TAILIEUCHUNG - Ebook Introductory circuit analysis (10th edition): Part 2
(BQ) Part 2 book "Introductory circuit analysis" has contents: The basic elements and phasors, series and parallel AC circuits, series parallel AC networks, methods of analysis and related topics, pulse waveforms and the RC response, nonsinusodial circuits, polyphase systems,.and other contents. | 14 The Basic Elements and Phasors INTRODUCTION The response of the basic R, L, and C elements to a sinusoidal voltage and current will be examined in this chapter, with special note of how frequency will affect the “opposing” characteristic of each element. Phasor notation will then be introduced to establish a method of analysis that permits a direct correspondence with a number of the methods, theorems, and concepts introduced in the dc chapters. THE DERIVATIVE In order to understand the response of the basic R, L, and C elements to a sinusoidal signal, you need to examine the concept of the derivative in some detail. It will not be necessary that you become proficient in the mathematical technique, but simply that you understand the impact of a relationship defined by a derivative. Recall from Section that the derivative dx/dt is defined as the rate of change of x with respect to time. If x fails to change at a particular instant, dx ϭ 0, and the derivative is zero. For the sinusoidal waveform, dx/dt is zero only at the positive and negative peaks (qt ϭ p/2 and p in Fig. ), since x fails to change at these instants of time. The derivative dx/dt is actually the slope of the graph at any instant of time. A close examination of the sinusoidal waveform will also indicate that the greatest change in x will occur at the instants qt ϭ 0, p, and 2p. The derivative is therefore a maximum at these points. At 0 and 2p, x increases at its greatest rate, and the derivative is given a positive sign since x increases with time. At p, dx/dt decreases at the same rate as it increases at 0 and 2p, but the derivative is given a negative sign since x decreases with time. Since the rate of change at 0, p, and 2p is the same, the magnitude of the derivative at these points is the same also. For various values of qt between these maxima and minima, the derivative will exist and will have values from the minimum to the maximum inclusive. A plot of the derivative
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