What is a circuit?

A circuit (also called an electrical network) is a collection of electrical multi-terminal devices that are connected in a specified manner. For the most part, we'll be concerned with two-terminal devices. A two terminal device is an electrical device with two lines or leads coming out of it.

An example of an electrical network consisting of four two-terminal devices is shown in figure 1. This figure has two pictures. The lefthand picture is a graphical representation of the circuit called a schematic diagram. The places where device terminals are connected will be called nodes. Each node is labelled with a letter. In figure 1, there are three nodes with the labels $a$, $b$, and $c$. The lefthand picture is often abstracted into a graphical representation that emphasizes the important connections with the network. Such a graph representation for the circuit is shown in the righthand picture. In this picture, you'll see that the circuit element is drawn as an arc and all of the nodes are simply drawn as a point. The righthand representation is called a graph. In a graph, the circuit elements are always represented as arcs (also called branches) and the terminals are always represented as points or nodes of the graph.

Figure 1: A simple electrical circuit and its graph

To characterize what a circuit does, we must be able to characterize the state of the circuit. The state of a circuit is determined by characterizing

• The voltage across each arc and
• the current through each arc.

Circuit analysis, therefore, is concerned with determining these two quantities for each branch of the circuit.