GATE Electrical Engineering - Complete Master Library

 

📘 Superposition Theorem – Worked Examples (GATE Level)

Superposition Theorem states that in a linear circuit with multiple independent sources, the current or voltage in any element is the algebraic sum of contributions from each source acting alone.

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🔹 Example 1: Two Voltage Sources in Series Network

Given:

• 10V source
• 5V source (opposite direction)
• Series resistance: 5Ω + 5Ω

Find: Current in the circuit.

Step 1: Activate 10V Source Only

Deactivate 5V source → Replace with short circuit.

Total Resistance = 5 + 5 = 10Ω

I₁ = 10 / 10 = 1A

Step 2: Activate 5V Source Only

Deactivate 10V source → Replace with short circuit.

I₂ = 5 / 10 = 0.5A

Direction opposite to I₁.

Final Current

I = I₁ − I₂ = 1 − 0.5 = 0.5A

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🔹 Example 2: Voltage Source + Current Source

Given:

• 8V voltage source
• 2A current source
• 4Ω resistor

Find: Voltage across resistor.

Step 1: Voltage Source Only

Deactivate current source → Open circuit.

I₁ = 8 / 4 = 2A

V₁ = 8V

Step 2: Current Source Only

Deactivate voltage source → Short circuit.

I₂ = 2A

V₂ = I₂ × R = 2 × 4 = 8V

Final Voltage

V = V₁ + V₂ = 8 + 8 = 16V

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🔹 Example 3: Power Calculation Using Superposition

Given:

• 12V source
• 6V source
• 6Ω resistor

Step 1: 12V Active

I₁ = 12 / 6 = 2A

Step 2: 6V Active

I₂ = 6 / 6 = 1A

Total Current

I = 2 + 1 = 3A

Power in 6Ω

P = I²R = 3² × 6 = 9 × 6 = 54W

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🔹 Example 4: Conceptual Trap (GATE Type)

If two equal sources produce equal and opposite currents in a resistor:

Net Current = 0
Voltage across resistor = 0
Power dissipated = 0

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🎯 Important Exam Notes

• Deactivate Voltage Source → Replace with Short Circuit
• Deactivate Current Source → Replace with Open Circuit
• Superposition applies only to linear circuits
• Power cannot be directly superposed (calculate after total current)

⚡ Practice More. Analyze Directions Carefully. Avoid Sign Errors.