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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) Figure 247 illustrates the concept 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
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Figure 247 De nition of a node
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Loop A loop is any closed connection of branches Various loop con gurations are illustrated in Figure 248
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Note how two different loops in the same circuit may include some of the same elements or branches Loop 1 Loop 2 vS
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Figure 248 De nition of a loop
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Mesh A mesh is a loop that does not contain other loops Meshes are an important aid to certain analysis methods In Figure 248, the circuit with loops 1, 2, and 3 consists of two meshes: loops 1 and 2 are meshes, but loop 3 is not a mesh, because it encircles both loops 1 and 2 The one-loop circuit of Figure 248 is also a one-mesh circuit Figure 249 illustrates how meshes are simpler to visualize in complex networks than loops are 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 de ne all of the
Node a Node c iS Node b Node a
Examples of nodes in practical circuits
Loop 3
1-loop circuit
3-loop circuit (How many nodes in this circuit )
2
Fundamentals of Electric Circuits
R3 Mesh 3 R1 + vS How many loops can you identify in this four-mesh circuit (Answer: 14) _ Mesh 1 R2 Mesh 3 iS
Mesh 4
Figure 249 De nition of a mesh
relevant variables as clearly as possible, and in systematic fashion Once the known and unknown variables have been identi ed, 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 suf cient to solve for all of the unknown variables The procedures required to write these equations are the subject of 3 and are very well documented and codi ed in the form of simple rules The analysis of electrical circuits is greatly simpli ed 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 rst 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 Consider the branch depicted in Figure 250, consisting of a single resistor Here, once a voltage vR is de ned across the resistor R, a current iR will ow through the resistor, according to vR = iR R But the voltage vR , which causes the current to ow, is really the difference in electric potential between nodes a and b: vR = va vb
(229)
Figure 250 Variables in a network analysis problem
What meaning do we assign to the variables va and vb Was it not stated that voltage is a potential difference Is it then legitimate to de ne the voltage at a single point (node) in a circuit 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 Thus, in Figure 250, the expression vR = va vb really signi es that vR is the difference between the voltage differences va vc and vb vc , where vc is the (arbitrary) ground potential Note that the equation vR = va vb would hold even if the reference node, c, were not assigned a potential of zero volts, since vR = va vb = (va vc ) (vb vc ) What, then, is this ground or reference voltage (230)
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