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1、Unit4 Analysis of Sinusoidal Alternating Electricity 正弦交流电的分析,R.M.S. (Effective) Values of Current and Voltage 电压和电流的有效值 The force between two current-carrying conductors is proportional to the square of the current in the conductors. The heat due to a current in a resistance over a period is also p
2、roportional to the square of that current. 两载流导体之间的作用力与导体中的电流的平方成正比。某段时间内电流通过一个电阻所产生的热量也正比于电流的平方。,New Words & Expressions: sinusoidal alternating electricity 正弦交流电 effective values 有效值 r.m.s. values = root mean square values 均方根值 square平方,This calls for knowledge of what is known as the root mean sq
3、uare (or effective) current defined as (Eq.1) The heat developed by a current i in a resistance r in time dt is (Eq.) 这便引出通常所说的均方根（或有效值）电流的概念，其定义如下：(Eq.1) 在dt时间里电流i通过电阻r产生的热量为(Eq.),It follows that the r.m.s. (effective) value of an alternating current is numerically equal to the magnitude of the ste
4、ady direct current that would produce the same heating effect in the same resistance and over the same period of time. 句型It follows that 译为“由此得出”。宾语从句里面含有一个定语从句。 由此可得出，交流电的均方根（或有效）值等于在相同电阻、相同时间内产生相同热量的恒稳直流电的大小。,New Words & Expressions: steady direct current 恒稳直流电,Let us establish the relationship be
5、tween the r.m.s. and peak values of a sinusoidal current, I and Im Hence :(Eq.2) The r.m.s. (effective) values of e.m.f. and voltage are,New Words & Expressions: peak values 峰值,In dealing with periodic voltages and currents, their r.m.s. (effective) value are usually meant, and the adjective “r.m.s.
6、” or “effective” is simply implied. 在涉及交流电压和电流时，通常指的值就是其均方根（有效）值，便将限定词“均方根（有效）”几个字略去，并不明指。,Representation of Sinusoidal Time Functions by Vectors and Complex Number 正弦时间函数的矢量和复数表示法,A.C. circuit analysis can be greatly simplified if the sinusoidal quantities involved are represented by vectors or com
7、plex numbers. Let there be a sinusoidal time function (current, voltage, magnetic flux and the like): 如果所涉及的正弦量用矢量和复数表示，便可大大地简化交流电路的分析。 设一正弦时间函数（电流、电压、磁通等）,New Words & Expressions: sinusoidal time function 正弦时间函数 vector 矢量 complex number 复数 sinusoidal quantity 正弦量 magnetic flux磁通 A.C. circuit=altern
8、ating current circuit 交流电路 D.C. circuit=direct current circuit 直流电路,It can be represented in vector form as follows. Using a right-hand set of Cartesian coordinates MON (Fig.1), we draw the vetor Vm to some convenient scale such that it represents the peak value Vm and makes the angle with the horiz
9、ontal axis OM (positive values of are laid off counter-clockwise, and negative, clockwise).,A makes angle with B: A与B之间成夹角 这个正弦时间函数可用如下的矢量形式表示。通过在笛卡尔坐标系的右侧MON（如图1所示）区域内，取恰当的比例画出矢量Vm，以便于代表该量的幅值Vm，并与横坐标形成角（逆时针方向为正，顺时针方向为负）。,New Words & Expressions: clockwise 顺时针方向 counter-clockwise 逆时针方向,Now we imagin
10、e that, starting at t=0, the vector Vm begins to rotate about the origin O counter-clockwise at a constant angular velocity equal to the angular frequency . At time t, the vector makes the angle t+ with the axis OM. Its projection onto the vertical axis NN represents the instantaneous value of v to
11、the scale chose.,现在假设从t=0开始，矢量Vm绕着原点O以等于角频率的恒定角速度逆时针旋转。则t时刻矢量与横坐标轴OM形成t+的夹角。它在纵轴NN上的投影便表示在已选用的比例尺下的瞬时值v。,New Words & Expressions: constant angular velocity 恒定角速度 angular frequency 角频率 instantaneous value 瞬时值,Instantaneous values of v, as projections of the vector on the vertical axis NN, can also be
12、 obtained by holding the vector Vm stationary and rotating the axis NN clockwise at the angular velocity , starting at time t=0. Now the rotating axis NN is called the time axis.,瞬时值v（即矢量在纵坐标NN上的投影）也能通过以下方法得到：即令矢量Vm不动，将轴NN以角速度从t=0开始顺时针旋转，此时旋转的轴NN称为时间轴。,New Words & Expressions: single-valued relation
13、ship 单值关系（一一对应关系） vectors of voltages (e.m.f.s, currents, magnetic fluxes） 电压（电势、电流、磁通）矢量,In each case, there is a single-valued relationship between the instantaneous value of v and the vector Vm. Hence Vm may be termed the vector of the sinusoidal time function v. Likewise, there are vectors of vo
14、ltages, e.m.f.s, currents, magnetic fluxes,etc. 两种情况下，瞬时值v和矢量Vm之间都存在单值关系。因此，Vm便可称为正弦时间函数v的矢量。同理，还有电压矢量、电势矢量、电流矢量、磁通矢量等。,“True” vector quantities are denoted either by clarendon type, e.g. A, or by , while sinusoidal ones are denoted by . Graphs of sinusoidal vectors, arranged in a proper relationshi
15、p and to some convenient scale, are called vector diagrams. 真正的矢量是用粗体字A，或 表示，而正弦矢量则用 表示。按合适的相对关系和某种恰当的比例画出的正弦向量的图解称为矢量图。,New Words & Expressions: e.g. ,i:di: =exempli gratia 例如 vector diagrams 矢量图,New Words & Expressions: real quantity 实量 imaginary quantity 虚量 complex plane 复平面 complex number 复数 abs
16、olute value 绝对值 modulus 模 phase 相位 argument 相角 complex peak value 复数幅值/峰值,Taking MM and NN as the axes of real and imaginary quantities, respectively, in a complex plane, the vector Vm can be represented by a complex number whose absolute value (or modulus) is equal to Vm, and whose phase (or argument) is equal to the angle . Th
