📘 GATE Electrical – Network Theory Advanced Practice Set (KCL & KVL) – Part A
This practice set is designed for serious GATE aspirants.
Difficulty Level: Moderate to Advanced.
📌 Problem 1 – Two Node Voltage Analysis
Node V1 connected to:
• 10Ω to 20V source
• 5Ω to ground
• 5Ω to Node V2
Node V2 connected to:
• 10Ω to ground
Find V2.
✔ Solution:
KCL at V1:
(V1 − 20)/10 + V1/5 + (V1 − V2)/5 = 0
Multiply by 10:
(V1 − 20) + 2V1 + 2(V1 − V2) = 0 V1 − 20 + 2V1 + 2V1 − 2V2 = 0 5V1 − 2V2 = 20 ...(1)
KCL at V2:
(V2 − V1)/5 + V2/10 = 0
Multiply by 10:
2(V2 − V1) + V2 = 0 2V2 − 2V1 + V2 = 0 3V2 − 2V1 = 0 ...(2)
Solving equations (1) and (2):
Final Answer: V2 = 4V
📌 Problem 2 – Three Loop KVL System
A circuit has three loops with resistances:
Loop 1: 4Ω
Loop 2: 6Ω
Loop 3: 8Ω
Common resistances between loops: 2Ω each.
Voltage source 12V in loop 1.
Find current in Loop 1.
✔ Approach:
Using mesh analysis:
(4 + 2 + 2)I1 − 2I2 − 2I3 = 12 −2I1 + (6 + 2 + 2)I2 − 2I3 = 0 −2I1 − 2I2 + (8 + 2 + 2)I3 = 0
After solving simultaneous equations:
Final Answer: I1 = 1.5 A
📌 Problem 3 – Power Calculation using KCL
A node connected to:
• 3Ω resistor to 15V source
• 6Ω resistor to ground
Find node voltage and power dissipated in 6Ω resistor.
✔ Solution:
KCL:
(V − 15)/3 + V/6 = 0
Multiply by 6:
2(V − 15) + V = 0 2V − 30 + V = 0 3V = 30 V = 10V
Power in 6Ω:
P = V² / R = 10² / 6 = 16.67W
Final Answer: V = 10V, Power = 16.67W
📌 Problem 4 – Mixed Loop & Node Analysis
Two resistors 4Ω and 8Ω in series across 24V source.
Parallel branch of 6Ω connected across 8Ω.
Find current in 6Ω branch.
✔ Solution Outline:
- Step 1: Find equivalent resistance of 8Ω || 6Ω
- Step 2: Add series 4Ω
- Step 3: Find total current
- Step 4: Use current division rule
Final Answer: Current in 6Ω = 1.6A
More Advanced Problems Continue in Part B...
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