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Circuit using maths and electricity laws/formulae

  1. Aug 6, 2015 #1
    1. The problem statement, all variables and given/known data

    Okay so we are given this circuit. I do not want to be told step by step what the answer (or worked solution is) but I am wanting some guidance about how I can start/continue on from what is given to us.

    We obviously need a understanding of Kirchoff's current law.

    Our task is to construct the remaining equations and then solve for the currents i1 to i8 in terms of V and R.

    2. Relevant equations

    Okay so I know Kirchoff's current law that says that there is a conservation of charge. that is if there is only two wires one has current going in, the other equal going out. So the sum of all currents at node = 0A, and total charge in closed loop is zero. Also know Ohm's law is V=IR.


    3. The attempt at a solution

    With that in mind we know:

    0=i1+i2+i3+i4

    and V=i6R+i7R+i8R

    We can for instance combine the left triangle which has R and 2R and 2R all in parallel which should give us ((1/R) + (1/2R) + (1/2R) ) -1? Am i heading down the right path? And since that all combines to be one resistor that is parallel to the bottom left triangle which has a R and 2R again?

    and so on and so forth? How do I do the current? Could it be like i2+i6=i7?

    Thanks a lot!
     

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  3. Aug 6, 2015 #2
    Have you thought of using unkown voltages instead ? You would only need three variables then .
     
  4. Aug 6, 2015 #3
    What do you mean? No I didn't think of it at all? Could you explain?
     
  5. Aug 6, 2015 #4
    Could you by any chance label the junctions ? It is going to be a bit difficult to explain without it .
     
  6. Aug 6, 2015 #5
    You mean like this?
     

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  7. Aug 6, 2015 #6
    Yes , that's better . Now , let potential at A be zero , and V at D .

    You will have three unknown voltages - V1 , say , at E , V2 at B , and V3 at C .
    Now write junction law at E , B and C , using voltages and resistances . You thus have three equations , three variables . Solve and find the variables' values .

    Can you now write each individual current ?

    Hope this helps .
     
  8. Aug 6, 2015 #7

    SammyS

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    @SteliosVas ,

    Use symmetry to simplify the circuit.
    ss-png.86935.png

    ss2-jpg.86936.jpg
     
    Last edited by a moderator: Aug 6, 2015
  9. Aug 16, 2015 #8
    What do you mean by symmetry? Sorry I do civil engineering not really too fond on electrical associated stuff.

    So do you mean look at the left hand side of the circuit and than take the same for right? But doesn't it matter that the top right branch has a voltage source?
     
  10. Aug 16, 2015 #9
  11. Aug 16, 2015 #10
    The circuit is symmetric about a line that goes through the middle of the voltage source, the middle of the circuit, and the middle of the resistance with i7 flowing through it. If you divide the voltage source in 2 voltage sources in series, both with potential difference V/2, and the resistor into two resistances R/2 in series, the 3 points on the symmetry axis all must have the same potential, If you connect them with wires, the rest of the circuit can be quickly solved with the rules for series and parallel resistors.
     
  12. Aug 16, 2015 #11
    Do you mean something like this?
     

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  13. Aug 16, 2015 #12

    SammyS

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    snapshot-jpg.87407.jpg

    Yes, something like that.

    You left out the 2R resistor between points E and C.

    However, it's not two separate circuits the way you described it. If you split it that way neither part would be a circuit.


    Here's a different question to clarify what convention you may be using regarding current.

    Which convention do you use for the direction of current flow?
    A: Is it "conventional current" in which current is considered to be due to the flow of positive charge? It tends to flow in the circuit from the positive terminal of the voltage source to the negative terminal.

    B: Is it "electron current" in which current is considered to be due to the flow of negatively charged electrons?​
     
  14. Aug 20, 2015 #13
    Okay well I would consider conventional current, that is it flows out of the positive terminal and than back into the negative...

    But I am still not sure, could I use matricies for this problem?
     
  15. Aug 20, 2015 #14

    SammyS

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    Yes, you could use matrices to solve this, but they are not needed.

    The solution can be worked out with some simple parallel/series combinations.

    Can you see that the current flowing from D to E must be equal to the current from E to A?
     
  16. Aug 20, 2015 #15
    Yes I understand that cause the value of the resistor is the same?

    Okay so my understanding is this. Since the current flowing through D to E = E to A
    Does that imply say that the current flowing from B to E is equal to E to C

    Or did you say the flow because what ever is entering junction E from the right is exiting from the top?

    Than B to C is parallel to C to D ?

    I sort of understand that you can combine together. So you can treat that top right hand corner as a circuit in series with say the top left? But parallel to the bottom two?

    Edit:
    Okay so it asks to come up with the remaining equations for i1 to i8

    Would I be wrong in saying the first two are?
    2Ri1+2Ri2+2Ri3+2Ri4 = V

    Making i1+... i4=V/2R

    The second being:

    Ri6+2Ri2-Ri7=V?
     
    Last edited: Aug 20, 2015
  17. Aug 20, 2015 #16

    SammyS

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    One does imply the other, but they're both true because of the symmetry in the circuit.

    This is not not enough reason to imply those equalities.

    No. That is definitely not true.

    The rest is not correct.
    I didn't read willem2's post #10 carefully enough, previously.

    That may be a simpler way to analyze this circuit.
     
  18. Aug 20, 2015 #17
    Okay analysing it your way. How should I start? It's more the beginning that is the most difficult.

    If you draw a line across the voltage source therefore anything lying on that line must (I think equal =0) so saying that one resistor will have value R/2 and the junction E a value and v/2?

    Using that should I than analyse the top and bottom segments ?
     
  19. Aug 20, 2015 #18

    SammyS

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    It is all the same voltage along that line. Maybe not zero.

    At any rate, you can connect all along that line with a wire.

    Which way do you want to analyze it?

    The way willem2 suggests?
     
    Last edited: Aug 20, 2015
  20. Aug 20, 2015 #19
    I guess it doesn't matter which way I analyse it. My understanding of series and parallel circuits and related laws.

    What I don't understand is what is meant by symmetrical and I guess what throws me is the voltage source
     
  21. Aug 20, 2015 #20

    SammyS

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    upload_2015-8-20_23-18-11.png

    Does this help ?
     

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