By G. Williams (auth.)
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Extra resources for An Introduction to Electrical Circuit Theory
A mesh in a network is derived from the mesh of a fisherman's net and it therefore consists of the branches around a space in the network. Considering the circuit shown in fig. 4 then abed, bcfe, and fihe are all meshes, although the network itself is non-planar. 6 i3 e i7 f Illustration of mesh currents Consider the topological graph shown in fig. 6 which has six nodes and seven branches. There are thus seven branch currents and seven branch voltages. If two mesh currents icx and i13 are assumed to flow clockwise around the two meshes as shown, then all of the branch currents may be specified in terms of the two mesh currents.
Effects of the substitution are to replace one resistanceless current source by two source branches containing resistance and to eliminate a mesh of the original network. Constrained mesh currents It is not always desirable to treat resistanceless sources by source substitutions. Resistanceless current sources may be treated by the topological concept of a constrained mesh current. As was demonstrated in the discussion on source substitutions, a resistanceless current source may create an apparent or pseudo mesh in a network and therefore the definition of a true topological mesh is one which exists in a network when all the sources have been reduced to their zero equivalents; for example a resistanceless current source is replaced by an open circuit.
Here, only voltages are used as unknown network variables and the branch volt-ampere equations are used to express the branch currents in terms of the branch voltages. Again, it is also possible to reduce the number of voltage variables by expressing some voltages in terms of others. This is done by writing Kirchhoffs voltage law for a loop and using the resulting equation to express one of the loop voltages in terms of the others. It is therefore possible to eliminate as many voltage variables as there are independent loops and the number of voltage variables required to solve the network is reduced from b to b - !.
An Introduction to Electrical Circuit Theory by G. Williams (auth.)