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Kirchoff's Law Problem

  1. Oct 2, 2013 #1
    1. The problem statement, all variables and given/known data

    In the following figure(Figure 1) the battery has emf 26.0V and negligible internal resistance. R1 = 4.10Ω . The current through R1 is 1.50A and the current through R3 = 5.00A
    What are the resistances of R2 and R3?
    (Image Attached)

    2. Relevant equations

    Kirchoff's Loop/Junction Rule

    3. The attempt at a solution

    I am having some real problems with Kirchoff's Rules. Can someone help me figure out how to begin? I started out by saying that Since the current through R3 is 5A, then that is the same as the current that gets split at the junction into I_1 through R_1 and I_2 through R_2. Also, I know that the voltage drop across R_1 is equal to the voltage drop across R_2 which is 6.15V. Using this, I said that (R_2)(I_2)=6.15V. I was given I_1 (the current through R_1) and I believe the current that enters the junction is the 5A that were given in the problem that go through R_3. Using that, I said that I_2 + I_1 = 5A. Knowing I_1, I found that I_2 should be .9A, which would make R2=6.833 Ohms. I don't know if this is right. Even if it is, how do I go about solving for R_3? I am very confused. Any help would be great.
     

    Attached Files:

  2. jcsd
  3. Oct 2, 2013 #2

    jedishrfu

    Staff: Mentor

    Last edited: Oct 2, 2013
  4. Oct 2, 2013 #3

    phinds

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    Uh ... you might want to take a remedial course in arithmetic here :smile:

    I mean, .9 + 1.5 = 5.0 ???
     
  5. Oct 2, 2013 #4
    Oh woops, I didn't see that. So in that case, I_2 = 3.5A, not 0.9. so the voltage drop across R_2 is the same as that across R_1, which I know is 6.15V. Therefore (3.5A)(R_2)=6.15V. Is this correct?
     
  6. Oct 2, 2013 #5

    jedishrfu

    Staff: Mentor

    Yeah that seems right. You got that from the loop thru the battery right?

    i1*r1 + i3*r3 - 26 = 0 with i1*r1 = (1.5)(4.1) = 6.15 V and since you know i2=3.5A ...

    ALso you should still read the wiki article as it mentions the restrictions on K's laws for AC circuits and when magnetic fields are present.
     
  7. Oct 2, 2013 #6
    Ok, thank you. So that would make R_2 = 1.757 Ohms. So how would I go about finding R_3? I already know the current through there, but what do I do about the EMF? Should I find the equivalent resistance of the top loop, then write another equation using Kirchoff's Law around the whole outer loop? So find R_eq for R_1 and R_2, then have I(R_eq)+I_3R_3-EMF=0? However, if I find R_eq, would the voltage drop be the same as each individual one, allowing me to solve for the current that would flow through R_eq?
     
  8. Oct 2, 2013 #7

    jedishrfu

    Staff: Mentor

    whats the voltage drop across R3? you were able to determine the voltage drop across R1 and R2.
     
  9. Oct 2, 2013 #8
    That is what I am unsure how to find. Would I have to find the equivalent resistance for R1 and R2 and then write another equation since I know the current through R3 already?
     
  10. Oct 2, 2013 #9

    jedishrfu

    Staff: Mentor

    Doesn't the problem say the voltage source is 26V and you know its 6.16V across the R1/R2 piece so now what is it across the R3?
     
  11. Oct 2, 2013 #10
    Is it just 26-6.16?
     
  12. Oct 2, 2013 #11

    phinds

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    Good question. Is it ?
     
  13. Oct 2, 2013 #12
    Im pretty sure it is, but I cannot think of why that would be. Any insight?
     
  14. Oct 2, 2013 #13

    jedishrfu

    Staff: Mentor

    Look at K voltage law again, what does it say about summing voltages in a loop?
     
  15. Oct 2, 2013 #14
    Ahh, so the emf + the voltage on each resistor has to add up to 0. Then once I solve for the voltage of R3, I know the current, so I can find the resistance. Is that correct in my thinking?
     
  16. Oct 2, 2013 #15

    jedishrfu

    Staff: Mentor

    Yes.
     
  17. Oct 2, 2013 #16
    Thank you very much for all of your help. I was having a lot of trouble visualizing this and the steps you have to break things down into. I really appreciate all of your help and putting up with what seems to be nothing short of my ignorance on how to approach this. I really appreciate it.
     
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