Hello i have some issues applying the mesh analysis on the following circuit, are my equations wrong ?

 

Hi,

A quick question...

Is i3 really a mesh current?
I ask because i2=i1/2 for example.
If not, there is another way to make a mesh current for that part of the circuit i think.
Also,where did you get the "12" from in equation (2) ?

Most important, what did you get for a final result?

 

Thanks for your time
what other way ?
Also i2 = - i1/2
and the 12 comes from 10+2 the two resistances on the I2 loop.

 

It appears to me that you have designated your loop currents I1, I2 and I3 with the capital letter "I" (red annotations), but the transformer currents in black are also I1 and I2. Yet in post #3 you say "Also i2 = - i1/2" using lower case "i"; are these the transformer currents? I see confusion looming.

Your equations look OK to me, but besides the constraint equation I1 =-2*I2 (where I1 and I2 are the transformer currents), you also need V2 = -2* V1.

Also, the relation I1 = -2*I2 (primary and secondary currents) needs to be expressed in terms of your loop currents, namely I1 - I3 = -2*(I2 - I3) where red means loop currents.

 

It appears to me that you have designated your loop currents I1, I2 and I3 with the capital letter "I" (red annotations), but the transformer currents in black are also I1 and I2. Yet in post #3 you say "Also i2 = - i1/2" using lower case "i"; are these the transformer currents? I see confusion looming.

Your equations look OK to me, but besides the constraint equation I1 =-2*I2 (where I1 and I2 are the transformer currents), you also need V2 = -2* V1.

Also, the relation I1 = -2*I2 (primary and secondary currents) needs to be expressed in terms of your loop currents, namely I1 - I3 = -2*(I2 - I3) where red means loop currents.

Hi,

Always good to hear your take on this stuff.

The lower case 'i' is partly my fault is i started to use lower case for the 'red' currents. I should have announced that i guess.

I questioned without testing the loop i3 (red) because it looped through the top of the transformer. The voltage on the right side of the transformer is twice that of on the left, and the left current into the transformer top is twice that of the current on the right top terminal.
So what do you think, is the loop i3 valid taking those two into account?
Have you worked through those equations to arrive at a result?

 

Thanks for your time
what other way ?
Also i2 = - i1/2
and the 12 comes from 10+2 the two resistances on the I2 loop.

Well i should probably try to solve your set of equations first but do you have to use mesh on this?

Are you considering the top two nodes of the transformer to be a super node?

 

Hi,

Always good to hear your take on this stuff.

The lower case 'i' is partly my fault is i started to use lower case for the 'red' currents. I should have announced that i guess.

I questioned without testing the loop i3 (red) because it looped through the top of the transformer. The voltage on the right side of the transformer is twice that of on the left, and the left current into the transformer top is twice that of the current on the right top terminal.
So what do you think, is the loop i3 valid taking those two into account?
Have you worked through those equations to arrive at a result?

It appears that the transformer is assumed to be ideal--coupling coefficient of 1 and infinite primary and secondary inductances.

I solved the more general case of coupling less than unity, and finite winding inductances. This solution becomes the one sought by allowing those parameters to become ideal.

But, just using the meshes given with the two constraints works OK too.

 

It appears that the transformer is assumed to be ideal--coupling coefficient of 1 and infinite primary and secondary inductances.

I solved the more general case of coupling less than unity, and finite winding inductances. This solution becomes the one sought by allowing those parameters to become ideal.

But, just using the meshes given with the two constraints works OK too.

Hi,

Could you post some results, perhaps in a PM?
I'd like to compare because i was not able to arrive at the results i think are the right ones using the OP's set of three equations. Yet i could get them using an alternate mesh and also with Nodal. That's the results i believe are valid though for the circuit given, and that might be another talking point later.

The alternate mesh is with the upper 8 ohm resistor drawn at the bottom of the circuit rather than at the top. I was able to reproduce the results that way.

At present i have to question the use of the mesh i3 with the transformer and i see now how the OP approached the idea for that mesh. If you can supply your results i can see what is going on right away i think.

 

Thank you everyone for your replies
I believe that with nodal analysis everything works fine the thing is i dislike this method and i want to go with mesh currents every time ( it always has to work both ways, right ? )
The result i get with those meshes is I3 = 16.84 amps. Which alternative meshes did you take MrAI ?

 

It appears to me that you have designated your loop currents I1, I2 and I3 with the capital letter "I" (red annotations), but the transformer currents in black are also I1 and I2. Yet in post #3 you say "Also i2 = - i1/2" using lower case "i"; are these the transformer currents? I see confusion looming.

Your equations look OK to me, but besides the constraint equation I1 =-2*I2 (where I1 and I2 are the transformer currents), you also need V2 = -2* V1.

Also, the relation I1 = -2*I2 (primary and secondary currents) needs to be expressed in terms of your loop currents, namely I1 - I3 = -2*(I2 - I3) where red means loop currents.

Thats interesting, probably that is what i am missing

Edit: that sure is the thing, thanks a lot

P.s. i am still interested on the alternative mesh

 

Thats interesting, probably that is what i am missing

Edit: that sure is the thing, thanks a lot

P.s. i am still interested on the alternative mesh

Hi,

If you want to try this here is the circuit redrawn to show the alternate mesh arrangement. This may or may not be easier for you but you decide.
Note the 'red' loop i3 is harder to draw but that includes all the components in that loop following the connections as appropriate.

 

Hi,

If you want to try this here is the circuit redrawn to show the alternate mesh arrangement. This may or may not be easier for you but you decide.
Note the 'red' loop i3 is harder to draw but that includes all the components in that loop following the connections as appropriate.

I see, thanks a lot for your effort