In mesh analysis, how do you handle a current source that lies on a shared edge between two meshes?

In mesh analysis, how do you handle a current source that lies on a shared edge between two meshes?

• A. Use a supermesh around the current source; write KVL for the supermesh; relate the mesh currents via the current source value
• B. Remove the current source and replace with its Norton equivalent
• C. Solve the two meshes independently and then enforce the current source relation
• D. The current source cancels out and can be ignored

Answer: (A)

When a current source sits on the border between two meshes, you can’t write independent KVL equations for those meshes because the current through the shared edge is fixed by the source. The standard approach is to form a supermesh that goes around both meshes, skipping the current source, and write a single KVL around the outer boundary of that combined loop. Then introduce a constraint that ties the two mesh currents to the current source: the current through the shared edge equals the source value, so the difference between the two mesh currents equals that current, with the sign determined by the direction of the source. Solve the KVL for the supermesh alongside the current-relationship constraint to find the mesh currents. This is why forming a supermesh and using the current-source relation is the correct method. Replacing the current source with a Norton equivalent, solving the meshes independently, or ignoring the current source would not satisfy the fixed current constraint on the shared edge.

When a current source sits on the border between two meshes, you can’t write independent KVL equations for those meshes because the current through the shared edge is fixed by the source. The standard approach is to form a supermesh that goes around both meshes, skipping the current source, and write a single KVL around the outer boundary of that combined loop. Then introduce a constraint that ties the two mesh currents to the current source: the current through the shared edge equals the source value, so the difference between the two mesh currents equals that current, with the sign determined by the direction of the source. Solve the KVL for the supermesh alongside the current-relationship constraint to find the mesh currents. This is why forming a supermesh and using the current-source relation is the correct method. Replacing the current source with a Norton equivalent, solving the meshes independently, or ignoring the current source would not satisfy the fixed current constraint on the shared edge.