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

Click For Summary

Discussion Overview

The discussion revolves around the behavior of a capacitor in an RC circuit, specifically addressing the conditions under which a capacitor is replaced by an open circuit or a short circuit. Participants explore the implications of these replacements in the context of determining the time constant and Thevenin resistance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants note that in part b, when t>0, the capacitor is replaced by an open circuit, while in part c, it is replaced by a short circuit, questioning the rationale behind this distinction.
  • One participant explains that the short circuit for the capacitor is used to find the Thevenin resistance as seen at the capacitor's terminals, which is necessary for determining the time constant, RC.
  • Another participant suggests that alternative methods, such as solving a differential equation or using Laplace Transforms, could also yield the same result, though they may involve more complex calculations.

Areas of Agreement / Disagreement

Participants express uncertainty about the replacement of the capacitor with a short circuit and whether there are alternative methods to achieve the same results. No consensus is reached on the best approach or the reasoning behind the capacitor's replacement.

Contextual Notes

Participants mention the need to analyze the circuit to determine the time constant, indicating that the discussion may depend on specific definitions and assumptions related to circuit analysis methods.

sammyqw
Messages
20
Reaction score
0

Homework Statement


image.png

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

The Attempt at a Solution


image.png

image.png

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?
 
Physics news on Phys.org
sammyqw said:
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.
 
  • Like
Likes   Reactions: sammyqw
gneill said:
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.
 
sammyqw said:
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.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 11 ·
Replies
11
Views
8K