Electric Circuits and Network Theorems

There are certain theorems, which when applied to the solutions of electric networks, wither simplify the network itself or render their analytical solution very easy.  These theorems can also be applied to an a.c. system, with the only difference that impedances replace the ohmic resistance of d.c. system.  Different electric circuits (according to their properties) are defined below :

1. Circuit.  A circuit is a closed conducting path through which an electric current either flows or is intended flow.

 2. Parameters.  The various elements of an electric circuit are called its parameters like resistance, inductance and capacitance.  These parameters may be lumped or distributed.

 3. Liner Circuit.  A linear circuit is one whose parameters are constant i.e. they do not change with voltage or current.

 4. Non-linear Circuit.  It is that circuit whose parameters change with voltage or current.

 5. Bilateral Circuit.  A bilateral circuit is one whose properties or characteristics are the same in either direction.  The usual transmission line is bilateral, because it can be made to perform its function equally well in either direction.

6. Unilateral Circuit.  It is that circuit whose properties or characteristics change with the direction of its operation.  A diode rectifier is a unilateral circuit, because it cannot perform rectification in both directions.

7. Electrical Network. a mixture of varied electrical components, connected in any manner whatever, is named an electrical network.

 8. Passive Network  is one that contains no supply of e.m.f. in it.

 9. Active Network  is one that contains one or over one supply of e.m.f.

 10. Node may be a junction in an exceedingly circuit wherever 2 or additional circuit components ar connected along.

 11. Branch  is that a part of a network that lies between 2 junctions.

12. Loop. it's a detailed path in an exceedingly circuit within which no part or node is encountered over once.

 13. Mesh. it's a loop that contains no alternative loop inside it. as an example, the circuit of Fig.  2.1 (a) has even branches, six nodes, 3 loops and 2  meshes whereas the circuit of Fig. 2.1 (b) has four branches, two nodes, six loops and 3 meshes. It ought to be noted that, unless declared otherwise, an electrical network would be assumed passive within the following treatment. {we will|we'll|we are going to} currently discuss the assorted network theorems that are of nice facilitate in resolution sophisticated networks.  Incidentally, a network is claimed to be fully solved or analyzed once all voltages and every one currents in its completely different parts square measure determined.

There area unit 2 general approaches to network analysis :

 (i) Direct methodology Here, the network is left in its original kind whereas determinant its totally different voltages and currents. Such strategies area unit typically restricted to fairly straightforward circuits and embody Kirchhoff’s laws,  Loop analysis, Nodal analysis, superposition theorem, Compensation theorem and Reciprocity theorem etc.

(ii) Network Reduction methodology Here, the initial network is born-again into a way less complicated equivalent circuit for fast calculation of various quantities.  This methodology may be applied to straightforward further as sophisticated networks. samples of this methodology area unit :  Delta/Star and Star/Delta conversions. Thevenin’s theorem and Norton’s Theorem etc.