Nodes, Branches & Loops

Quick Answer

A node is a stretch of conductor at one potential, however many components land on it. A branch is one element's path between two nodes. A loop is any closed walk through the circuit that returns to its start without passing through any node twice. Counting nodes and branches settles how many equations a solution needs.

The word that causes trouble is node. It is not the dot on the drawing; the dot only says that two lines are joined. A node is everything electrically continuous with that dot, so two parts at opposite corners of a schematic joined by nothing but wire sit on one node, and a junction with six components on it is still one node. Get that wrong and the equation count is wrong before any algebra starts.

A branch is the path through a single element between two nodes, and it carries one current along its whole length. A loop is any closed walk that returns to its starting node without passing through any node twice. A mesh is the special case of a loop with nothing inside it, which is what you see as a window in a planar drawing.

The counting is what makes the vocabulary worth having. A connected network of N nodes gives N − 1 independent current equations, one for each node but the reference. Its B branches give B − N + 1 independent loop equations. Nodal analysis takes the first route and mesh analysis the second, and the two counts are rarely the same, which is how you choose between them.