Circuit Theory #15 | Mesh-Current Method — Intro + Worked Example 1

Instructor: Dr. Süleyman Burak ÇELİK

Fifteenth lesson in the Circuit Theory series. This lesson introduces the mesh-current method and then solves a three-mesh circuit step by step. Main ideas: - Choose one clockwise mesh current for each independent loop - Write KVL around each mesh - For a shared resistor, use the difference between neighboring mesh currents - Solve the simultaneous equations and then recover the requested branch current Worked example: - Left source: 28 V - Bottom source: 8 V - Resistors: 6 ohm, 2 ohm, 4 ohm, 12 ohm - Unknown mesh currents: `i1`, `i2`, `i3` - Final values: `i1 = -13/3 A`, `i2 = -10/3 A`, `i3 = -5/6 A` - Requested branch current: `i = 1 A` upward through the 2 ohm branch Main takeaway: - Mesh analysis turns circuit solving into a systematic set of KVL equations - Negative mesh-current results simply mean the real current direction is opposite to the assumed direction - Shared-branch currents must be written carefully, using the relative mesh directions