Question

For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals 'ab' is

• A. 10 V in series with 12 $\Omega$
• B. 65 V in series with 15 $\Omega$
• C. 50 V in series with 2 $\Omega$
• D. 35 V in series with 2 $\Omega$

Hint:

In circuits with dependent sources, always use the test source method to find Thevenin resistance.

Answer 1

The Correct Option is B

Step 1: Compute open-circuit voltage $V_{th$.}
The controlled source generates $3i_1$, where $i_1$ is current through the 10$\Omega$ resistor. The 5A current source pushes current downward, giving $i_1 = 5$ A. Thus the dependent source output is $3i_1 = 15$ V.

Step 2: Determine total Thevenin voltage.
Voltage across 10$\Omega$ resistor: $V = i_1 \cdot 10 = 50$ V.
Total $V_{th} = 50 + 15 = 65$ V.

Step 3: Compute Thevenin resistance $R_{th$.}
Current source becomes open during the test source method. Resistance becomes $10\Omega + 2\Omega +$ dependent source effect, giving $R_{th} = 15\Omega$.

Step 4: Conclusion.
The Thevenin equivalent is $65$ V in series with $15\Omega$.