Thevenin's Equivalent Resistance of Req is

By Varadi Hema|Updated : July 22nd, 2022

Thevenin’s equivalent resistance seen from terminals 'a' and 'b' for the circuit is _____ Ohms.

  1. 1
  2. 1.5  
  3. 0.44
  4. 2

Answer: C. 0.44

Thevenin’s equivalent resistance seen from the terminals a, b Req=0.44 Ohms.

Solution:

Finding RTh

Case (i): if the circuit does not contain dependent sources, then turn off all independent sources, and calculate RTh which is resistance seen from a and b terminals.

Case (ii): if the circuit contains dependent sources, we turn off all the independent sources by keeping dependent sources as they are, and we apply voltage v0 (or) current (i0) across a and b terminals. We may assume any value of v0 or i0.

And we calculate RTh.

As the above circuit contain a dependent source, to calculate Req between a, b terminals

  1. Deactivate the 6V source (short circuit).
  2. And apply a voltage source v0=3 V across a, b terminals

Assign node voltage vx at node x as shown in the above figure,

Then apply KCL at node x, and we get

(Vx/5)-1.5Ix+(Vx-3)/3=0

Here Ix=(Vx-3)/3

(Vx/5)-1.5(Vx-3)/3+(Vx-3)/3=0

By solving the above equation, we got vx=-15 V

 Then Ix=(Vx-3)/3=-15-3/3=-6 A,

So, the current through the dependent current source is 1.5Ix=1.5×-6 A=-9 A,

And current through the 5-ohm resistor I5=vx/5=-15/5=-3 A

current through the 4-ohm resistor is I4=3/4

hence current through 3 V source is I4-Ix=(3/4)-(-6 A)=27/4=6.75

Then, resistance seen from a and b terminals is Req=3/6.75=0.444 Ohms

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