RC Circuit Transient Response Analysis

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Discussion Overview

The discussion revolves around the transient response analysis of RC circuits, specifically focusing on calculating the output voltage (VO) at various time intervals after a switch is opened or closed. Participants explore different scenarios involving the circuit's behavior before and after the switch operation, including time constants and voltage equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Participants discuss the calculation of output voltage VO at specific times (t = 0−, t = 0+, t = t1, and t → ∞) after the switch operation.
  • Some participants suggest determining the time constant for the circuit and writing the voltage expression as a function of time.
  • There are multiple attempts to calculate VO using the formula Vo.e^(-t/RC), with varying results and some participants expressing confusion over their calculations.
  • One participant mentions a similar question with a different time constant and output voltage, leading to a discussion about the correctness of their calculations.
  • Participants clarify the role of Thevenin equivalents and the behavior of the circuit when the switch opens or closes, including the initial and final voltage values.
  • There is a discussion on the time constant involving different resistors in the circuit, with some participants correcting earlier assumptions about which resistors are in play.
  • One participant questions the applicability of the same equation to a different circuit scenario, prompting further analysis of the expected behavior when the switch closes.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct calculations for VO, as multiple competing views and calculations are presented. There is ongoing uncertainty regarding the correct application of formulas and the values used in calculations.

Contextual Notes

Participants express uncertainty about the initial conditions of the capacitor and the impact of different resistor values on the time constant. Some calculations are based on assumptions that may not hold true across different scenarios, leading to discrepancies in results.

Who May Find This Useful

This discussion may be useful for students and individuals interested in understanding the transient response of RC circuits, particularly in the context of homework problems and circuit analysis techniques.

  • #31
for t=24μs I get Vo as 6 x 0.1236 = 0.742V.
 
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  • #32
dudforreal said:
for t=24μs I get Vo as 6 x 0.1236 = 0.742V.

Where'd the 6 come from?
 
  • #33
Isn't that Vth?
 
  • #34
dudforreal said:
Isn't that Vth?

Perhaps we're looking at different problems? I thought you'd stated that Vo goes from 0V to 3.322V?
 
  • #35
oh sorry...so it is 3.322 x 0.1236 = 0.411V.
 
  • #36
dudforreal said:
oh sorry...so it is 3.322 x 0.1236 = 0.411V.

That looks good. The numbers and calculation are good.
 
  • #37
Gotta go catch some zZ's now. I'll check back in the morning (my morning, that is).

:zzz:
 
  • #38
I think that my answer is wrong because when I used this equation on a different question with the same circuit with the voltage source being 4V, R1 = 1600, R = 2000 and C = 10n the answer I got was 0.798V but the correct answer is 1.4239V.
 
  • #39
Good morning. (*YAWN*)

I took another look at the problem. A small correction is required to the time response formula.

This time the exponential is starting at zero and heading towards a final value that's equal to the Thevenin voltage of the resistor network. So the form is:
V_o(t) = V_{th} \left(1 - e^{-t/\tau} \right)

Regarding your "different question with the same circuit", apply the above suggested formula and recheck your result -- also check to see if the time t1 to be plugged in is the same for both problems.
 
  • #40
ok cool i got the answer. Now for the second part of the question with the switch between the resistor and the voltage source, my answer for the time before and after 0 as 0V and it is going to -5(7500/17500) = -2.143V.
 
  • #41
dudforreal said:
ok cool i got the answer. Now for the second part of the question with the switch between the resistor and the voltage source, my answer for the time before and after 0 as 0V and it is going to -5(7500/17500) = -2.143V.

Yes, that's what I see for that circuit.
 
  • #42
ok thanks i got the answer :smile:
 

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