AC circuit analysis -- mesh and nodal

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Discussion Overview

The discussion revolves around analyzing an AC circuit using mesh and nodal analysis techniques. Participants are attempting to determine the current in the circuit based on given values and are sharing their equations, results, and challenges encountered during the analysis.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents their mesh analysis equations and results for the currents I1, I2, I3, and I4, seeking verification for part (a) and assistance with part (b).
  • Another participant suggests that the fixed potential difference created by V3 allows for simplifications in the loop equations, specifically omitting Z2 from loop 2.
  • A participant expresses uncertainty about their approach to calculating the current through Z4 and shares updated equations for their analysis.
  • Concerns are raised about the correct treatment of voltage supplies in loop analysis, particularly regarding the signs used in the equations.
  • Multiple participants share their current calculations and express confidence in their results, while others seek clarification on their methods.
  • Some participants discuss the choice of reference nodes in nodal analysis and the concept of supernodes, indicating varying levels of understanding and experience.
  • There are repeated requests for guidance on how to proceed with the analysis, with some participants feeling uncertain about their progress.

Areas of Agreement / Disagreement

Participants generally do not reach consensus on the best approach to the problem, with multiple competing views on the application of mesh and nodal analysis, as well as differing interpretations of the circuit's behavior. Some express confidence in their calculations, while others remain uncertain and seek further clarification.

Contextual Notes

Participants mention potential errors in their equations and the need for careful consideration of voltage sources and node connections. There are unresolved issues regarding the treatment of certain components in the circuit and the implications of swapping elements like V3 and Z2.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in AC circuit analysis, particularly those looking to understand mesh and nodal methods and the common challenges faced in applying these techniques.

  • #181
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.
 
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  • #182
gneill said:
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.
 
  • #183
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.
 
  • #184
Something's gone wrong with your development or solving of EQUATION B. You're okay up to this point:
Ben Yates said:
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.
 
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  • #185
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
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..
 
  • #187
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?
 
  • #188
Joe85 said:
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,
 
Last edited:

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