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What are the currents at each resistor?

  1. Aug 15, 2016 #1
    1. The problem statement, all variables physics_problem_1.jpg and given/known data

    2. Relevant equations
    I3 + I1= I2


    3. The attempt at a solution
    attemptedsolution.jpg
     
  2. jcsd
  3. Aug 15, 2016 #2

    TSny

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    Hello and welcome to PF!

    It is very important to specify the directions that you are assuming for each of the three currents. Otherwise, there is no way for us to check the signs in your equations.

    For each equation you should state whether it comes from a junction rule or from a loop rule; and, tell us which junction/loop corresponds to each equation.
     
  4. Aug 15, 2016 #3
    Equation #1- Kirchoff's junction current rule
    Equation #2- Upper Loop clockwise from 20V source
    Equations #3- Lower Loop rule counterclockwise
     
  5. Aug 16, 2016 #4

    TSny

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    Please specify the direction you are choosing for ##I_1##, the direction you are choosing for ##I_2##, and the direction you are choosing for ##I_3##. This is essential for getting the correct signs in the equations.
     
  6. Aug 16, 2016 #5
    That's probably where my mistake is at, but I3 counterclockwise, I 2 counterclockwise, and I 1 counterclockwise? This is the part I'm a little confused about because I've been learning kirchoff's rules from a book and khan's academy. They all flow to the closest stronger volt source?
     
  7. Aug 16, 2016 #6

    TSny

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    It would be clearer if you specified ##I_1## as to the right or to the left through the 30Ω resistor. Similarly for the other two currents. On your circuit diagram, these directions should be indicated with arrows.
     
  8. Aug 16, 2016 #7
    I 1 to the right, I 3 to the right, and i 2 to the left as assumed from my first equation I 1 +I 3=i 2
     
  9. Aug 16, 2016 #8

    TSny

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    Note that the equation I1 + I3 = I2 would have also resulted from taking I1 to the left, I3 to the left and I2 to the right.

    But, OK. We now have definite directions for the currents: I1 to the right, I3 to the right, and I2 to the left.

    Your junction equation I1 + I3 = I2 is correct.

    Let's look at your loop equation for the top loop. You wrote

    20 - 30I1 + 5I2 - 10 = 0.

    There is a sign error in this equation. Can you explain why you chose each of the four signs on the left?
    Why +20? Why - 30I1? Why +5I2? Why -10?
     
  10. Aug 16, 2016 #9

    TSny

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    It is important to note that you generally will not know ahead of time the correct directions for the currents. That is part of what you will determine when solving the problem. But, the nice thing is that you can assume any direction you want for any of the currents. If your initial choice of direction for a current turns out to be wrong, then you will get a negative answer for that current. The negative sign indicates that the current is actually in the opposite direction from what you initially assumed.

    So, for example, if you end up getting I2 = -4 A, then the current I2 will be 4 A in a direction opposite of what you initially chose when setting up your equations.

    But it is essential to make an initial choice for the direction of each current and stick with that choice while setting up the signs in your equations.
     
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