📘 Mixed Advanced GATE-Level Numerical Set (Network Theory)
This section contains high-quality mixed problems combining KCL, KVL, Superposition, Thevenin and Norton. Designed for serious GATE aspirants.
🔹 Problem 1 – Node Voltage + KCL
Node V connected to: 10V through 5Ω, 20V through 10Ω, Ground through 20Ω. Find V.
Solution:
(V − 10)/5 + (V − 20)/10 + V/20 = 0
Multiply by 20:
4(V − 10) + 2(V − 20) + V = 0 4V − 40 + 2V − 40 + V = 0 7V = 80 V = 11.43V
🔹 Problem 2 – Mesh + KVL
Two loops share 4Ω resistor. Left loop has 20V and 2Ω. Right loop has 6Ω. Find I1.
(2+4)I1 − 4I2 = 20 −4I1 + (6+4)I2 = 0
Solve equations:
I1 = 2A
🔹 Problem 3 – Superposition (Three Sources)
V1 = 15V, V2 = 5V (opposite), Current Source = 2A, R = 5Ω.
I1 = 15/5 = 3A I2 = 5/5 = 1A (opposite) I3 = 2A Total = 3 − 1 + 2 = 4A
🔹 Problem 4 – Thevenin Equivalent
Voltage Source = 30V, R1 = 10Ω, R2 = 20Ω, Load RL = 15Ω. Find load current.
Step 1: Vth
Vth = 30 × (20/30) = 20V
Step 2: Rth
Rth = (10×20)/30 = 6.67Ω
Step 3: Load Current
I = 20/(6.67+15) I = 0.92A
🔹 Problem 5 – Norton Conversion
Thevenin Equivalent: Vth = 12V, Rth = 4Ω. Convert to Norton.
IN = Vth / Rth IN = 12 / 4 IN = 3A RN = 4Ω
🔹 Problem 6 – Maximum Power Transfer
Vth = 24V, Rth = 6Ω. Find RL for maximum power and Pmax.
RL = Rth = 6Ω Pmax = 24² / (4×6) Pmax = 576/24 Pmax = 24W
🔹 Problem 7 – Conceptual Trap
If two sources produce equal and opposite voltage across resistor, what is power dissipated?
Net Voltage = 0 Current = 0 Power = 0
🎯 Final Summary
This mixed set integrates all major network theory tools. Practice repeatedly to improve speed and accuracy. This level of preparation is required for top GATE ranks.
Strong Practice + Strong Concepts = Strong Rank
.png)
No comments:
Post a Comment