Math Is Fun Forum

ninjaman

Member

Registered: 2013-10-15

Posts: 61

j notation, equivalent circuit resistance

hello

I have a circuit with values
v1 = 20 + j0
r1 = 15 +j0
l1 = 0 +j10
c1 = 0 - j5

I have to use superposition and division of complex conjugate numbers.
the resistor, inductor and voltage source are in series. the capacitor is in parallel with the voltage source

I added the resistor and inductor, (15 + jo) + (0 + j10) = 15 + j10, find the conjugate of this 15 - j10
so then product over sum for the components that are in parallel. the inductor/resistor || capacitor

    (0 - j5)*(15 - j10)
(15 + j10)*(15 - j10)

for the numerator I got

0 x 15 = 0
0 x -j10 = 0
-j5 x 15 = -j75
-j5 x -j10 = (j^2)50 = -50   minus 50 because of (j^2) = -1

so the result is -50 -j75, which im not sure about

then the second line

15 x 15 = 225
15 x -j10 =-j150
j10 x 15 = j150
j10 x -j10 = -(j^2)100,    (j^2) = -1 x -100 = 100

225 -j150 +j150 +100, the middle terms cancel leaving 225 + 100 = 325

so I have,     -50 -j75/325

then I divide each of the numerator by the denominator so,

-50/325 = -0.153846

-75/325 = -0.230769

I think I can use this to find polar notation r and theta(the zero with a line through)

im not sure if any of this is right though, any help would be great thanks

simon

ninjaman

Member

Registered: 2013-10-15

Posts: 61

Re: j notation, equivalent circuit resistance

hello

could someone please let me know if this is correct as I have been told that I have done this wrong though I didn't inform the person of how I did it. this is using division of conjugate complex numbers.

I have followed the method my tutor showed me and I think this is correct.

any help or a push in the write direction would be great!!!

thanks
simon

Bob

Administrator

Registered: 2010-06-20

Posts: 10,629

Re: j notation, equivalent circuit resistance

so the result is -50 -j75, which I'm not sure about

That is correct for the complex number bit.  I didn't post earlier because I don't know the physics using complex numbers.  I suggest:

Explain to me the formulas for this and then I can check the rest.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob