Find the Thevenin equivalent (V_TH and R_TH) between terminals A and B of the circuit given below.

Steps to Solve

1. Identify the circuit components

Identify the resistances and the voltage source in the circuit:

• $R_1 = 68 , \Omega$
• $R_2 = 100 , \Omega$
• $R_3 = 120 , \Omega$
• $V_S = 100 , V$

2. Calculate the total resistance ($R_{TH}$)

To find $R_{TH}$, remove the independent voltage source (replace with a short circuit), then find the equivalent resistance seen from terminals A and B.

Using parallel and series resistance formulas:

• $R_{AB} = R_2 \parallel R_3 = \frac{R_2 \cdot R_3}{R_2 + R_3} = \frac{100 \cdot 120}{100 + 120} = \frac{12000}{220} \approx 54.55 , \Omega$

Now, combine $R_{AB}$ with $R_1$:

• $R_{TH} = R_1 + R_{AB} = 68 + 54.55 \approx 122.55 , \Omega$

3. Determine the open-circuit voltage ($V_{TH}$)

To find $V_{TH}$, calculate the voltage across the terminals A and B. Use the voltage divider rule:

• First, find $I_S$ using Ohm’s Law:
  $$ I_S = \frac{V_S}{R_1 + R_2 + R_3} = \frac{100}{68 + 100 + 120} = \frac{100}{288} \approx 0.347 , A $$

• Next, find $V_{R_2}$ to determine $V_{TH}$:
  $$ V_{R_2} = I_S \cdot R_2 = 0.347 \times 100 \approx 34.7 , V $$

Hence,
$$ V_{TH} = V_{R_2} = 34.7 , V $$

4. Summary of Thevenin Equivalent

Finally, the Thevenin equivalent voltage and resistance can be summarized as:

• $V_{TH} \approx 34.7 , V$
• $R_{TH} \approx 122.55 , \Omega$