Circuit Theory #17 | Supermesh Analysis Examples - Current Source Constraints

Instructor: Dr. Süleyman Burak ÇELİK

Seventeenth lesson in the Circuit Theory series. This lesson continues mesh-current analysis with two supermesh examples. Main ideas: - A current source on the outer boundary can directly set one mesh current - A current source between two meshes creates a constraint equation between mesh currents - When the shared current source blocks a direct KVL path, combine the surrounding meshes into a supermesh - Write KVL around the supermesh, then solve it together with the current-source constraints Worked example 1: - Boundary current source gives `i3 = 10 A` - Shared current source gives `i1 - i2 = -2` - Supermesh KVL gives the missing equation - Results: `i1 = 2 A`, `i2 = 4 A`, `i3 = 10 A` - Source voltage: `V1 = -2 V` Worked example 2: - Boundary current source gives `i2 = -2 A` - Shared current source gives `i3 - i1 = 5 A` - Supermesh KVL simplifies to `i1 + i3 = 7` - Results: `i1 = 1 A`, `i2 = -2 A`, `i3 = 6 A` Main takeaway: - Current sources do not make mesh analysis harder; they change the equation type - Use current-source constraints first, then write KVL only around valid supermesh paths - A negative mesh current simply means the real current direction is opposite to the chosen reference