Engineering First Order Transient: RC Circuit

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To find Vc(t) in the RC circuit, the equivalent resistance (Req) is crucial for determining the time constant (τ = RC). The capacitor, once fully charged, acts as a voltage source, complicating the nodal or mesh analysis due to an imbalance in equations. Users suggest finding the Thévenin equivalent around the capacitor to simplify calculations. Clarification is needed on whether to consider the circuit before or after t=0, as this affects the time constant. Understanding these concepts is essential for solving the problem effectively.
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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