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Solved Problems-8

Obtain Thevenin’s equivalent circuit with respect to terminals AB in the networks shown below.
  1. Description: 1931.png
  2. Description: 1938.png
  3. Description: 1945.png
  4. Description: 1952.png
  5.  Description: 1959.png
  1. With AB open, the current is,
I = Description: 5226.png

Thevenin voltage,
Vth = Description: 5234.png
Description: 5240.png 
Description: 5249.png 
Thevenin impedance,
Description: 5255.png 
Description: 1991.png 
Thus, the Thevenin’s equivalent circuit is shown in the figure.
  1. Here, Thevenin voltage,
Vth = Description: 5261.png
Description: 5267.png
Vth = Description: 5273.png
Thevenin impedance,
Zth = Description: 5279.png
Description: 5285.png
Description: 5295.png

Thus, the Thevenin’s equivalent circuit is shown in the figure.
  1. Description: 2029.png
Here, with AB open, equivalent impedance,
Description: 5301.png
∴ Main current, Description: 5307.png
∴ Thevenin voltage,
Description: 5313.png
Description: 5319.png
∴ Thevenin impedance, Description: 5325.png
  1. The circuit is redrawn as shown considering two capacitors in parallel.
∵ Description: 5331.png
Thevenin voltage is given as,
Description: 5342.png
Description: 5348.png

∴ Thevenin impedance, Description: 5354.png
  1. To find Vth
With AB open, current of the dependent source can flow through the capacitor only.
Description: 2082.png
 Description: 5360.png
∴ Thevenin voltage,
Description: 5366.png
To find IN
Description: 2099.png
Converting the dependent current source into voltage source, by KVL,
Description: 5372.png
and Description: 5380.png
Solving for INDescription: 5386.png 
∴ Thevenin impedance, Description: 5392.png 

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