The superposition theorem is a powerful tool used in electrical circuit analysis to simplify complex circuits that contain multiple voltage sources. It allows us to analyze the circuit by considering the effects of each individual voltage source separately and then combining the results.

The theorem is applicable in circuits that contain a number of voltage sources, which means that option D is the correct answer. This is because in circuits with multiple voltage sources, it can be difficult to determine the overall response of the circuit due to the interactions between the sources. The superposition theorem helps us overcome this difficulty by analyzing each source separately and then combining the results.

Here is a detailed explanation of how the superposition theorem works:

1. Principle of Superposition:
The superposition theorem is based on the principle of linearity, which states that the response of a linear circuit to multiple input signals can be determined by summing the responses to each individual input signal. In other words, the total response of a circuit is equal to the sum of the individual responses caused by each input signal.

2. Steps to Apply the Superposition Theorem:
To apply the superposition theorem, follow these steps:

- Disable all but one voltage source: In the circuit, disable all voltage sources except one and replace them with short circuits.

- Analyze the circuit: With only one voltage source active, analyze the circuit using any suitable circuit analysis technique such as Kirchhoff's laws or nodal analysis. Determine the voltages, currents, and power dissipation in the circuit.

- Repeat for other voltage sources: Repeat steps 1 and 2 for each voltage source in the circuit, considering one voltage source at a time.

- Combine the results: Once the analysis is done for each voltage source, combine the results by adding the voltages, currents, and power dissipation obtained for each source. This will give you the overall response of the circuit.

3. Advantages of the Superposition Theorem:
The superposition theorem offers several advantages in circuit analysis:

- Simplifies complex circuits: By considering the effects of each voltage source separately, the superposition theorem simplifies the circuit analysis process, especially for circuits with multiple sources.

- Allows for step-by-step analysis: The theorem allows us to analyze the circuit in a step-by-step manner, focusing on the impact of each individual voltage source. This makes it easier to understand and troubleshoot the circuit.

- Applies to linear circuits: The superposition theorem is applicable to linear circuits, which are commonly encountered in electrical engineering. It is not limited to circuits with passive or active elements only.

Overall, the superposition theorem is a valuable technique for analyzing circuits with multiple voltage sources. It simplifies the analysis process and allows for a step-by-step approach to understanding the circuit's behavior.