AC circuit analysis -- mesh and nodal

[Student12345]

Hi I am doing part b) and have made a basic error somewhere and can't for the life of me see where and am hoping someone can Point me in the right direction. I am getting an I that does not match my mesh I ( -9.2+j17.3) I have narrowed it down to the V3 I'm using of 14.14+j14.14 as part as when I do (v1/z1+v3/z5+v2/z3+v3/z3) I get 60+j37.07
If I change it to 14.14-j14.14 I get the correct answer but I can't see where I do that.

 

[gneill]

Hi I am doing part b) and have made a basic error somewhere and can't for the life of me see where and am hoping someone can Point me in the right direction. I am getting an I that does not match my mesh I ( -9.2+j17.3) I have narrowed it down to the V3 I'm using of 14.14+j14.14 as part as when I do (v1/z1+v3/z5+v2/z3+v3/z3) I get 60+j37.07
If I change it to 14.14-j14.14 I get the correct answer but I can't see where I do that.

You'll have to present your work in more detail. What you've written above does not contain a correct node equation (or any equation, since an equation requires that a relationship be expressed, usually of the form <something> = <something else>).

 

[Student12345]

You'll have to present your work in more detail. What you've written above does not contain a correct node equation (or any equation, since an equation requires that a relationship be expressed, usually of the form <something> = <something else>).

Sorry I'm trying not to waffle on I obviously didn't put enough in. I have the following equation which I believe is correct

-v20(1/z1+1/z4+1/z5+1/z3)+(v1/z1+v3/z5+v2/z3+v3/z3)=0

When I input my values of

-v20((1/2)+(1/-j5)+(1/j4)+(1/4))+((120/2)+((14.14+j14.14)/j4)+(j120/4)+((14.14+j14.14)/4)=0

I get -v20(0.75+j0.05)+(60+j37.07)=0

From working backward from my mesh I result I know I need the second part to be (67.7+j30) so I know I'm close but I just can't see where I've gone wrong

 

[gneill]

Okay. You're node equation looks fine, and the version with the values plugged in looks okay too. So the problem must lie in the final reduction.

When I work from your

-v20((1/2)+(1/-j5)+(1/j4)+(1/4))+((120/2)+((14.14+j14.14)/j4)+(j120/4)+((14.14+j14.14)/4)=0

I end up with v20 = 86.376 + j45.758

So it looks like you'll need to take a closer look at your complex arithmetic.

 

[Student12345]

Okay. You're node equation looks fine, and the version with the values plugged in looks okay too. So the problem must lie in the final reduction.

When I work from your

-v20((1/2)+(1/-j5)+(1/j4)+(1/4))+((120/2)+((14.14+j14.14)/j4)+(j120/4)+((14.14+j14.14)/4)=0

I end up with v20 = 86.376 + j45.758

So it looks like you'll need to take a closer look at your complex arithmetic.

Ok thanks for your help I have had another look and spotted a couple of mistakes -v20 somehow became v20=

 

[gneill]

There's not much I can do to sort out your arithmetic. But I might suggest that you begin by eliminating the imaginary values from all the denominators of the individual terms and then forming a common denominator (20 looks promising). Since the expression is set equal to zero you can then discard the denominator leaving you with a simpler sum.

 

[Student12345]

There's not much I can do to sort out your arithmetic. But I might suggest that you begin by eliminating the imaginary values from all the denominators of the individual terms and then forming a common denominator (20 looks promising). Since the expression is set equal to zero you can then discard the denominator leaving you with a simpler sum.

Its ok I found my mistake hidden amongst bad handwriting. All sorted on a)and b) Thanks for your help.

 

[Ben Yates]

Apologies in advance if this isn't in the correct format, I am new to this...

I too have struggled with part b) reading through this thread I have tried to see where I am going wrong, but currently pulling my hair out...

I understand [V20] - [V30] = 14.14+j14.14, (supernode) [EQUATION A]
and also 0 = -[V20]((1/2)+(1/-j5)+(1/j4)+(1/4))+((120/2)+(14.14+j14.14/j4)+(j120/4)+(14.14+j14.14/4))

giving... 0 = -[V][/20]((1/2)+(1/-j5)+(1/j4)+(1/4))+((120/2) + (60+3.535-j3.535+j30+3.535+j3.535)
0 = -[V20]((1/2)+(1/-j5)+(1/j4)+(1/4))+67.07+j30
67.07+j30 = [V20]((1/2)+(1/-j5)+(1/j4)+(1/4))
67.07+j30 = 0.5([V20])+j0.2([V20])-j0.25([V20])+0.25([V20]), [EQUATION B]

However when solving EQUATION A and EQUATION B I seem to get [V20] = 90.1068+j40.3042 and [V30] = 75.9668+j26.1642

then [V20] /[Z4] = (A) = 90.1068+j40.3042/-j5 = -8.06+j18.02 (A)

this is obviously different from the actual answer of -9.152+j17.275 (A) which is what I got for question a.

