Thevenin’s Equivalent Resistance of Req is

Answer: C. 0.44

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

Solution:

Finding R_Th

Case (i): if the circuit does not contain dependent sources, then turn off all independent sources, and calculate R_Th 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 R_Th.

As the above circuit contain a dependent source, to calculate R_eq 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 v_x at node x as shown in the above figure,

Then apply KCL at node x, and we get

(V_x/5)-1.5I_x+(V_x-3)/3=0

Here I_x=(V_x-3)/3

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

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

 Then I_x=(V_x-3)/3=-15-3/3=-6 A,

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

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

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

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

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

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