Thevenin equivalent of a network

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Discussion Overview

The discussion revolves around finding the Thevenin equivalent of a circuit across specified terminals, focusing on the calculation of both the Thevenin voltage (Vth) and Thevenin impedance (Zth). The context includes a homework problem involving a dependent source, with participants exploring various methods to arrive at the solution.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • The initial poster presents their calculations for Vth and expresses difficulty in determining Zth due to the presence of a dependent source.
  • Another participant suggests calculating the Norton current (In) as a potential method to find Zth, noting the relationship Zth = Vth/In.
  • The initial poster seeks assistance specifically with finding Vth, indicating a preference for that aspect of the problem.
  • A participant points out a typo in the loop equation provided by the initial poster, suggesting a correction that could affect the calculations.
  • The initial poster acknowledges the correction and expresses gratitude, indicating that the revised equation worked for them.

Areas of Agreement / Disagreement

Participants generally agree on the need to correct the loop equation, but there is no consensus on the methods for calculating Zth, as the initial poster continues to seek help with that aspect.

Contextual Notes

The discussion highlights potential limitations in the initial poster's approach, particularly regarding the handling of the dependent source and the accuracy of their equations. The resolution of the loop equation remains contingent on the correction suggested by another participant.

bishshoy007
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Homework Statement



The question is to find the Thevenin equivalent of the network across the terminals a,b.
The circuit is as follows:--
pbxqs.jpg

The solution is Zth = 12.166 angle(136.3*)ohm and Vth = 7.35 angle(72.9*)
I can find out the Vth, that's easy. But I can get the Zth right coz there is the dependent source. Please help ! I have tried almost 50 times, with different methods.

Homework Equations



The two basic laws (comon everyone knows this):--

Kirchoffs' Voltage law = sum of voltages in a loop = 0
Kirchoffs' node law = sum of current through a node = 0

The Attempt at a Solution



k9yk9s.jpg

First I have lumped all series reactances.
At node 1 :--
5 + 0.2V0 = -V0/(8+4j)
Solving V0 = -16.22 - 2.7j

Now writing the KVL for the loop :--
Vth + V0 - (4 - 2j)*0.2-V0 = 0
Solving we get Vth = 2.16 + 7.027j = 7.35 angle(72.89*)

For the Zth I have tried solving by adding a dummy current source at the terminals a,b. It didnt work. Then i tried adding a voltage source across the (8 + 4j) impdedance. Still I couldn't get the answer correct.
 
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You can calculate the Norton current In.
Zth = Vth/In.
 
Yes I haven't tried that. But still I would like to have the thevenin voltage. Any mind helping me, with the solution.
 
There is a typo in the equation of the loop, otherwise it is correct. I have not checked your calculations.

The equation should be

Vth + Vo - (4-2j)*0.2*Vo = 0

You have posted:

Vth + Vo - (4-2j)*0.2-Vo = 0
 
Thanks buddy. It works like a charm.
 

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