Engineering AC circuit analysis -- mesh and nodal

[gneill]

Ahhhhhh how frustrating! Haha I was soo bloody close albeit for one final mistake. That has had me stumped for the last few days thank you very much for the guidance

I'm glad I could help.

 

[rob1985]

right so for question a I have the following.

loop 1 is 120=(2+j5)I1+ (j5)I2
loop 2 is -14.142+j14.142= (j5)I1 - (j1)I2 - (j4)I3
loop 3 is -j120 = -(j4)I2 + (4+ j4)I3

So my question is once I plug these into a complex matrix by decomposition excel program given to me by the university. This happens. Now I believe all my calcs are correct. so I've messaged the university. However once I get the three solutions (white boxes on photo) what do I do then. Because as far as I can tell that gives me i1, i2, and i3 . To find the total circuit current do I just add them all together.

 

[gneill]

Check your V3 value in your Loop 2 equation.

You're looking to solve for the current through Z4. Which mesh currents flow through Z4?

 

[rob1985]

-14.142-j14.142= (j5)I1 - (j1)I2 - (j4)I3

yes sorry that was a typo. I've changed it in the spreadsheet but still no joy. so am I right in saying that once the spreadsheet is fixed I can add all three equations together to get the total current in the circuit

 

[gneill]

-14.142-j14.142= (j5)I1 - (j1)I2 - (j4)I3

yes sorry that was a typo. I've changed it in the spreadsheet but still no joy.

You may have to do as the spreadsheet suggests and "nudge" one or more of the zero entries away from zero.

so am I right in saying that once the spreadsheet is fixed I can add all three equations together to get the total current in the circuit

What does "the total current in the circuit" mean? There are three different sources and various currents flow in different places and different directions in the circuit. For mesh currents they often flow in opposite directions through a given path, so "summing" the total current is not a well defined operation.

What is it you're trying to accomplish by summing currents?

 

[rob1985]

I've got to determine what I is. Your right summing the currents won't work. I think I need to do loop 1 - loop 2 which is i1 - i2.

ive sorted the spread sheet out thank you. Am I right in saying that 3 three results in the polar form boxes are i1 , i2 and i3 respectively

 

[gneill]

I've got to determine what I is. Your right summing the currents won't work. I think I need to do loop 1 - loop 2 which is i1 - i2.

That's right.

ive sorted the spread sheet out thank you. Am I right in saying that 3 three results in the polar form boxes are i1 , i2 and i3 respectively

Your results look good.

 

[rob1985]

that gives me -4.23 + j-1.75 or 4.58 angle 202.48 doesn't seem right to me

 

[gneill]

that gives me -4.23 + j-1.75 or 4.58 angle 202.48 doesn't seem right to me

Can you show the details of your calculation?

Note that you should be able to take advantage of the Excel spreadsheet to add the currents since their rectangular components are available in the solution area.

 

[rob1985]

In polar form
i1 = radius 2.84 angle -53.69
i2 = radius 4.78 angle -57.12
i3 = radius 2.85 angle -50.74
In rectangular form
i1 = 1.68 + j-2.29
i2 = 2.55 + j-4.04
i3 = 1.81 + j-2.21

to find I at the point required = i1-i2

1.68 + j-2.29 - 2.55 + j-4.04 = -4.23 + j-1.75
I don't know how to work it out on the spread sheet, I've done them with a calculator

 

[gneill]

The solution area on the spreadsheet has the currents in rectangular form:

If you are familiar with Excel you should be able to sum the requisite cells...

Edit: Also, be sure to pay attention to the exponential notation! Don't lose the power of ten in the values.

Edit 2: Be careful when finding the phase angle of the result. Check which quadrant the vector is in.

 

[rob1985]

Unfortunately I am not familiar with excel and don't know how to add cells together with an exponential term in them. Also on the calculator do I just type in 1.68 Exp 01. to give 4.5667 etc. I know it might sound like a daft question

And am I right in saying all the angles lie in the 4th quarter.

 

[gneill]

Unfortunately I am not familiar with excel and don't know how to add cells together with an exponential term in them.

They're just numbers in the cells. They happen to be displayed using exponential notation. To add the contents of a couple of cells:

1. select an empty cell somewhere where you'd like the result to end up and type an "="
2. select the first cell. The address of that cell should appear in the result cell.
3. Type "+".
4. select the second cell. It's address will appear in the destination cell.
5. Hit the <enter> key. The sum of the two cells will be displayed in the result cell.

Also on the calculator do I just type in 1.68 Exp 01. to give 4.5667 etc. I know it might sound like a daft question

That sounds right. If it's a problem, just convert the number to a plain format number before doing the math. "E+01" just means "x 10¹".

And am I right in saying all the angles lie in the 4th quarter.

Yes.

