Short Answer:

Superposition theorem is a method used in electrical circuit analysis to solve circuits that have multiple independent sources. It states that in a linear circuit, the total current or voltage in any element is equal to the algebraic sum of the currents or voltages caused by each independent source acting alone, while all other independent sources are turned off.

To apply the theorem, we analyze the circuit multiple times—each time considering only one source active and replacing all other independent voltage sources with short circuits and current sources with open circuits. Finally, we add the individual results to get the total response.

Detailed Explanation:

Superposition theorem

Superposition theorem is a very useful technique for analyzing linear electrical circuits with more than one independent source (voltage or current). The principle behind this theorem is that the effect of each independent source can be calculated separately, and the total effect on any branch or element in the circuit is simply the sum of those individual effects.

This approach simplifies the analysis of complicated circuits, especially when finding voltages across elements or currents through elements, without solving the entire system at once.

Key conditions for applying the theorem:

• The circuit must be linear (i.e., obeys Ohm’s Law and superposition).
• The elements involved must be resistors, capacitors, inductors, and independent/dependent sources.
• Non-linear components like diodes or transistors cannot be analyzed using this theorem.

Steps to apply superposition theorem

1. Identify all independent sources
   • These can be independent voltage or current sources.
2. Turn off all sources except one
   • Replace all other voltage sources with short circuits (0 V).
   • Replace all other current sources with open circuits (0 A).
   • Keep dependent sources active since they rely on circuit variables.
3. Analyze the simplified circuit
   • Use Ohm’s Law, Kirchhoff’s Laws, mesh or nodal analysis to find the response (current or voltage) in the element of interest due to that one active source.
4. Repeat for each source
   • Repeat steps 2 and 3 for each independent source in the circuit.
5. Add all individual responses algebraically
   • The total current or voltage is the sum of all the individual contributions from each source.

Example understanding

Suppose a circuit has two voltage sources and a resistor. To find the current through the resistor:

• First, consider only the first voltage source, replace the second with a wire (short circuit), and calculate the current.
• Then, consider only the second voltage source, replace the first with a short circuit, and calculate the current.
• Finally, add both currents algebraically (considering direction) to get the total current through the resistor.

Advantages of superposition theorem

• Simplifies the analysis of circuits with multiple sources.
• Helps in understanding the individual contribution of each source.
• Useful in signal analysis, AC/DC mixed circuits, and control systems.

Limitations of superposition theorem

• Applicable only to linear circuits.
• Not suitable for finding power directly, since power is not a linear function (you must calculate total current/voltage first).
• Becomes lengthy for circuits with many sources, though conceptually clear.

Conclusion:

Superposition theorem is a powerful tool in electrical circuit analysis that allows you to simplify and solve circuits with multiple independent sources. By analyzing the circuit one source at a time and summing their effects, it becomes easier to understand and calculate the overall behavior of the circuit. Though limited to linear systems, it remains one of the most effective methods for analyzing complex networks.