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A question of electricity regarding emf and voltage

  1. May 1, 2014 #1
    1. The problem statement, all variables and given/known data
    A relay is required to operate 800m from its power supply, The power supply has negligible internal resistance.

    The relay requires 16V and a current of 0.60A to operate

    A cable connects the relay to the power supply and two of the wires in the cable are used to supply power to the relay.

    The resistance of each of these wires is 0.0050 ohms/ meter
    What is the minimum emf of the power supply

    My answer: 18.4V Correct answer: 20.8V


    2. Relevant equations
    I state them below :))


    3. The attempt at a solution
    Ok here is how I imagined the problem, there is a CABLE that is going out of the positive terminal of the battery and going to the relay which is 800m long, then there is another CABLE going back to the negative terminal of the battery which is also 800 m. Now inside each CABLE[/B is 2 wires of length 800m each of resistance 800 x 0..5 = 4 ohms. but since these two wires are in the same CABLE, they are like two parallel 4 ohms resistor so the combined resistance is
    4 x 4 / 4 + 4 = 2 ohms (The whole resistance of ONE CABLE ) and since there is two then the total resistance is 2 ohms + resistance of relay + 2 ohms = 4 ohms + resistance of relay
    Now resistance of relay = V across relay / I passing through it = 16 / 0.6 = 26.7 ohms so TOTAL resistance = 30.7 ohms so to find the emf of the circuit we use V = IR where R is total resistance and I is the current (0.6A)
    V = 30.7 x 0.6 = 18.4!!!
    Where did I go wrong?? :((
    Thanks for the help
     
  2. jcsd
  3. May 1, 2014 #2

    gneill

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    Staff: Mentor

    The term "cable" for wiring is taken to mean multiple wires bundled into a single package.

    Your interpretation of the wiring is not correct. There is only one cable. Two wires within that cable are used to supply power to the relay.
     
  4. May 1, 2014 #3
    If this was the case why would he write:
    The resistance of each of (((these wires))) is 0.0050 ohms/ meter
    is it just there to trick me into thinking that it is a parallel connection?
    I forgot to mention the question was MCQ so once I calculated 18.4 and found it in the list I chose it.
    Thanks :))
     
  5. May 1, 2014 #4

    gneill

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    Staff: Mentor

    The cable consists of multiple wires. The author is referring to the individual wires within the cable. Two wires of the cable are used to connect the relay to the voltage source.

    attachment.php?attachmentid=69291&stc=1&d=1398963355.gif

     

    Attached Files:

  6. May 1, 2014 #5
    Omg You were soo helpful!! :))) Thanks so much for helping me and for spending your time on the drawing :))))
    Thanks a ton :))))
     
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