What is Superposition Theorem?

Short Answer:

Superposition Theorem is a method used in electrical circuit analysis to determine the total current or voltage in any part of a linear circuit containing multiple independent sources. According to this theorem, the total response is found by considering one source at a time while turning off all other independent sources.

This means we calculate the effect of each source separately and then add all the individual effects to get the final result. It simplifies the analysis of circuits with more than one voltage or current source, especially in complex networks.

Detailed Explanation:

Superposition Theorem

The Superposition Theorem states:
In any linear electrical circuit with multiple independent sources (voltage or current), the voltage across or current through an element is equal to the algebraic sum of the voltages or currents caused by each independent source acting alone, with all other independent sources replaced by their internal resistances.

  • Voltage sources are replaced with short circuits (0V).
  • Current sources are replaced with open circuits (0A).

This method is applicable only for linear circuits, which means the circuit components follow Ohm’s Law (resistors, capacitors, inductors, etc.).

Steps to Apply Superposition Theorem

  1. Identify All Independent Sources:
    • List all voltage and current sources in the circuit.
  2. Turn Off All but One Source:
    • For each step, keep only one source active.
    • Replace voltage sources with short circuits.
    • Replace current sources with open circuits.
  3. Analyze the Circuit for That Single Source:
    • Use Ohm’s Law or any standard method (like mesh or nodal analysis) to find the current or voltage.
  4. Repeat for Each Source:
    • Repeat the above steps for each independent source separately.
  5. Add the Results:
    • Add all the individual currents or voltages algebraically (consider signs) to get the final answer.

Example of Superposition Theorem

Suppose a circuit has two voltage sources and a few resistors. You want to find the current through one particular resistor:

  • Step 1: Keep only the first voltage source active, short the second, and calculate the current through the resistor.
  • Step 2: Now, deactivate the first source and activate the second one. Calculate the current again.
  • Step 3: Add both current values (taking sign into account) to get the total current through the resistor.

Applications of Superposition Theorem

  • Analyzing circuits with multiple power sources
  • Simplifying AC and DC network calculations
  • Studying control systems and signal circuits
  • Finding voltage or current in one specific part of the circuit
  • Used in communication and power systems

Limitations of Superposition Theorem

  • Applicable only for linear circuits
  • Not valid for power calculations (since power is not a linear function)
  • Time-consuming for circuits with many sources
  • Not applicable in circuits with non-linear components (like diodes or transistors)
Conclusion:

Superposition Theorem helps in breaking down complex circuits with multiple sources into simpler single-source circuits. By analyzing one source at a time and then adding the results, it provides a clear and step-by-step way to understand current and voltage distribution. Though it is limited to linear circuits, it remains one of the most powerful tools in electrical circuit analysis and is widely used in both theoretical and practical applications.