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辨析交流电的最大值、平均值和有效值及其关系,对掌握交流电知识、理解交流电的应用极为重要.一、三个物理量的区别与联系在讲述《交流电的产生》一节中(学生已有三角函数知识)学生理解交流电的最大值不难、较为容易地看到:(1)这是一个特殊的瞬时值,它产生于线圈平面与中性面垂直时.(2)该值的大小由线圈的面积、匝数、磁感应强度和转子的转速决定的,可以根据ε_m=nBS(?)或ε_m=2BLvn来计算.交流电的平均值在《交流电》一章中没有涉及,但在法拉第《电磁感应》中已给出公式“ε=n△Q/△t”这个电动势是指△t时间内的平均值,如取从中性面起转动,在T/4时间内的平均电动势ε=4nBS/T=2nBS(?)/π,而nBS(?)为最大值、这里可以T/4时间内的平均值与最大值的关系:ε=2εm/π=0.636ε_m(取T/4或T/2均有此关系,而一周内平均值为零).理解和计算交流电的有效值既非常重要又有一定难度.高中教材对有效值的规定:“让交流电和直流电通过同样阻值的电阻、如果它们在同一时间内产生的热量相等、这一交流电电流有效值就跟这个直流电的电流相等”简而言之从“热”的等效角度来认识交流电的有效值.根据焦耳定律Q=i~2Rt(交流)、Q=I~2Rt(直流),可以看出热量不是与电流的平均值有关,而是与电流平方后的平均值有关.
Discriminating the maximum, average and effective value of AC power and its relationship are very important for mastering the knowledge of AC and understanding the application of AC. The difference and connection between the three physical quantities are described in the section “The Generation of AC Electricity” (students Knowledge of trigonometric functions It is not difficult and easy for students to understand the maximum value of AC current: (1) This is a special momentary value that arises when the coil plane is perpendicular to the neutral plane. (2) The size of the value is The area of the coil, the number of turns, the magnetic induction, and the rotational speed of the rotor are determined according to ε_m=nBS(?) or ε_m=2BLvn. The average value of the alternating current is not covered in the chapter “AC power,” but in Faraday “Electromagnetic induction” has given the formula “ε = n △ Q / △ t” This electromotive force refers to the average time △ t, such as taking from the neutral surface rotation, the average electromotive force in the T / 4 time ε = 4nBS / T=2nBS(?)/π, and nBS(?) is the maximum value, where the relationship between the average value and the maximum value in T/4 time: ?=2?m/?=0.636?_m (take T/4 or T/ Both have this relationship, and the average value is zero for one week.) Understanding and calculating the effective value of AC is very important Difficulty. The high school textbooks stipulate the effective value: “Let alternating current and direct current pass the resistance of the same resistance, if they generate the same amount of heat at the same time, the effective value of this alternating current is equal to the current of this direct current”. In other words, the effective value of AC is known from the “hot” equivalent point of view. According to the Joule’s law, Q=i~2Rt(AC) and Q=I~2Rt(DC), it can be seen that the heat is not related to the average value of the current. Instead, it is related to the average squared current.