Question

With dependent sources, Thevenin's resistance is found by:

• A. Open-circuit method
• B. Short-circuit method
• C. Applying a test source (V/I)
• D. Ignoring sources

Hint:

When solving circuits with dependent sources, choosing \(V_{test} = 1\text{ V}\) or \(I_{test} = 1\text{ A}\) simplifies calculations.
If \(V_{test} = 1\text{ V}\), then \(R_{th} = \frac{1}{I_{test}}\).
Remember to always set all independent sources to zero before applying the test source.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the standard procedure to find the Thevenin equivalent resistance (\(R_{th}\)) of an electrical network that contains dependent sources.

Step 2: Detailed Explanation:

• In networks containing only independent sources, \(R_{th}\) is determined by deactivating all independent sources (short-circuiting voltage sources and open-circuiting current sources) and calculating the equivalent resistance across the load terminals.

• When dependent sources are present in the network, they cannot be deactivated because their value depends on other branch currents or voltages within the circuit, which remain active during deactivation.

• To find the Thevenin resistance in such cases, all independent sources are deactivated first.

• Next, an external test source (either an independent voltage source \(V_{test}\) or an independent current source \(I_{test}\)) is connected across the terminals where \(R_{th}\) is to be determined.

• The resulting terminal current \(I_{test}\) (if a voltage source is applied) or terminal voltage \(V_{test}\) (if a current source is applied) is calculated.

• The Thevenin resistance is then computed using Ohm's Law:
\[ R_{th} = \frac{V_{test}}{I_{test}} \]
• This method is universally valid for any linear network containing both independent and dependent sources.

Step 3: Final Answer: Thevenin's resistance is found by applying a test source (V/I).