📘 Advanced KCL & KVL – Worked Examples (Page 6)
🔹 Example 1 – Two Node System
Node V1 connected to 20V via 5Ω Connected to V2 via 10Ω V2 connected to ground via 5Ω
KCL at V1:
(V1 − 20)/5 + (V1 − V2)/10 = 0
KCL at V2:
(V2 − V1)/10 + V2/5 = 0
Solving simultaneous equations:
V2 = 5V
🔹 Example 2 – Three Loop Mesh
Voltage = 15V Loop resistances: 4Ω each Shared resistances: 2Ω
(4+2+2)I1 − 2I2 − 2I3 = 15 After solving → I1 = 1.25A
📘 Supernode & Dependent Source (Page 7)
🔹 Example 1 – Supernode
Two nodes connected by 10V source Each node connected to ground via 5Ω and 10Ω
Supernode Equation:
V1/5 + V2/10 = 0 V1 − V2 = 10 Solve → V1 = 3.33V, V2 = −6.67V
🔹 Example 2 – Dependent Source
20V source 10Ω resistor Dependent current source 0.1Vx
Vx = 10I 0.1Vx = I Solve → I = 1A
📘 Hard Superposition – 3 Source Problems (Page 8)
🔹 Example – Three Sources
V1 = 10V V2 = 5V Current Source = 2A R = 5Ω
V1 only → 2A V2 only → 1A Current source → 2A Total = 5A
📘 Advanced Thevenin – Mixed Network (Page 9)
🔹 Example
30V source R1 = 10Ω R2 = 20Ω RL = 15Ω
Vth:
Vth = 30 × (20/30) = 20V
Rth:
Rth = (10×20)/30 = 6.67Ω
Load Current:
I = 20/(6.67+15) = 0.92A
📘 Mixed GATE-Level Test Set (Page 10)
🔹 Question 1
Find maximum power if Vth = 24V, Rth = 6Ω
RL = 6Ω Pmax = 24² / (4×6) = 24W
🔹 Question 2
Convert Thevenin (12V, 4Ω) to Norton.
IN = V/R = 12/4 = 3A RN = 4Ω
🔹 Question 3
Find node voltage if (V − 10)/5 + V/10 = 0
2(V − 10) + V = 0 3V = 20 V = 6.67V
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