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The equivalent resistance of the circuit

  1. Sep 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the equivalent resistance of the circuit shown, for circuit 3.7b, the one in the upper right :
    https://scontent-ort2-1.xx.fbcdn.net/v/t34.0-12/14429160_641550399338143_303002326_n.png?oh=ad8d346cfcaff147c9cd7a9d2b509411&oe=57E6C47C


    2. Relevant equations
    Rseries=Rtotal =R1+R2+.....+RN
    Rparallel=(Rtotal)-1=(R1)-1+(R2)-1+.....

    3. The attempt at a solution
    So for my attempt, my assumption was that:
    • The 18 and 12 Ω resistors were in series, so I combined them.
    • I assumed the 20 Ω resistor at the top was in parallel with the 60Ω resistor under it and combined that.
    • Then, the equivalent resistance of the 20 and 60 Ω resistors was in series with the 40 Ω resistor.
    Now, I am stuck and confused on where to continue. I was going to assume that the equivalent resistor of 55 Ω(from 60,20, and 40) was in parallel with the diagonal 50 Ω resistor and go from there, but it just seemed wrong. Please, can anyone tell me if I am on the right track or I messed up somewhere?
     
  2. jcsd
  3. Sep 22, 2016 #2

    QuantumQuest

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    You have the two equations in "Relevant Equations". Now, how can you tell if two resistors are in series or parallel? If they are in series, then the one terminal point of one is directly connected to one terminal of the other. If they are connected in parallel, they have two common terminals.

    Starting from the right part of the circuit, the 18 and 12 Ω resistors are in series as you say. Now, it would be a good idea to sketch a diagram with a new resistor to substitute these two. You keep on moving from right to left across the circuit. Do you see immediately which resistors are to be taken into account?
     
  4. Sep 22, 2016 #3

    CalcNerd

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    You cannot take shortcuts. The 20 Ω resister is in parallel with the 60 Ω that is still embedded in the circuit. So you have to determine this imbedded resistance first, it is NOT 60Ω. Continue with your original series of 12 and 18 and calculate them in parallel with the adjoining 60 Ω resister. Calculate that value in parallel with the 30 Ω. Then calculate the resulting value in parallel with the 75 Ω.
    .
    Just keep whittling down on the circuit.
    .
    Understanding the overall results should help you be able to get a feel for such circuits be inspection ie once you become familiar with these types of problems, you will be able to make an educated guess before you even start. ie an educated guess would be that the Resistance is probably 15-20 Ωs for you to ballpark your results.
     
  5. Sep 22, 2016 #4

    CWatters

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    That's OK. Redraw the circuit after this step and you should see another obvious parallel combination.

    Yes that's also OK but it wouldn't be the most obvious step. See above.

    No that's wrong. They aren't in series.

    Redraw the circuit after each step, don't keep referring back to the original.
     
  6. Sep 22, 2016 #5
    Thanks for the response. I'm sorry, but I am confused: Can I combine the 60 and 20, or do I leave the 60 till the end.

    And is the obvious parallel circuit with the 60 ohm diagonal?
     
  7. Sep 22, 2016 #6
    So, I did what I thought was correct(probably not), but is the awnser 80 ohms equivalent resistance? I apologize again, I dont have an answer book to check.
     
  8. Sep 22, 2016 #7
    I did it real quick and my final answer was 20 ohms.
    I could however be wrong though because I'm taking circuits now like you.

    My method of solving was to solve that top portion like you did and then ignore it and go back to the right side. If you just keep solving from the right and work your way towards the source you should be fine.
     
  9. Sep 22, 2016 #8
    Could you tell me your general method?
     
  10. Sep 22, 2016 #9

    QuantumQuest

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    Why don't you follow what I and the other persons suggested, i.e going step by step and redrawing the circuit, with an equivalent resistor each time, till you find the final resistance? If you're trying to do it in some quick way, without knowing first the step by step method, how could you learn about solving such exercises/ problems in general?
     
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