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Use Ohm's law and KVL to find the value of R:

  1. Jan 21, 2013 #1
    1. The problem statement, all variables and given/known data

    http://img853.imageshack.us/img853/2038/homeworkprob18.jpg [Broken]

    (everything copied above is as given, except 'I3' was supposed to just be 'I', but more simple for me if 'I3')

    Use Ohm's law and KVL to find the value of R


    2. Relevant equations
    V= IR

    KVL, and maybe KCL:

    KVL = Summation of potential in a loop = 0


    3. The attempt at a solution


    150V - 50V - (I1)(20Ω) = 0

    100V = (I1)(20Ω)

    I1 = 5A

    V (on diagram)= (20Ω)(5A)

    V = 100V

    and I just go straight to saying V = 100V over the 5Ω resistor because it is in parallel with V on the diagram, right?

    So, 100V = (5Ω)(I2)

    I2 = 20A

    I1 + I2 = I3

    I3 = 25A

    V= I/R ; R = V/I

    R = 50V / 25A because 50V was the potential drop across R

    R = 2Ω

    I didn't see the potential drop across R until I was halfway posting this, but is this correct anyway? It looks weird, and I do not know what the correct answer is.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 21, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Your result looks fine.

    Yes, you can go right to "100V/5Ω". In fact, you should recognize that the 50V dropped across R means that the parallel pair of resistors must have 100V across it (that's KVL combined with the shared potential drop of parallel branches) so that the total drop equals the supply voltage.

    Also, knowing the potential drop across the 5 and 20 Ohm resistors tells you the current through each of them. This should tell you something about the current through R, and knowing both the current and potential drop for R...
     
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