Superposition Theorem – Working Principle

The Superposition Theorem is a fundamental principle in electrical circuit analysis. It is used to determine the current or voltage in any branch of a linear circuit that contains multiple independent sources (voltage or current sources).

➤ Working of Superposition Theorem:

Linear Circuit Requirement:
- The circuit must be linear (i.e., the components like resistors, capacitors, and inductors should obey Ohm’s law).
One Source at a Time:
- Only one independent source is considered at a time, while all other independent sources are “turned off.”
- Turning off sources means:
  - Voltage source → Replace it with a short circuit.
  - Current source → Replace it with an open circuit.
Analyze the Circuit:
- Solve the circuit using standard techniques (Ohm’s law, Kirchhoff’s laws, etc.) to find the contribution of the active source to the desired current or voltage.
Repeat for All Sources:
- Perform the same process for each independent source one by one.
Add the Results:
- The total current or voltage at any point is the algebraic sum of the individual contributions from each source.

➤ Key Points:

Applies only to linear circuits.
Helps break down complex circuits with multiple sources into simpler parts.
Uses basic circuit-solving methods like voltage division, current division, or mesh analysis.
The final result is obtained by summing the effects of all sources.

➤ Example:

For a circuit with two voltage sources, V₁ and V₂, and resistors R₁ and R₂:

First, turn off V₂ (replace with a short circuit) and calculate the current due to V₁.
Then, turn off V₁ and calculate the current due to V₂.
Add both currents to find the total current.

➤ When to Use It:

Useful when analyzing circuits with multiple sources.
Simplifies calculations instead of solving all equations simultaneously.
Helps understand how each source affects the circuit independently.

✅ Q1. The Superposition Theorem is applicable to which type of circuits?

A) Only nonlinear circuits
B) Only circuits with capacitors and inductors
C) Linear circuits with multiple independent sources
D) Circuits without any sources

✔ Correct Answer: C) Linear circuits with multiple independent sources

Explanation:
The Superposition Theorem applies only to linear circuits where the circuit components obey Ohm’s law and have multiple independent sources like voltage or current sources.

✅ Q2. When applying the Superposition Theorem, how do you handle an independent voltage source that is not being considered at the moment?

A) Replace it with an open circuit
B) Keep it as it is
C) Replace it with a short circuit
D) Remove it permanently

✔ Correct Answer: C) Replace it with a short circuit

Explanation:
When analyzing one source at a time, other independent voltage sources are replaced by short circuits, which means they behave as a wire with zero resistance.

✅ Q3. How should an independent current source be treated when it is not being analyzed?

A) Replaced with a short circuit
B) Left unchanged
C) Replaced with an open circuit
D) Removed and ignored

✔ Correct Answer: C) Replaced with an open circuit

Explanation:
Independent current sources that are not under analysis are replaced with open circuits, meaning no current can flow through them while calculating the contribution from other sources.

✅ Q4. After calculating the effects of each source separately, what is the final step in the Superposition Theorem?

A) Multiply the individual effects
B) Ignore the sources one by one
C) Add the individual effects algebraically
D) Average the individual effects

✔ Correct Answer: C) Add the individual effects algebraically

Explanation:
The final solution is found by summing the individual contributions from each source algebraically, considering the direction and polarity of currents and voltages.

✅ Q5. Which of the following is a limitation of the Superposition Theorem?

A) It cannot be used for DC circuits
B) It cannot be used in nonlinear circuits
C) It requires only one source in the circuit
D) It works only if there is a single load

✔ Correct Answer: B) It cannot be used in nonlinear circuits

Explanation:
The Superposition Theorem is not valid for nonlinear circuits where elements do not follow Ohm’s law, such as circuits containing diodes or transistors operating in nonlinear regions.