node analysis, complex values, lost in formula somewhere

Discussion in 'Homework Help' started by ninjaman, May 30, 2016.

  1. ninjaman

    Thread Starter Member

    May 18, 2013
    306
    1
    Hello,
    upload_2016-5-30_17-24-31.png

    This is the circuit and my attempt:
    upload_2016-5-30_17-24-13.png
    upload_2016-5-30_17-25-17.png
    I don't know if any of this is correct, I have no confidence when dealing with maths. I have copied the process from an example question substituting the values from the question above. I think it is o.k past the first "simplify" bit, the second "simplify" is where I think I am going wrong. 1 x -j5 = -j5, then j2 x -j5 =-j10?
    I got 25 for the denominator as 5x5, again not too good at this. I have a book that I am reading but really struggling.
    Any advice or help would be great

    Thanks

    Simon
     
  2. AlbertHall

    Well-Known Member

    Jun 4, 2014
    1,951
    387
    Methinks j2 x -j5 = +10
    (But it's been a loooong time)
     
  3. DGElder

    Member

    Apr 3, 2016
    345
    85
    j * j = -1
    -1 * j * j = 1
    j2 * -j5 = 10
     
  4. ninjaman

    Thread Starter Member

    May 18, 2013
    306
    1
    upload_2016-5-30_19-3-18.png
    this is what i have, was any of the other stuff above it correct?

    many thanks for those that helped out.
    i read through the node analysis on this site and didnt really like it, i found it a little confusing. so i am going elsewhere to get help with the nodal analysis.

    thanks
    simon
     
  5. Jony130

    AAC Fanatic!

    Feb 17, 2009
    3,957
    1,097
    If you have time try watch this video about node analysis

    And your simplification ((1 + i2)/(i5) *(-i5)/(-i5)) looks good.
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    How did you make the following transition?

    eqns.png
     
  7. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    Oh, almost forgot, your Part (b) is pretty ambiguous. Is the Thevenin equivalent supposed to be for the entire circuit as shown, or is one of the impedances supposed to be the load. Similarly, is the load for the max power absorption part supposed to be one of the existing impedances (i.e., change the value to something) or is it supposed to be a new impedance connected between A and B.
     
  8. ninjaman

    Thread Starter Member

    May 18, 2013
    306
    1
    i used this example provided in the coursework
    upload_2016-5-30_20-18-58.png
    upload_2016-5-30_20-19-18.png
    upload_2016-5-30_20-19-39.png
    upload_2016-5-30_20-19-57.png
    upload_2016-5-30_20-20-23.png
    I haven't yet gotten to the second part (B). But it says above to use the complex conjugate of the Thevenin impedance. whatever that is? I have some idea.
     
  9. ninjaman

    Thread Starter Member

    May 18, 2013
    306
    1
    upload_2016-5-30_20-28-34.png
    this is the last of it. i have no clue whether or not it is correct, i am following along with the example and changing values for what i have. I hate this. if i were to get work as a technician would i have to know this stuff and do it for my job?

    thanks all
    simon
     
  10. DGElder

    Member

    Apr 3, 2016
    345
    85
    the complex conjugate of x + yj is x - yj

    So for maximum power transfer from source to load the magnitude of the impedances must match and the reactances must be of equal magnitude and opposite sign. For example a capacitive source into an inductive load.
     
  11. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    You are going to have a very hard time if you just try to find some example somewhere that is somewhat similar to the problem you are actually trying to solve and then just try to plug things into the way they solved it without any understanding of whether you are even doing things that make sense.

    For instance, let's look at the pair of equations that caught my eye. From the example:

    eqns002.png

    How did they get from the first to the second? They simply distributed the (1 + j) in the denominator across the second factor (i.e., A(B+C) = AB + AC) and then noted that (1+j)/(1+j) is 1

    How did you go from this example to:

    eqns.png

    It makes no sense (to me).

    You really need to spend some time learning about complex numbers and how to work with them. You are trying to jump way too far ahead without learning the tools you need. That would be like a carpenter trying to build a house without learning how to use a saw or a level or a square.
     
  12. MrAl

    Well-Known Member

    Jun 17, 2014
    2,438
    492

    Hello,

    When you try to simplify:
    (1+2j)/(2-5j)

    you multiply top and bottom by the complex conjugate of the denominator, which you tried to do, but when you did that you get "10" as the denominator, which cant be right because a complex number multiplied by it's complex conjugate results in the sum of squares of the two magnitudes which in this case are 2 and 5. So the denominator should not be 10 it should be 29 because 2^2+5^2=29.
    So to write it out:
    (2-5j)*(2+5j)=29


    I did not check anything else yet, but try that part again.

    Ok checked that other part, where in the denominator you multiply:
    (2*j)*(1/(2*j)+1/(2-5*j)+1/5)

    You can see there are three terms in (1/(2*j)+1/(2-5*j)+1/5)
    but you end up with four terms after the multiply is completed.
    That says you did not multiply correctly in the denominator.
    Example:
    a*(A+B+C)=a*A+a*B+a*C

    and note we get three terms on the right.
    Also note that a form such as (a+b)/(c+d) actually is two terms not just one, just like (a+b)/c is two terms a/c+b/c.
     
    Last edited: May 30, 2016
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