Calculating Rth and τ for a Switched Circuit: A Homework Solution

  • Thread starter Thread starter ainster31
  • Start date Start date
  • Tags Tags
    Computing
Click For Summary
SUMMARY

The discussion focuses on calculating the Thevenin equivalent resistance (Rth) and the time constant (τ) for a switched circuit. The correct Rth value after the switch is flipped for t>0 is established as 2 ohms, contrary to the expected 3 ohms. The analysis emphasizes that only the right side of the circuit, which includes a 2 ohm resistor and an inductor, is relevant for determining τ, as the two sides become independent due to the short circuit after the switch is closed.

PREREQUISITES
  • Understanding of Thevenin's theorem
  • Knowledge of circuit analysis techniques
  • Familiarity with inductors and resistors in electrical circuits
  • Basic concepts of time constants in RL circuits
NEXT STEPS
  • Study Thevenin's theorem applications in circuit analysis
  • Learn about calculating time constants in RL circuits
  • Explore the effects of switching in electrical circuits
  • Review short circuit analysis in complex circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing switched circuits and their transient responses.

ainster31
Messages
158
Reaction score
1

Homework Statement



sQWh9sF.png


Homework Equations


The Attempt at a Solution



I'm trying to calculate Rth so I can compute τ. The problem is that after the switched is flipped for t>0, here is what is left:
rxZkCds.png


So you would expect Rth to be 3 ohms but it is actually 2 ohms.

Solution for reference:
KSpKitJ.png
 
Physics news on Phys.org
The circuit you have drawn is for the left side of the circuit after the switch is closed. That part is irrelevant. The part with the time constant is the right side of the circuit, which has just the 2 Ohm resistor and the inductor. After the switch is closed, the two sides of the circuit are independent of each other, because of the short circuit between them.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
4K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 42 ·
2
Replies
42
Views
7K
  • · Replies 8 ·
Replies
8
Views
1K
  • · Replies 19 ·
Replies
19
Views
5K