Multi-loop Networks

A multi-loop network contains junctions, so different branches may carry different currents. It is solved by combining charge conservation at junctions with energy conservation around closed loops.

Systematic method

• Draw and label an assumed current in each branch.
• Write independent junction equations using ΣIin=ΣIout.
• Choose independent loops.
• Write each loop equation using consistent potential-rise and potential-drop signs.
• Solve the simultaneous equations and interpret negative currents.
• Substitute results back into every equation.