 

[rob1985]

Right so once I've got rid of the exponential sign the results come out as followed.

i1 = 4.566713472 + j -6.224865387
i2 = 7.067532754 + j -10.92749295
i3 = 4.92009011 + j -6.007402841

So i1 - i2 to find i = (4.566713472 + j -6.224865387) - (7.067532754 + j -10.92749295)
So i = 2.500819282 + j -4.702627563

So this is the answer to part a) i believe by mesh analysis.

 

[gneill]

I don't understand how you got rid of the exponential notation. It should involve a simple decimal point shift of the numbers (the mantissa). Can you show your work?

Your result for the current $I$ is not correct.

 

[rob1985]

Thanks gneill, I've sorted my maths out now.

i1 = 16.811946 + j -22.879203
i2 = 25.963628 + j -40.154424
i3 = 18.059026 + j -22.095398
So i = (i1 - i2)
(16.811946 + j -22.879203) - (25.963628 + j -40.154424) = -9.151682 + j17.275221

This is by mesh analysis, now for nodal analysis lol

 

[rob1985]

So part b) find I by nodal analysis

So I have the following

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

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

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

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

can this equation be simplified anymore, does anyone know

 

[gneill]

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

can this equation be simplified anymore, does anyone know

It doesn't get much prettier. You could put everything over a common denominator, but it wouldn't make things any easier to deal with when it comes to the complex arithmetic required when the numbers are inserted. I suggest collecting the V3 terms (as you did for V20) and then start plugging in given values to continue the reduction of terms.

 

[WeeChumlee]

Hi Rob1985

I too am working on this and just can't seem to get it right.
My equation is similar to yours.
I have used different terminology but if I use your terminology I have:
(V1-V20 / Z1) - (V20/Z4) - (V30/Z5) + ((V2+V30)/Z3)
Obviously wrong as does not get the answer from mesh analysis.
Just can't see where...

 

[The Electrician]

Hi Rob1985

I too am working on this and just can't seem to get it right.
My equation is similar to yours.
I have used different terminology but if I use your terminology I have:
(V1-V20 / Z1) - (V20/Z4) - (V30/Z5) + ((V2+V30)/Z3)
Obviously wrong as does not get the answer from mesh analysis.
Just can't see where...

You need to be careful with your notation. Read post #46 in this thread.

You need more parentheses, for example (V1-V20 / Z1) should be ((V1-V20) / Z1)

Also, you have (V1-V20 / Z1) - (V20/Z4) - (V30/Z5) + ((V2+V30)/Z3) which is not an equation, but just an expression. You must equate expressions to zero, and of course you will need more than one equation.

 

[WeeChumlee]

Hi Electrician

Yes indeed, that was me being lazy and not putting all parentheses in, silly of me.
What I have is this:
((V1-V20) / Z1) - (V20/Z4) - (V30/Z5) + ((V2+V30)/Z3) = 0
V20-V30 = 14.14+j14-14

 

[WeeChumlee]

Darn:
Was of course
V20-V30 = 14.14+j14.14

 

[WeeChumlee]

Carrying on from this as I am getting nowhere..

((V1-V20) / Z1) - (V20/Z4) - (V30/Z5) + ((V2+V30)/Z3) = 0
V30 = V20 - V3
((V1-V20) / Z1) - (V20/Z4) - ((V20-V3)/Z5) + ((V2+(V20-V3))/Z3) = 0

When I put the values into get V20 and divide that by Z4 I get 8.78 - j16.59
Not the answer I got for the mesh analysis which was -9.1 + j17.3

If someone could point me in the right direction I would be most grateful.

 

[The Electrician]

Carrying on from this as I am getting nowhere..

((V1-V20) / Z1) - (V20/Z4) - (V30/Z5) + ((V2+V30)/Z3) = 0
V30 = V20 - V3
((V1-V20) / Z1) - (V20/Z4) - ((V20-V3)/Z5) + ((V2+(V20-V3))/Z3) = 0

When I put the values into get V20 and divide that by Z4 I get 8.78 - j16.59
Not the answer I got for the mesh analysis which was -9.1 + j17.3

If someone could point me in the right direction I would be most grateful.

If I solve these two equations:
((V1-V20) / Z1) - (V20/Z4) - (V30/Z5) + ((V2-V30)/Z3) = 0
V30 = V20 - V3

with the sign of V2+V30 changed (in red above) to V2-V30, I get the correct answer for V20 and V30. And, after dividing by Z4 I get the correct current.

But with the + sign you have I don't get what you got for the current I even with the incorrect values it gives for V20 and V30; check your solution method.

 

[WeeChumlee]

Thanks Electrician

Yes, I totally see that sign change, that was an error of mine.
Funny thing is that I had it right the first time but got the wrong answer so in trying to get the right answer that was a change I made.
I had used an online calculator to try and get the answer, I must have made a syntax error or something.
Just did it all on paper right now and voila, answer is as expected.
Probably serves me right for trying to cut corners.
At least I know my Math is still OK. :)

Many thanks for pointing me in the right direction, really appreciate you guys giving up your time to help.

 

[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,