Finding the equivalent resistance of an RL cct & step input

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Homework Help Overview

The discussion revolves around determining the inductor current in an RL circuit before and after a switch is closed. Participants are examining the equivalent resistance of the circuit and how it changes with the switch's position.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing the calculation of equivalent resistance, particularly questioning why certain resistors are considered or ignored when the circuit is altered. There are attempts to clarify the application of Thevenin's theorem and the implications of short-circuiting components.

Discussion Status

The discussion is active, with participants exploring different interpretations of the circuit's behavior. Some have offered guidance on analyzing the circuit using Thevenin equivalents, while others are questioning the assumptions made about the resistors' roles in the circuit after the switch is closed.

Contextual Notes

There are indications of confusion regarding the treatment of resistors in the circuit when applying Thevenin's theorem, as well as the implications of short-circuiting the voltage source. Participants are also referencing an attached document for circuit details, which may contain additional context.

sugz
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Homework Statement



Determine the inductor current i(t) for both t<0 and t>0 for the circuit shown in the attached document"Circuit 1.

Homework Equations

The Attempt at a Solution



Before t=0, i=(25)/(3+2) = 5A
After t=0, i(t)=i(0)e^(-t/tow)
tow=L/R=4/(6/5)

However, the solution states that the equivalent resistance of the circuit is 2, whereas I got 6/5. I am not sure how they were able to get this. Can someone help?
 

Attachments

  • Circuit 1.PNG
    Circuit 1.PNG
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After t = 0, the switch closes, so the left half of the circuit is short circuited. Since you need the equivalent resistance seen from the terminals of the inductor, and since the 3 Ohm resistor is part of the short-circuited loop, there's only the 2 Ohm resistor to account for.
 
Or let me put it this way. Write a Thevenin equivalent of the left loop, with the terminals slightly to the right of the short circuit. That should make it easier to see.
 
Why is it that when you short circuit the voltage source, you ignore the 3 ohm resistor as well? The circuit I get is attached in the file
 

Attachments

  • 20150311_222746.jpg
    20150311_222746.jpg
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Check your Thevenin resistance again. If you attached a voltage source to the terminals, what would happen? Would there be a voltage difference across the resistor? Would the resistor affect anything?
 
Wouldn't there be a voltage difference across the 3 ohm resistor?
 
From Ohm's law, V = IR. So you want the voltage across the resistor. Well, you know the resistance. So what's the current through the resistor?

Or perhaps no current would ever travel through the resistor if there's another path to take that has 0 resistance...hint hint

So in other words, does the resistor have a potential difference across it?
 
sugz said:
Why is it that when you short circuit the voltage source, you ignore the 3 ohm resistor as well? The circuit I get is attached in the file
Sketch the circuit given, and draw a closed loop showing the path that current through the inductor follows after the switch has been closed.
 

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