  • Another participant confirms the calculations but asks for clarification on the specific problems faced.
  • The original poster questions the discrepancy between their calculated time constant and the one provided in the problem, suggesting a potential misunderstanding of the circuit's behavior before t=0.
  • A later reply clarifies that the time constant is indeed \tau=6RC for t<0, but notes that this changes at t=0 due to the circuit's alteration.

Areas of Agreement / Disagreement

Participants generally agree on the calculations being correct, but there is ongoing uncertainty regarding the interpretation of the time constant and its change at t=0. The discussion remains unresolved regarding the implications of these differences.

Contextual Notes

There are limitations regarding the assumptions about the time constant before and after t=0, as well as the interpretation of the step function in the context of the problem.

RoKr93
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Homework Statement


2013-07-03163445_zps93be684f.jpg



Homework Equations


vc(t) = vc(∞) + [vc(0+) - vc(∞)]*e-t/τ (Voltage in a driven RC circuit)

τ = RC (time constant for an RC circuit)


The Attempt at a Solution


2013-07-03163504_zpse1bdce44.jpg


I'm pretty shaky with these sorts of problems and am quite unconfident of my work here. Step functions tend to confuse me and I'm not quite certain I interpreted this one right- I understand it to mean Vin(t) = V0 when t ≤ τ. Also, my time constant appears to be inconsistent with the one given in the problem, but I'm not sure if it's supposed to be the same thing.

Would appreciate some clarification.
 
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Your calculations are correct. What problems do you have?
 
Okay, great. I just haven't performed many of these problems and wasn't sure. But one question persists: why does my time constant differ from the given one? Is 6RC the time constant before t=0?
 
Yes, we have \tau=6RC for t&lt;0. But the circuit changes at t=0 so \tau also changes.
 

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