GATE Electrical Engineering - Complete Master Library

 

📘 GATE Electrical – Network Theory Advanced Practice Set (KCL & KVL) – Part B

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Difficulty Level: Advanced Focus: Supernode, Dependent Sources, Multi-Loop Mesh Analysis

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📌 Problem 5 – Supernode Analysis

Two nodes V1 and V2 are connected by a 10V voltage source. V1 connected to ground through 5Ω. V2 connected to ground through 10Ω. Find V1 and V2.

✔ Solution:

Since a voltage source connects V1 and V2 → Use Supernode.

Equation 1 (Supernode KCL):

V1/5 + V2/10 = 0

Equation 2 (Voltage constraint):

V1 − V2 = 10

Solve equations:

Multiply first equation by 10:

2V1 + V2 = 0 ...(1)

V1 = V2 + 10 ...(2)

Substitute (2) into (1):

2(V2 + 10) + V2 = 0 2V2 + 20 + V2 = 0 3V2 = −20 V2 = −6.67V

V1 = 3.33V

Final Answer: V1 = 3.33V, V2 = −6.67V

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📌 Problem 6 – Dependent Source (GATE Level)

A circuit contains: 10Ω resistor connected to 20V source. A dependent current source of value 0.1Vx where Vx is voltage across 10Ω. Find current through 10Ω.

✔ Solution Outline:

Let current through 10Ω = I

Then Vx = 10I

Dependent source = 0.1 × 10I = I

Apply KCL:

20 − 10I − V = 0 (after simplification)

Solving gives:

Final Answer: I = 1A

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📌 Problem 7 – Three Mesh Analysis

Three loops share 2Ω resistors between them. Loop 1 has 15V source. Each loop has 4Ω resistor. Find I1 using mesh method.

✔ Mesh Equations:

(4 + 2 + 2)I1 − 2I2 − 2I3 = 15 −2I1 + (4 + 2 + 2)I2 − 2I3 = 0 −2I1 − 2I2 + (4 + 2 + 2)I3 = 0

After solving simultaneous equations:

Final Answer: I1 = 1.25A

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📌 Problem 8 – Maximum Power Condition (Using KCL/KVL)

A load resistor RL connected across Thevenin equivalent circuit. Given Rth = 5Ω. Find RL for maximum power transfer.

✔ Solution:

Maximum power occurs when:

RL = Rth

Final Answer: RL = 5Ω

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🎯 Advanced Exam Insights

• ✔ Voltage source between nodes → Think Supernode
• ✔ Dependent source → Express variable clearly
• ✔ Mesh method preferred when loops < nodes
• ✔ Speed + clarity = Rank improvement

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Advanced Problems Complete. Next: Superposition Theorem – Full GATE Level Series.