Finding the equivalent resistance of an RL cct & step input

In summary: When you short circuit the voltage source, you ignore the 3 ohm resistor as well. This is because the 3 ohm resistor is part of the short-circuited loop.
  • #1
sugz
110
0

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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  • #2
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.
 
  • #3
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.
 
  • #4
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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  • #5
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?
 
  • #6
Wouldn't there be a voltage difference across the 3 ohm resistor?
 
  • #7
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?
 
  • #8
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.
 

1. What is the purpose of finding the equivalent resistance of an RL circuit?

The equivalent resistance of an RL (resistor-inductor) circuit is used to simplify the circuit and make it easier to analyze. It is also useful in determining the time constant of the circuit and the behavior of the circuit in response to a step input.

2. How is the equivalent resistance of an RL circuit calculated?

The equivalent resistance of an RL circuit can be calculated by finding the total resistance of the circuit and adding it to the resistance of the inductor, which is equal to its impedance (XL = 2πfL). This is known as the total impedance of the circuit.

3. What is a step input and how does it affect the RL circuit?

A step input is a sudden change in the input voltage or current of a circuit. In an RL circuit, a step input causes the inductor to produce a back-emf (electromotive force) which resists the change in current. This results in a slower rise or fall in the current through the circuit compared to a pure resistive circuit.

4. What factors can affect the equivalent resistance of an RL circuit?

The equivalent resistance of an RL circuit can be affected by the values of the resistance and inductance in the circuit, as well as the frequency of the input signal. Additionally, the presence of other components such as capacitors or diodes can also affect the equivalent resistance.

5. How is the equivalent resistance of an RL circuit used in practical applications?

The equivalent resistance of an RL circuit is used in many practical applications, such as in power supplies, motors, and filters. It is also used in designing and analyzing complex electronic circuits to determine the overall behavior and performance of the circuit.

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