Question

What is the superposition theorem in IIT?

Answer 1

The Superposition Theorem is a fundamental principle in electrical engineering, particularly in circuit analysis. It helps simplify circuits with multiple sources (voltage or current sources) by considering one source at a time and then adding their effects. Here's how it works:

Superposition Theorem:

1. Step 1: Consider a circuit with multiple independent sources (voltage or current sources).
   

1. Step 2: To find the effect of one source, turn off all other sources:
   

  - Replace all independent voltage sources with short circuits (basically, a wire).
  - Replace all independent current sources with open circuits (a break in the circuit).

1. Step 3: Calculate the contribution of the active source (the one you haven’t turned off) to the desired parameter (voltage or current).
   

1. Step 4: Repeat the above steps for each source in the circuit.
   

1. Step 5: Finally, add up the individual contributions from all the sources to get the total effect in the circuit.
   

Example:

Consider a circuit with two voltage sources (V₁ and V₂), and you want to find the voltage across a resistor (R).

1. Turn off V₂: Replace V₂ with a short circuit. Find the voltage across R due to V₁ alone.
   

1. Turn off V₁: Replace V₁ with a short circuit. Find the voltage across R due to V₂ alone.
   

1. Add the voltages: The total voltage across R is the sum of the voltages calculated in steps 1 and 2.
   

Important Notes:

1. Superposition works only for linear circuits, where parameters like resistance, inductance, and capacitance don’t change with the voltage or current.
   

1. It simplifies the analysis of complex circuits, especially when dealing with multiple sources.
   

This method is commonly used in IIT exams for analyzing circuits with multiple voltage or current sources.