Question

This is problem 4 from chapter 6 of the course text. Find the Thevenin equivalent seen at the terminal A-B. Select which answer below provides the correct Vs and resistance Rth of the Thevenin equivalent.
Vs1 12V
Is2 0.4A
R1 60ohms
R2 60ohms
R3 40ohms
A) Vs = 3V, Rth = 160 Ohm

B) Vs = -3V, Rth = 160 Ohm

C) Vs = 9V, Rth = 30 Ohm

D) Vs = -9V, Rth = 30 Ohm

E) Vs = 3V, Rth = 30 Ohm

F) Vs = -3V, Rth = 30 Ohm

G) Vs = 9V, Rth = 120/7 Ohm

H) Vs = -9V, Rth = 120/7 Ohm

Answer 1

Answer:

Option C is correct.

Vs = 9 V, Rth = 30 ohms

Explanation:

In the circuit diagram, there are two sources, so, using superposition, we'll find voltage across A and B, Vab, with respect to each of the sources.

Taking the voltage source as primary source.

We will open circuit the current source just like it is presented in the first drawing of the 2nd image I have added to this solution.

By open-circuiting the current source, the three resistors R₁, R₂ and R₃ are in series.

This means that the Vab is the voltage across the R₃ resistor.

Using voltage divider rule,

Vab = (R₃/R₁ + R₂ + R₃) Vs₁

Vab = [40/(60 + 60 + 40)] (12)

Vab = 3 V

Taking the current source as the primary source.

We will now short circuit the voltage source as shown in the 2nd drawing of the 2nd image I have attached to this solution.

As shown in the 2nd drawing of the 2nd file I attached to this solution, the R₂ is in parallel with R₁ and R₃, that is R₂//(R₁ + R₃)

Using the current divider rule

Current in the (R₁ + R₃) branch = [R₂/(R₂ + (R₁ + R₃))] Is₂ = (60/(60 + 60 + 40)) (0.4) = 0.15 A

Vab = voltage across the R₃ resistor = IR₃ = 0.15 × 40 = 6 V

Total voltage across A and B, Vab = Vab due to Vs₁ + Vab due to Is₂ = 3 + 6 = 9 V

And for the Rth, we open-circuit the current source and short-circuit the voltage source simultaneously and look at the resistance of the setup from the AB terminal, as shown in the first drawing of the 3rd file attached to this solution.

It is evident that R₃ is in a parallel combination with (R₁ + R₂)

Rth = (R₁ + R₂)//R₃ = (60 + 60)//40 = 120//40 = (120× 40)/(120 + 40) = 30 ohms

The image of the thevenin equivalent of the circuit as seen from terminals AB is presented in the 2nd drawing on the 3rd image attached.