📘 Superposition Theorem – Complete Theory & Detailed Worked Examples
🔹 1. Introduction
Superposition Theorem is one of the most important tools in linear circuit analysis. It is frequently asked in GATE, IES and PSU exams both directly and indirectly. It helps analyze circuits containing multiple independent sources.
🔹 2. Statement of Superposition Theorem
In a linear bilateral network containing multiple independent sources, the current or voltage in any element is equal to the algebraic sum of currents or voltages produced by each independent source acting alone.
🔹 3. Important Conditions
- Applicable only to linear circuits (R, L, C)
- Does NOT apply directly to power calculation
- Dependent sources must NOT be deactivated
- Voltage source → Replace with short when deactivated
- Current source → Replace with open when deactivated
🔹 4. Step-by-Step Method
Step 2: Keep only one source active at a time.
Step 3: Replace other voltage sources by short circuits.
Step 4: Replace other current sources by open circuits.
Step 5: Solve the circuit normally using KCL or KVL.
Step 6: Repeat for all sources.
Step 7: Add algebraically (consider sign and direction).
🔹 5. Worked Example 1 – Two Voltage Sources
Given:
- V1 = 12V
- V2 = 6V (opposite polarity)
- Resistor = 6Ω
Step 1: V1 Active Only
I1 = 12 / 6 = 2A
Step 2: V2 Active Only
I2 = 6 / 6 = 1A (Opposite direction)
Step 3: Net Current
I = 2 − 1 = 1A
🔹 6. Worked Example 2 – Voltage + Current Source
Given:
- Voltage Source = 10V
- Current Source = 2A
- Resistor = 5Ω
Voltage Source Only
I1 = 10/5 = 2A
Current Source Only
I2 = 2A
Total Current
I = 2 + 2 = 4A
🔹 7. Worked Example 3 – Three Source Circuit
V1 = 10V V2 = 5V Current Source = 1A R = 5Ω
I1 = 2A I2 = 1A I3 = 1A Total = 4A
🔹 8. Worked Example 4 – Sign Confusion Type
If two sources produce equal opposite current in resistor, net current becomes zero.
I = I1 − I2 If I1 = I2 → I = 0
🔹 9. Common Exam Mistakes
- Forgetting to deactivate sources properly
- Adding magnitudes without sign
- Calculating power using superposition directly
- Ignoring direction assumption
🎯 Final Summary
Superposition simplifies multi-source circuits. It builds foundation for Thevenin and Norton. Understanding direction and sign is critical for GATE.
Strong Superposition Skills = Strong Multi-Source Analysis
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