First Order RC Circuit Analysis: Homework Equations and Attempted Solution

AI Thread Summary
The discussion focuses on analyzing a first-order RC circuit using the equation vc(t) = vc(∞) + [vc(0+) - vc(∞)]*e-t/τ, where τ = RC represents the time constant. The participant expresses uncertainty about interpreting step functions and the time constant, noting a discrepancy between their calculated τ and the one provided in the problem. Clarification reveals that the time constant can differ before and after t=0, with τ being 6RC for t<0 and changing at t=0. The conversation emphasizes the importance of understanding how circuit conditions evolve over time. Overall, the analysis highlights common challenges in mastering RC circuit problems and the need for clear interpretation of time constants.
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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