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# Chapter 4 - G Rizzoni Principles and Applications of...

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G. Rizzoni, Principles and Applications of Electrical Engineering Problem solutions, Chapter 4 4.1 Chapter 4 Instructor Notes The chapter starts by developing the dynamic equations for energy storage elements. The analogy between electrical and hydraulic circuits ( Make The Connection: Fluid (hydraulic) Capacitance , p. 138, Make The Connection: Fluid (hydraulic)Iinertance , p. 150, Table 4.2) is introduced early to permit a connection with ideas that may already be familiar to the student from a course in fluid mechanics, such as mechanical, civil, chemical and aerospace engineers are likely to have already encountered. A Focus on Measurements boxes : Capacitive displacement transducer and microphones , pp. 147-148, permits approaching the subject of capacitance in a pragmatic fashion, if so desired. The instructor wishing to gain a more in-depth understanding of such transducers will find a detailed analysis in 1 . Next, signal sources are introduced, with special emphasis on sinusoids. The material in this section can also accompany a laboratory experiment on signal sources. The emphasis placed on sinusoidal signals is motivated by the desire to justify the concepts of phasors and impedance, which are introduced next. The author has found that presenting the impedance concept early on is an efficient way of using the (invariably too short) semester or quarter. The chapter is designed to permit a straightforward extension of the resistive circuit analysis concepts developed in Chapter 3 to the case of dynamic circuits excited by sinusoids. The ideas of nodal and mesh analysis, and of equivalent circuits, can thus be reinforced at this stage. The treatment of AC circuit analysis methods is reinforced by the usual examples and drill exercises, designed to avoid unnecessarily complicated circuits. Two Focus on Methodology boxes (pp. 165 and 180) provide the student with a systematic approach to the solution of basic AC analysis problems using phasor and impedance concepts. The capacitive displacement transducer example is picked up again in Focus on Measurements: Capacitive displacement transducer (pp.175-177) to illustrate the use of impedances in a bridge circuit. This type of circuit is very common in mechanical measurements, and is likely to be encountered at some later time by some of the students. The homework problems in this chapter are mostly exercises aimed at mastery of the techniques. 1 E. O. Doebelin, Measurement Systems – Application and Design, 4 th Edition, McGraw-Hill, New York, 1990. Learning Objectives 1. Compute currents, voltages and energy stored in capacitors and inductors. 2. Calculate the average and root-mean-square value of an arbitrary (periodic) signal. 3. Write the differential equation(s) for circuits containing inductors and capacitors.

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Chapter 4 - G Rizzoni Principles and Applications of...

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