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Current through resistor parallel to two different batteries

  1. Sep 9, 2014 #1
    1. The problem statement, all variables and given/known data

    I'm sorry that I have no pic, but please bear with my description.

    The circuit diagram is made up of 3 horizontal lines. On the top line, there's battery A, (-) on the left, (+) on the right, and an arrow going to the right (>) to show direction of current.

    On the middle line, there's the 2 Ω resistor.

    And on the bottom line, there's battery B, (+) on left, and (-) on right.

    Battery A has an e.m.f, of 2.0 V and an internal resistance of 1 Ω. For battery B, the values are 1.0 V and 2 Ω. A and B are connected to a 2 Ω resistor. Using Kirchoff's Law, calculate current through the resistor.

    2. Relevant equations

    Both of Kirchoff's Law.
    I1 = I2 + I3
    E = IR1 + IR2

    3. The attempt at a solution

    I tried taking the top and middle, and treated it as one circuit, and did the same with the middle and bottom. Then I applied Kirchoff's second law. In this way, I managed to get two equations with three different variables.

    2 * I3 + I1 = 2
    - 2 * I3 + 2 * I2 = 1

    Where I1 is the current leaving battery A, I3 is the current entering the middle section after entering a junction, and I2 is the other current going toward the bottom section.

    Then by using I = I1 + I2 + I3, as well as the two equations, I substituted the values around, until I managed to make the equation in terms of I3.

    The value I got is 0.375 A.

    The answer is supposed to be 0.42 A.

    It would be great if someone can point out where I did wrong.
     
  2. jcsd
  3. Sep 9, 2014 #2
    Welcome to PF !

    As per the circuit description you have given , 0.375 A is the correct answer . So I think you have got it right .

    Either the answer key is wrong or the original question description is somewhat different from what you have given.
     
  4. Sep 9, 2014 #3
    Thank you for clarifying. I'll see if I've misunderstood somewhere.
     
  5. Sep 10, 2014 #4

    rude man

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    Homework Helper
    Gold Member

    Tanya has it right.
     
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