Finding the equivalent resistance of an RL cct & step input

AI Thread Summary
The discussion centers on determining the inductor current i(t) in an RL circuit before and after a switch is closed. For t<0, the inductor current is calculated as 5A, while for t>0, the current follows an exponential decay based on the time constant. A key point of contention is the equivalent resistance, with one participant calculating it as 6/5 Ohms, while the solution states it is 2 Ohms. The reasoning provided explains that when the switch closes, the 3 Ohm resistor is effectively short-circuited, leaving only the 2 Ohm resistor to contribute to the equivalent resistance. The discussion emphasizes the importance of understanding Thevenin equivalents and the impact of short-circuiting on circuit analysis.
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?
 

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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
 

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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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