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Branch

A branch is any portion of a circuit with two terminals connected to it. A branch may consist of one or more circuit elements. In practice, any circuit element with two terminals connected to it is a branch.

Node

A node is the junction of two or more branches (one often refers to the junction of only two branches as a trivial node). In effect, any connection that can be accomplished by soldering various terminals together is a node. It is very important to identify nodes properly in the analysis of electrical networks.

Loop

A loop is any closed connection of branches.

Mesh

A mesh is a loop that does not contain other loops. Meshes are an important aid to certain analysis methods

Network Analysis

The analysis of an electrical network consists of determining each of the unknown branch currents and node voltages. It is therefore important to define all of the relevant variables as clearly as possible, and in systematic fashion. Once the known and unknown variables have been identified, a set of equations relating these variables is constructed, and these are solved by means of suitable techniques. The analysis of electrical circuits consists of writing the smallest set of equations sufficient to solve for all of the unknown variables. The analysis of electrical circuits is greatly simplified if some standard conventions are followed. The objective of this section is precisely to outline the preliminary procedures that will render the task of analyzing an electrical circuit manageable.

Circuit Variables

The first observation to be made is that the relevant variables in network analysis are the node voltages and the branch currents. This fact is really nothing more than a consequence of Ohm’s law. Whenever we reference the voltage at a node in a circuit, we imply an assumption that the voltage at that node is the potential difference between the node itself and a reference node called ground, which is located somewhere else in the circuit and which for convenience has been assigned a potential of zero volts.

Ground

The choice of the word ground is not arbitrary. This point can be illustrated by a simple analogy with the physics of fluid motion. Consider a tank of water, located at a certain height above the ground. The potential energy due to gravity will cause water to flow out of the pipe at a certain flow rate. In analogous fashion, in every circuit a point can be defined that is recognized as “ground” and is assigned the electric potential of zero volts for convenience. Note that, unless they are purposely connected together, the grounds in two completely separate circuits are not necessarily at the same potential