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Total power of resistors in a circuit

  1. Feb 1, 2017 #1
    1. The problem statement, all variables and given/known data
    In this problem we are asked to calculate the total power of the resistors in the circuit below.
    First.JPG
    2. Relevant equations

    ##P=I^2R##

    3. The attempt at a solution
    My solution goes like this:
    PT=PR1+PR2+PR3+PR4+PR5
    I can find PR1 and PR5 immediately from the given current generators:
    PR1=IG1^2*R1
    PR5=IG2^2*R5
    Second.JPG
    Since i know those powers one i dont need the current generators and can transform the right and left sides to thevenin equivalents:
    Clearly
    ET1=-ET2
    ET1=E1=24V and RT1=R1=12Ω (i hope i got this right)
    Third.JPG
    Forth.JPG
    Now we can see that we have this type of situation. I transformed the resistor 3 as in the picture and can divide the circuits into 2 and the powers of the resistors will the sum of two.
    Fifth.JPG
    I will be solving the left one:
    Re=R3R2/(R3+R2)=4Ω
    I=ET1/(Re+R1) = 24/18 = 4/3 A
    and the power of two element are P3'+P2=Re*(4/3)^2 and that times 2 is the total power.
    Something is wrong here. The result should yield 312 W and i just dont get that. What is wrong?
     
  2. jcsd
  3. Feb 1, 2017 #2

    Hesch

    User Avatar
    Gold Member

    PR1 and PR5 are correct.

    Now, what are the voltages across R2, R3 and R4 ? ( Forget about Thevenin and so on )
     
  4. Feb 1, 2017 #3

    gneill

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    Staff: Mentor

    I'm not liking your Thevenin equivalents. In particular, I don't like the Thevenin Resistance value. What happens when you suppress both sources in the sub-circuit that you're converting?

    I also think you're missing out on further opportunities to directly calculate powers in certain resistors. You should have a formula for power when you know the voltage across a resistor, as well as one for when you know the current through it.
     
  5. Feb 1, 2017 #4
    Oh, how dumb of me. I have the voltage across R2 and R4 and it's 24V for the R2 and -24 for the R4 so the voltage across R3 is -48V right? If so the formula is ##P=\frac{U^2}{R}##
     
  6. Feb 1, 2017 #5
    Is the above corrrect?
     
  7. Feb 1, 2017 #6

    gneill

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    Staff: Mentor

    Right.
     
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