Rate of change

Chapter Rate of change

Teach Yourself Electricity and Electronics Third Edition Book
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Summary of Contents

Teach Yourself Electricity and Electronics Third Edition Book

  • If you freeze time at so-many-and-a-quarter seconds, say t446.25 seconds, thevoltage will be1 V. The wave will be exactly at its positive peak. If you stop time atso-many-and-three-quarter seconds, say t446.75 seconds, the voltage will be exactly at its negative peak, 1 V.At intermediate times, say, so-many-and-three-tenths seconds, the voltage willhave intermediate values.Rate of changeBy examining the diagram of Fig. 12-1, you can see that there are times the voltage isincreasing, and times it is decreasing. Increasing, in this context, means “getting morepositive,” and decreasing means “getting more negative.” The most rapid increase involtage occurs when t0.0 and t1.0 in Fig. 12-1. The most rapid decrease takesplace when t0.5.Notice that when t0.25, and also when t0.75, the instantaneous voltage is notchanging. This condition exists for a vanishingly small moment. You might liken thevalue of the voltage at t0.25 to the altitude of a ball you’ve tossed straight up into theair, when it reaches its highest point. Similarly, the value of voltage at t0.75 is akin tothe position of a swing at its lowest altitude.If n is any whole number, then the situation at tn.25 is the same as it is for t0.25; also, for tn.75, things are just the same as they are when t0.75. The sin-gle cycle shown in Fig. 12-1 represents every possible condition of the ac sine wave hav-ing a frequency of 1 Hz and a peak value of plus-or-minus 1 V.216 Phase12-1A sine wave with period 1 second and frequency 1 Hz.