AC Steady State Analysis for Node V1 and V2 using Ohm's Law and KCL

Click For Summary

Discussion Overview

The discussion revolves around the analysis of an AC steady state circuit at nodes V1 and V2 using Ohm's Law and Kirchhoff's Current Law (KCL). Participants are attempting to derive steady state expressions in terms of AC functions and are exploring the implications of combining impedances in the circuit.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant outlines the initial problem and attempts to convert circuit elements to phasors, listing the impedances of resistors, capacitors, and inductors.
  • Another participant suggests that the impedance in the equation should be replaced with the series impedance of the capacitor and inductor, indicating that the branches can contain multiple elements.
  • A participant calculates the combined impedance of the capacitor and inductor, arriving at a value of -j1990, and considers using nodal analysis for further calculations.
  • There is mention of a previous attempt to combine impedances using a parallel configuration, which was described as complicated.
  • One participant indicates they have solved the problem, but does not provide details on the solution.

Areas of Agreement / Disagreement

Participants express uncertainty about the correct approach to combine impedances and whether nodal analysis is the best method. There is no consensus on the solution, as one participant claims to have solved the problem while others are still exploring different methods.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in combining impedances or the implications of their choices in analysis methods. There are indications of potential errors in earlier calculations that remain unaddressed.

butleRonius
Messages
4
Reaction score
0

Homework Statement



Steif.ch06.p41_1.jpg

Find the steady state expressions in terms of Acos(wt+theta) for nodes v1 and v2.

Homework Equations



Ohm's law
KCL
Node Analysis

The Attempt at a Solution


Convert to phasors and find impedances-> R1= 50 Ohms R2= 30 Ohms
C1= -j2500=1/j*4e-4 Ohms C2= -j2000=1/j5e-4 Ohms
L1= j5 Ohms L2= j10 Ohms

I'm not getting an acceptable answer when I use Wolfram to solve the systems produced. I believe the error is that I need to combine the impedances of the capacitor and the inductor coming off of node 2, but I'm not sure since there is another node there. It's quite possible there are multiple errors on my part.
 

Attachments

  • 20140928_170958.jpg
    20140928_170958.jpg
    19.7 KB · Views: 510
Last edited:
Physics news on Phys.org
Hi butleRonius. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

There is no restriction on what impedance can comprise each branch; it doesn't have to be a single element. In your eqn (2) you need to replace 1/(j3E4) by 1/(z) where z is the series impedance of the capacitor and inductor.

So there's a little sub-exercise for you, determining that series impedance before using it in eqn (2).
 
Last edited by a moderator:
so -j2000 + j10 = -j1990

Sub that in: v2/-j1990

Solve using nodal?

I actually tried combining as (Zc+ZL) || Zr but that turned into a nightmare

Thanks.
 
Solved. Thank you.
 
butleRonius said:
so -j2000 + j10 = -j1990
Sub that in: v2/-j1990 ✔ [/size][/color]

Solve using nodal?
Sure, go ahead.
I actually tried combining as (Zc+ZL) || Zr but that turned into a nightmare
A little bit of work involved, yes, but it simplifies the circuit to one with no nodes so the subsequent analysis is shorter. Swings and roundabouts ...
 

Similar threads

  • · Replies 15 ·
Replies
15
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
13
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K