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Find the voltage of an inductor in an LR circuit

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data

    at t=0 switch S is closed. Just after the switch is closed what are i1, i2, the potential difference across V2 across resistor 2, and Vl across the inductor? A long time after the switch is closed, what are i1, i2, V2, and Vl?

    Emf = 12V, R1= 15 ohms, R2 = 25 ohms, and L = 5.0 H

    Now switch S is opened at t'=0. Just after the switch is opened, what are i1, i2, V2, and Vl?

    2. Relevant equations
    V=iR
    Vl= -Ldi/dt

    3. The attempt at a solution

    So just after t=0 no current passes through the inductor, so the Vl=12V and V2=0V. Using ohms law, the current in Resistor 1 is i=V/R => i1=0.8A

    A long time after the switch is closed the inductor now acts like a wire, and R1 & R2 are in paralell, therefore, i1=0.8 A and i2=0.48 A V2= 12V and Vl= 0V.

    When the switch is opened at t'=0 R1 & R2 are now in series with the inductor. So i1=i2 => i=V/(R1+R2)= 0.3A. The voltage on the inductor will be 12V to oppose the change in magnetic flux of the circuit. And V2=iR2=7.5V.

    So I am pretty positive about the first two parts of this question. It is really the opening of the switch at t'=0 that I am stuck on. Am I right to say that the Voltage through the inductor is 12V?
     

    Attached Files:

  2. jcsd
  3. Apr 28, 2013 #2
    anyone want to attempt to help?
     
  4. Apr 28, 2013 #3

    gneill

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    Staff: Mentor

    Your first two parts look okay.

    For the the time when the switch re-opens, you've got a problem. There's no voltage source V in the remaining circuit, so it shouldn't play a role in your calculations. Instead, what do you know about the current through an inductor with regards to sudden changes?
     
  5. Apr 28, 2013 #4
    The current will change continuously, so the current through the inductor should be 0.3 A i do believe.
     
  6. Apr 28, 2013 #5

    gneill

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    Nope. Inductors resist a change in current. That's why you wrote that the initial current through the inductor was zero when the switch first closed.

    This time, at the instant when the switch opens at t'=0, the current must remain the same as immediately before the switch opened.
     
  7. Apr 28, 2013 #6
    Okay, so after a long time the inductor acts like a wire which I can then find the current acting on resistor 2. Once the switch is opened, then that current through two will be the current through the inductor which I can then use to find its voltage?
     
  8. Apr 28, 2013 #7

    gneill

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    Yes, the initial current around the loop will be the same as the inductor current immediately prior to the switch opening. Use KVL around the loop to determine all the voltages.
     
  9. Apr 28, 2013 #8
    So the current through the inductor when the switch is opened should be 0.48 A. Giving a voltage of 2.4 V on the inductor, 12 V on resistor 2 and 7.2 volts on resistor 1? This seems odd.... I feel like I have broken the law of conservation on energy?
     
  10. Apr 28, 2013 #9

    SammyS

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    That's correct for the current throught the inductor.

    If the current through the inductor is 0.48 A, then what is the current through R1 and R2 ?

    attachment.php?attachmentid=58314&d=1367173841.jpg
     
  11. Apr 28, 2013 #10
    Well if the current through the inductor is 0.48 A and the switch is open, then we have a series of elements which means that the current through resistors 1 & 2 would also be 0.48 A.
     
    Last edited by a moderator: Apr 29, 2013
  12. Apr 29, 2013 #11

    gneill

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    Nope. The circuit is drawing on the energy stored in the inductor's magnetic field. That potential energy was put there while the switch was closed and the current through the inductor built up.

    You need to check the polarities of the potential drops that you are summing up; Which way does the current flow through each resistor when the switch opens?
     
  13. Apr 29, 2013 #12

    SammyS

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    That's correct.

    What is the voltage drop across each resistor?

    After answering that, What's the voltage across the inductor?
     
  14. May 17, 2013 #13
    So this is a late response, but I do have the concept down for finding the voltage on the inductor when the switch is opened at t'=0. Since the current inside an inductor must change continuously, then the current flowing through the inductor must be the same as the current flowing through resistor two before the switch was opened for t'=0. This would be the 0.48A. To provide this continuous flow of current the inductor creates a momentary spike in its voltage as the release of energy stored in the magnetic field of the inductor depletes. Therefore, the voltage in the inductor at t'=0 is 19.2V. I found this odd because it seems like the laws of physics were broken, but since the inductor has to change continuously, conservation of charge must be instated and the voltage then spikes. Thanks for everyone's help, it allowed me to score a 98 on my exam.
     
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