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How to Apply Ohm's Law?

  1. May 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Apply Ohm's law and the nature of parallel circuits to determine the total current in a parallel circuit with three resistors: 3Ω, 6Ω, and 9Ω, respectively. The total voltage in the circuit is 12V. Explain your reasoning.

    2. Relevant equations
    Ohm's Law


    3. The attempt at a solution
    I tried to plug the values into Ohm's law, but I don't think that is how I am supposed to go about this.

    I am not asking for someone to give me the answer outright, just a place to start here!
    All answers will be appreciated! :wink:
     
  2. jcsd
  3. May 22, 2016 #2

    cnh1995

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    It is necessary to show your working. Did you calculate their equivalent resistance first or did you directly apply Ohm's law? Both ways work fine.
     
  4. May 22, 2016 #3
    Hi,
    I just tried to apply Ohm's Law directly. I realized it wasn't going to work, because I have more values than are in that formula. But here is as far as I got.
    First I added up all of the Ohms and got 18Ω. Then, I plugged it into the formula,

    V/R = 12/18 = 0.6666666667

    And I guess that could be right, I just figured that because of how I went about adding up the Ohms that it wasn't.

    Thanks!
     
  5. May 22, 2016 #4

    SteamKing

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    Why would you add the resistance values together when you are told specifically that the resistors are in parallel?

    Do you not understand what "parallel" means in this context?


    ff0c8e0c446c3ab7fbf095ca4496d9c2.png
     
  6. May 22, 2016 #5
    As I said, I did not think I was doing it correctly. It was simply me attempting to go about the problem, not really having any idea how. I guess what I am really asking is how I would use this information in a formula.
     
  7. May 22, 2016 #6

    cnh1995

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    Have you studied the concept of equivalent resistance of a series/parallel network?
     
  8. May 22, 2016 #7
    No. That is what I was trying to get a grasp of.
     
  9. May 23, 2016 #8

    cnh1995

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    Ok. What do you understand from the fact that they are in parallel?
     
  10. May 23, 2016 #9
    I understand that by parallel it means there are multiple resistors that are side by side next to each other. What I am not understanding is how to apply this information to use it in a formula..
     
  11. May 23, 2016 #10

    cnh1995

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    What can you say about voltage across parallel components?
     
  12. May 23, 2016 #11
    I think I have figured it out, using the formula for total resistance.


    equation15.gif = 3x6x9/3+6+9 = 162/8 = 9
    Then I used the formula for total current:


    equation20.gif
    12/9= 1.33333333333333
     
  13. May 23, 2016 #12

    cnh1995

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    No. The equivalent resistance of parallel combination of 3Ω, 6Ω and 9Ω is not 9Ω.
    The formula in your image is true for only two resistors in parallel.
     
  14. May 23, 2016 #13
    Oops I think I used the wrong formula. Here is the formula for multiple resistors:
    equation14.gif Which would make 18, correct?

    So then 12/18 is 0.666666667.
     
  15. May 23, 2016 #14

    cnh1995

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    Have you studied the theory behind series and parallel components in a circuit? Do you understand what happens to voltage or current when components are in series or parallel?
    No. Equivalent resistance of resistances in parallel is less than the least of them.
     
  16. May 23, 2016 #15
    Thank you for trying to assist me with this, and sorry if I don't seem to be understanding this. Could you tell me what formula is supposed to be used here then if it wasn't the one I used above?
     
  17. May 23, 2016 #16

    cnh1995

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    Well, the formula in your above post is correct but it doesn't give 18 ohm. Try again using that formula.
     
  18. May 23, 2016 #17
    What does 1/Rn stand for/mean though? Because all of the values I have are the resistors and the voltage...
     
  19. May 23, 2016 #18

    cnh1995

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    1/Requivalent...
     
  20. May 23, 2016 #19
    Does that mean you would add all of the resistors + the equivalent of all of the resistors? So then it would be 36?
     
  21. May 23, 2016 #20
    I will give you a couple of hints.

    One. For resistors in parallel the resistance of the combined resistors is less than the smallest resistor.

    Two. The smallest resistor is 3 ohms. The current through that resistor at 12 volts is 4 amps.

    Therefor the parallel resistance of all the resistors is less than 3 ohms, and the combined current will be greater than 4 amps.
     
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