Advanced Practice Problems – KCL & KVL (GATE Level)
These problems are designed for serious aspirants preparing for GATE, ESE and competitive exams.
📌 Problem 1 – Node Voltage Analysis
A node is connected to three resistors:
2Ω to 10V source,
4Ω to ground,
6Ω to 5V source.
Find node voltage V.
✔ Solution:
Apply KCL at node V:
(V − 10)/2 + V/4 + (V − 5)/6 = 0
Multiply entire equation by 12:
6(V − 10) + 3V + 2(V − 5) = 0
6V − 60 + 3V + 2V − 10 = 0 11V − 70 = 0 V = 70/11
Final Answer: V = 6.36 V (approx)
📌 Problem 2 – Loop Current Method
A single loop contains:
12V source, 2Ω resistor and 4Ω resistor.
Find loop current.
✔ Solution:
Apply KVL:
12 − 2I − 4I = 0 12 − 6I = 0 I = 2A
Final Answer: I = 2A
📌 Problem 3 – Multiple Node System
Two nodes V1 and V2 are connected by 3Ω resistor.
Node V1 connected to 12V source via 6Ω.
Node V2 connected to ground via 3Ω.
Find V2.
✔ Approach:
- Write KCL at Node V1
- Write KCL at Node V2
- Solve simultaneous equations
( V1 − 12 )/6 + ( V1 − V2 )/3 = 0 ( V2 − V1 )/3 + V2/3 = 0
Solve equations to get:
Final Answer: V2 = 4V
🎯 Exam Insight
- ✔ GATE loves node voltage method
- ✔ Reduce equation size by multiplying LCM early
- ✔ Keep sign convention consistent
- ✔ Practice solving within 2–3 minutes
Next Level:
Superposition Theorem – Numerical + GATE PYQs (Advanced)
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