First Order Transient: RC Circuit

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SUMMARY

The discussion focuses on analyzing a first-order transient response in an RC circuit, specifically determining the voltage across the capacitor, Vc(t). The key equation used is Vc = Vs*e^(-t/RC), where Vc(0+) = Vc(0) = Vc(0-). Participants emphasize the need to find the equivalent resistance (Req) to calculate the time constant accurately. The discussion also highlights the importance of considering the timing of the analysis, particularly before or after t=0, as it significantly impacts the time constant.

PREREQUISITES
  • Understanding of RC circuits and their transient behavior
  • Familiarity with the concept of equivalent resistance (Req)
  • Knowledge of Thévenin's theorem for circuit simplification
  • Basic calculus for analyzing exponential functions
NEXT STEPS
  • Learn how to calculate equivalent resistance in complex circuits
  • Study Thévenin's theorem and its application in circuit analysis
  • Explore the derivation and application of the time constant in RC circuits
  • Investigate the effects of initial conditions on capacitor voltage in transient analysis
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing transient responses in RC circuits will benefit from this discussion.

jclay06
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Homework Statement



http://i.thespiffylife.com/files/1/trans1.jpg

i have to find Vc(t)

Homework Equations



I know that Vc(0+) = Vc(0) = Vc(0-) and Vc = Vs*e^(-t/RC)

The Attempt at a Solution



What I'm unsure on is what the equivalent resistance of the circuit would be so I could find the time constant. I know since the Capacitor is fully charged it now behaves as a voltage source, but for any nodal / mesh equation I come up with I'm always one equation short of having equal unknowns & equations.
So ... any help on how to find the Req would be nice.
 
Last edited by a moderator:
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jclay06 said:

Homework Statement



http://i.thespiffylife.com/files/1/trans1.jpg

i have to find Vc(t)

Homework Equations



I know that Vc(0+) = Vc(0) = Vc(0-) and Vc = Vs*e^(-t/RC)

The Attempt at a Solution



What I'm unsure on is what the equivalent resistance of the circuit would be so I could find the time constant. I know since the Capacitor is fully charged it now behaves as a voltage source, but for any nodal / mesh equation I come up with I'm always one equation short of having equal unknowns & equations.
So ... any help on how to find the Req would be nice.

Find the Thévenin equivalent around the capacitor.

EDIT: Before, or after t=0? Which will affect the time constant?
 
Last edited by a moderator:

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