Can anyone point out where I have gone wrong? thanks.

 

[gneill]

Something's gone wrong with your development or solving of EQUATION B. You're okay up to this point:

67.07+j30 = [V20]((1/2)+(1/-j5)+(1/j4)+(1/4))

then you go and distribute V20 across all the terms on the right. Why bother doing that? Reduce the purely numerical part to a single complex value as you did to arrive at the "67.07+j30" term. Then you'll have a simple division left to find V20.

 

[Ben Yates]

Something's gone wrong with your development or solving of EQUATION B. You're okay up to this point:

then you go and distribute V20 across all the terms on the right. Why bother doing that? Reduce the purely numerical part to a single complex value as you did to arrive at the "67.07+j30" term. Then you'll have a simple division left to find V20.

I've now arrived at the correct answer, many thanks!

 

[mangue1]

hi guys I am stuck at this point:
v1/z1 + v2/z3 - (v20/ z1+z3+z4+z5) + (v3/z5+z3)
can someone help me to proceed please..

 

[Joe85]

Hi Guys,

Hope it's ok to bump an old thread. I'm working on the same problem and seem to be stuggling to come up with the correct answer for Nodal analysis.

My Analysis thus far:

V₃₀ = V₂₀ - V₃

V₂₀ - V₁/Z₁ + V₂₀/Z₄ + V₂₀ - V₃/Z₅ + (V₂₀ - V₃) - V₂/Z₃ = 0

Expanding:

V₂₀/Z₁ - V₁/Z₁ + V₂₀/Z₄ + V₂₀/Z₅ - V₃/Z₅ + V₂ - V₂₀ + V₃/Z₃ = 0

Collecting the V₂₀'s and isolating:

V₂₀ (1/Z₁ + 1/Z₄ + 1/Z₅ - 1/Z₃) - V₁/Z₁ - V₃/Z₅ + V₂/Z₃ + V₃/Z₃ = 0

V₂₀ (1/Z₁ + 1/Z₄ + 1/Z₅ - 1/Z₃) + V₃ (1/Z₃ - 1/Z₅) + V₂/Z₃ - V₁/Z₁ = 0

From this point on I enter the figures into the equations and utilise complex conjugates and/or common denominators to reduce down to a single rectangular complex number.

Am i on the correct path here?

 

[Joe85]

Hi Guys,

Hope it's ok to bump an old thread. I'm working on the same problem and seem to be stuggling to come up with the correct answer for Nodal analysis.

My Analysis thus far:

V₃₀ = V₂₀ - V₃

V₂₀ - V₁/Z₁ + V₂₀/Z₄ + V₂₀ - V₃/Z₅ + (V₂₀ - V₃) - V₂/Z₃ = 0

Expanding:

V₂₀/Z₁ - V₁/Z₁ + V₂₀/Z₄ + V₂₀/Z₅ - V₃/Z₅ + V₂ - V₂₀ + V₃/Z₃ = 0

Collecting the V₂₀'s and isolating:

V₂₀ (1/Z₁ + 1/Z₄ + 1/Z₅ - 1/Z₃) - V₁/Z₁ - V₃/Z₅ + V₂/Z₃ + V₃/Z₃ = 0

V₂₀ (1/Z₁ + 1/Z₄ + 1/Z₅ - 1/Z₃) + V₃ (1/Z₃ - 1/Z₅) + V₂/Z₃ - V₁/Z₁ = 0

From this point on I enter the figures into the equations and utilise complex conjugates and/or common denominators to reduce down to a single rectangular complex number.

Am i on the correct path here?

So i think i have figured this out. I took another look at my equations and think i may have been led astray with the (V₂₀ - V₃) - V₂/Z3

I think it should actually look like this:

V₂₀/Z₁ - V₁/Z₁ + V₂₀/Z₄ + V₂₀/Z₅ - V₃/Z₅ + V₂₀ - V₂ - V₃/Z₃ = 0

V₂₀ (1/Z₁ + 1/Z₄ + 1/Z₅ + 1/Z₃) - V₁/Z₁ - V₃/Z₅ - V₃/Z₃ - V₂/Z₃ = 0

From that point i solved using complex conjugates to produce:

V₂₀(0.75 - J.0.05) - (67.071 - J30) = 0

V₂₀(0.75 - J.0.05) = (67.071 + J30)

V₂₀ = (67.071 + J30)/(0.75 - J.0.05)

Converted to both to polar form to divide instead of using a complex conjugate.

73.475∠ 24.098 / 0.752 ∠-3.814

= 87.706 ∠ 27.912

Convert back to Rectangular:

V₂₀ = 86.34 + J45.74

I = V₂₀/Z₄
= 86.34 + J45.74/-J5

= -228.7 + J431.7/25

= -9.15 + J17.27A

The same as my answer for MEsh Analysis.

Would greatly appreciate if someone could validate my method or let me know if i have fluked my way to what i think is the correct answer. :)Many thanks,