- #176

Student12345

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If I change it to 14.14-j14.14 I get the correct answer but I can't see where I do that.

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- Engineering
- Thread starter his_tonyness
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In summary: Once that's sorted out, use whatever technique you're familiar with to solve the three equations in three...I'll leave that to you.In summary, the current through Z2 is I=V3/Z2.

- #176

Student12345

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If I change it to 14.14-j14.14 I get the correct answer but I can't see where I do that.

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- #177

gneill

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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 said:

If I change it to 14.14-j14.14 I get the correct answer but I can't see where I do that.

- #178

Student12345

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gneill said: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

- #179

gneill

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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.

- #180

Student12345

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gneill said:

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=

- #181

gneill

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- #182

Student12345

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gneill said:

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

- #183

Ben Yates

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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] =

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.

- #184

gneill

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

- #185

Ben Yates

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gneill said: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!

- #186

mangue1

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

can someone help me to proceed please..

- #187

Joe85

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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:

V

V

Expanding:

V

Collecting the V

V

V

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?

- #188

Joe85

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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 (VJoe85 said:

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:

V_{30}= V_{20}- V_{3}

V_{20}- V_{1}/Z_{1}+ V_{20}/Z_{4}+ V_{20}- V_{3}/Z_{5}+ (V_{20}- V_{3}) - V_{2}/Z_{3}= 0

Expanding:

V_{20}/Z_{1}- V_{1}/Z_{1}+ V_{20}/Z_{4}+ V_{20}/Z_{5}- V_{3}/Z_{5}+ V_{2}- V_{20}+ V_{3}/Z_{3}= 0

Collecting the V_{20}'s and isolating:

V_{20}(1/Z_{1}+ 1/Z_{4}+ 1/Z_{5}- 1/Z_{3}) - V_{1}/Z_{1}- V_{3}/Z_{5}+ V_{2}/Z_{3}+ V_{3}/Z_{3}= 0

V_{20}(1/Z_{1}+ 1/Z_{4}+ 1/Z_{5}- 1/Z_{3}) + V_{3}(1/Z_{3}- 1/Z_{5}) + V_{2}/Z_{3}- V_{1}/Z_{1}= 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?

I think it should actually look like this:

V

V

From that point i solved using complex conjugates to produce:

V

V

V

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:

V

= 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,

Last edited:

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