Thevenin's Theorem Explained

Thevenin's Theorem is a powerful tool in electrical circuit analysis that simplifies complex linear circuits. It states that any linear, active, two-terminal network can be replaced by a much simpler equivalent circuit.

This equivalent circuit consists of:

• A single voltage source. This is known as the Thevenin voltage source, often denoted as \(V_{th}\).
• A single resistor. This is known as the Thevenin resistance, often denoted as \(R_{th}\).

Crucially, these two components, the Thevenin voltage source and the Thevenin resistance, are always connected in a series configuration to represent the original complex network between its two terminals.

Applying Thevenin's Theorem to the Question

The question asks us to fill in the blanks in the statement about Thevenin's Theorem:

"Thevenin's Theorem states that, any linear active Double terminal network containing voltage and resistance sources can be replaced by a ________ Voltage source in _______ with ________ resistance."

Based on the definition of Thevenin's Theorem:

1. The complex network is replaced by a Single Voltage source.
2. This Voltage source is connected in Series with a resistance.
3. The resistance is a Single resistance.

Therefore, the blanks should be filled with "Single", "Series", and "Single".

Selecting the Correct Option

Let's look at the options provided:

• Option 1: Single, Parallel, Single (Incorrect - The components are in series, not parallel)
• Option 2: Single, Parallel, Two (Incorrect - The components are in series, and there is only one resistance)
• Option 3: Single, Series, Single (Correct - This matches the description of the Thevenin equivalent circuit)
• Option 4: Single, Series, Two (Incorrect - There is only one resistance in the equivalent circuit)

The statement correctly filled is: "Thevenin's Theorem states that, any linear active Double terminal network containing voltage and resistance sources can be replaced by a Single Voltage source in Series with Single resistance."