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Potential Difference and Power in Resistor Circuit

  1. May 5, 2014 #1
    1. The problem statement, all variables and given/known data
    I attached a screenshot of the problem(s) that my professor gave in a practice exam.

    2. Relevant equations
    ∑I = 0 at each junction
    ∑V = 0 at each closed loop
    P = I2R = V2/R
    Rseries = R1 + R2 +...

    3. The attempt at a solution
    Part A:
    I think the current I in the center, broken line of current, is zero because that wire is broken. Then
    I1+I2 = 0. So I1 = I2 = I

    Going around the large loop, starting from the battery at the top:

    V + V - IR - IR = 0
    2V = 2IR
    V=IR
    12 = I(10)
    I = 1.2

    In the bottom loop...

    Va + V - IR + V = Vb
    Va - Vb = -2V + IR
    Va - Vb = -2(12) + (1.2)(10)
    Va - Vb = 12V in absolute value...
    Is absolute value what I'm looking for? +12V is the answer in the solutions my professor provided.

    Part B:
    Rseries = R1 + R2 +...
    Rseries = 10 + 10
    Rseries = 20

    P = I2R = V2/R
    P = (1.2)2(20) = 28.8W
    P = (12)2/(20) = 7.2W

    These aren't equal. I tried it with R in parallel as well (Req = 5), and it's still wrong. In the answers provided each of the power equations are multiplied by 2 and R = 10. Why is all of this?

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. May 5, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Va-Vb=-12 V, The potential increases from a to b by 12 V. Look at your notes, what Uab means, it might be Vb-Va.

    The 28.8 V is correct. The voltage is 24 V across the two series resistors, so P=242/20, the same as before.

    ehild
     
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