Circuit Theory #12 | The Supernode Method — Voltage Source Between Two Nodes

Instructor: Dr. Süleyman Burak ÇELİK

Twelfth lesson in the Circuit Theory series. When a voltage source connects two non-reference nodes, we cannot write separate KCL equations because the current through it is unknown. The solution: the supernode. The concept: - Draw a boundary around both nodes and the voltage source - Write KCL for the entire boundary (internal elements cancel) - Add a constraint equation from the voltage source The circuit: - 10 V source between V1 and V2 (+ at V1) - 13 Ohm between V1 and V2 (inside the supernode, NOT in KCL) - 5 Ohm from V1 to ground, 4 Ohm from V2 to ground - 3 A source leaves V1, 14 A source enters V2 KCL for the supernode: V1/5 + V2/4 + 3 - 14 = 0 Multiply by 20: 4V1 + 5V2 = 220 Constraint: V1 - V2 = 10 Solution: V1 = 30 V, V2 = 20 V Covers content from TR lecture d20.