RC Circuit Problem: Hi, Is Capacitor Replaced by Short Circuit?

[sammyqw]

Homework Statement

2. Homework Equations [/B]
KCL, Node Analysis , Mesh Currents

The Attempt at a Solution

Hi, in part b when t>0 the capacitor is replaced by an open circuit , however in part c the capacitor is replaced by a short circuit why is that?Aren't inductors the only ones replaced by short circuits?

 

[gneill]

Hi, in part b when t>0 the capacitor is replaced by an open circuit , however in part c the capacitor is replaced by a short circuit why is that?Aren't inductors the only ones replaced by short circuits?

They were looking for the resistance that the capacitor "sees" in order to determine the time constant, RC. One way to do that is to remove the capacitor and determine the Thevenin resistance as seen at those terminals. The author of the solution decided to find the Thevenin resistance by determining the short circuit current and the open circuit voltage. Divide the voltage by the current and voila, Thevenin resistance. That short circuit for the capacitor is just the application of that method.

 

[sammyqw]

They were looking for the resistance that the capacitor "sees" in order to determine the time constant, RC. One way to do that is to remove the capacitor and determine the Thevenin resistance as seen at those terminals. The author of the solution decided to find the Thevenin resistance by determining the short circuit current and the open circuit voltage. Divide the voltage by the current and voila, Thevenin resistance. That short circuit for the capacitor is just the application of that method.

Is there any other way to find the same answer that you may know? Thanks for your help.

 

[gneill]

Is there any other way to find the same answer that you may know? Thanks for your help.

I suppose one could work out and solve a differential equation for the circuit, but that would likely be a lot of work for the same result. Or one could analyze the circuit using Laplace Transforms, again arriving at the same result after more work than necessary.

One way or another, in order to determine the time constant some work has to be done analyzing the circuit. The Thevenin equivalent is a common approach.