Using Mesh Analysis to Solve for Current and Voltage in Complex Circuits

[ash-kennard]

this question is part of my electronics CW, I've done it before, but briefly. and looking back at all my old notes I've realized that every single one I've done before has 2 sources and only 2 loops, whereas you can see from the image below that this has 3 and its getting me in quite a kerfuffle. help is appreciated

"With the calculated value of R1, determine the current through resistor R5 using mesh analysis. Using this current value, determine the voltage across resistor R5.

You need to clearly indicate the mesh current directions and voltage drop directions. Your answer should include Kirchhoff’s law Voltage (KVL) equations for each loop and method that you used for solving simultaneous equations. "


my attempt at the solution gets stuck at the KVL rule. i am fairly certain I am wrong but so far I've gotten this far: left mesh=I1 top right mesh=I2 bottom left =I3

i believe all the loops are clockwise

I1= V=R1*(I1-I2)+R4*(I1-I3)
I2= 0=R5*(I2±I3)+R1*(I2-I1)+R5*I2
I3= 0=R3*I3+R4*(I3-I1)+R5(I3±I2)

can someone please give me a heads up how to keep this going as its really bothering me now.

regards ash kennard

EDIT: R20 was mean to be R2, but multisim wouldn't let me change it for some reason :S

EDIT: i think i have the KVL down now, but the places i have"±" i am confused which sign to have. an input on that for now would be awesome. cheers guys xxx

 

[MATLABdude]

The direction of the loops is completely arbitrary. Maintain consistency, and the directions will work themselves out properly once you've performed your analysis.

EDIT: And if all the loops are assumed to have current going clockwise through them, you can see that the currents due to I2 and I3 will be going in opposite directions through R5, and will thus have a negative sign.

 

[ash-kennard]

so it is this?

I1= V=R1*(I1-I2)+R4*(I1-I3)
I2= 0=R5*(I2-I3)+R1*(I2-I1)+R5*I2
I3= 0=R3*I3+R4*(I3-I1)+R5(I3-I2)

 

[tiny-tim]

hi ash-kennard!

(try using the X₂ icon just above the Reply box )

so it is this?

I1= V=R1*(I1-I2)+R4*(I1-I3)
I2= 0=R5*(I2-I3)+R1*(I2-I1)+R5*I2
I3= 0=R3*I3+R4*(I3-I1)+R5(I3-I2)

looks fine … now solve!

(except too many "=" signs and "I"s … perhaps you could write eg "Mesh₁:" instead of "I₁ =" ? )

 

[ash-kennard]

bollocksed the calculation of R1, so here's the new picture haha

 

[ash-kennard]

just a quick on now, if i have
mesh 1:
V=R1*(I1-I2)+R4*(I1-I3)
mesh 2:
0=R5*(I2-I3)+R1*(I2-I1)+R5*I2
mesh 3:
0=R3*I3+R4*(I3-I1)+R5(I3-I2)

rearranged so they can be solved using a matrix will they look like this?
mesh 1:
I1*(R1+R4)-I2*(R1)-I3*(R4)=V
mesh 2:
-I1*(R1)+I2*(R1+R2+R5)-I3*(R5)=0
mesh 3:
-I1*(R4)-I2*(R5)+I3*(R3+R4+R5)=0

is this right? if so i can crack out a matrix i think :)

 

[tiny-tim]

looks ok

 

[ash-kennard]

brilliant, thank you very much tiny-tom and matlabdude. ill let you know how i get on

 

[ash-kennard]

hi again, had another snag. just need to know what [URL]http://upload.wikimedia.org/math/d/e/a/deaad034b920ebb32655dd9c00a80a7b.png[/URL]

means before i can substitute it into the rows like in this example

http://upload.wikimedia.org/math/d/e/a/deaad034b920ebb32655dd9c00a80a7b.png

 

[ash-kennard]

ignore that last one I am going to try a different method haha

 

[WesleyPipes]

You're not forced to use a matrix to solve. Just solve your first two equations for different unknowns and substitute into the third.

 

[ash-kennard]

solved it using the matrix, cheers lads xxx