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Solving complex circuits: network theorems
Objectives
On completion of this chapter you should be able to:
1. recognise a complex circuit.
2. apply âsense arrowsâ to complex circuits.
3. identify junctions (ânodesâ) and loops (âmeshesâ) in complex circuits.
4. recognise complex circuits to which the following ânetwork analysisâ techniques may be applied:
a. Kirchhoffâs Loop Equation method.
b. Superposition Theorem method.
c. Delta-Star/Star-Delta Transformation method.
d. ThĂ©veninâs Theorem method.
5. define Kirchhoffâs âCurrent Lawâ and âVoltage Lawâ.
6. solve complex circuits using Kirchhoffâs âLoop Analysisâ method.
7. solve complex circuits, using the âSuperposition Theoremâ.
8. solve complex circuits, using the âDelta-Star/Star-Delta Transformationâ method.
9. solve complex circuits, using âThĂ©veninâs Theoremâ.
Introduction
In the companion book, An Introduction to Electrical Science, we learnt that electrical circuits are categorized according to the way in which their various components are connected relative to each other.
And we learnt that there are four such categories as shown in Figure 1.1. We also learnt that the term, âcomplex circuitâ, is nothing more than a category into which we can place any circuit that isnât connected in âseriesâ, âparallelâ, or âseriesparallelâ. Used in this context, then, the term âcomplexâ doesnât mean âcomplicatedâ, although many complex circuits are indeed complicated! âComplex circuitsâ are often referred to as ânetworksâ, so the analysis of complex circuits is often referred to as ânetwork analysisâ.
Figure 1.1
A basic example of a circuit within each of these categories is shown in Figures 1.2aâd. We need to bear in mind, however, that there are countless variations of the examples of series-parallel and complex connections having various degrees of difficulty.
We also learnt how to solve series, parallel, and series-parallel circuits. By âsolveâ, we mean determining the equivalent resistance of the circuit, as well as the currents through, and the voltage drops across, each of their components.
Unfortunately, the techniques we use to solve series, parallel, and series-parallel circuits cannot be used to solve complex circuits. Well ⊠this is only partly true, because we may need to use those techniques to simplify parts of a complex circuit,...
