[Solved] For the given circuit, determine the Thevenin equivalent circuit at terminals a–b...

Question:

For the given circuit, determine the Thevenin equivalent circuit at terminals a–b.

(Insert circuit diagram image here if needed)

Solution:

Step 1: Find Open-Circuit Voltage (V_th)

With terminal a open, no current flows through the 10Ω resistor, so V_a = V_n.

Applying KCL at node n:

(Vn - 6)/8 - Vn/4 = 0
        

Solving:

(Vn - 6)/8 = Vn/4
Vn - 6 = 2Vn
Vn = -6 V
        

Therefore:

Vth = -6 V

Step 2: Find Thevenin Resistance (R_th)

Turn off the 6V source (replace with short circuit). Apply a test voltage V_t at terminal a.

KCL at node n:

Vn/8 + (Vn - Va)/10 - Va/4 = 0
        

Solving:

5Vn + 4(Vn - Va) - 10Va = 0
9Vn = 14Va
Vn = (14/9)Va
        

Test current:

It = (Va - Vn)/10
It = (Va - 14/9 Va)/10
It = -Va/18
        

Therefore:

Rth = -18 Ω

Final Answer:

Thevenin Equivalent: Vth = -6 V, Rth = -18 Ω

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