4正弦交流电的分析

A makes angle φ with B: A与B之间 成φ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φ角（逆 时针方向为正，顺时针方向为负）。
New Words & Expressions:
恒定角速度
角频率 瞬时值

ቤተ መጻሕፍቲ ባይዱ
Instantaneous values of v, as projections of the vector on the vertical axis NN’, can also be obtained by holding the vector Vm stationary and rotating the axis N’N clockwise at the angular velocity ω, starting at time t=0. Now the rotating axis N’N is called the time axis.

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.” or “effective” is simply implied.


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 square (or effective) current defined as (Eq.1)
D.C. circuit=direct current circuit 直流电路

It can be represented in vector form as follows. Using a righthand 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 φ with the horizontal axis OM (positive values of φ are laid off counter-clockwise, and negative, clockwise).
在一复数平面内，取MM’和NN’分别为实数轴和虚数轴，矢 量Vm可用一复数来表示，该复数的绝对值（即模）等于 Vm，其相位角等于φ。此复数称为某一已知正弦量的复数 峰值。 New Words & Expressions:

real quantity
实量
imaginary quantity 虚量
absolute value 绝对值
瞬时值v（即矢量在纵坐标N’N上 的投影）也能通过以下方法得到： 即令矢量Vm不动，将轴N’N以角 速度ω从t=0开始顺时针旋转，此 时旋转的轴N’N称为时间轴。

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 voltages, 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。 New Words & Expressions:
现在假设从t=0开始，矢量Vm绕着 原点O以等于角频率ω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ωt+φ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
angular frequency instantaneous value
clockwise 顺时针方向
counter-clockwise 逆时针方向

Now we imagine 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 ω. At time t, the vector makes the angle ωt+φ with the axis OM. Its projection onto the vertical axis NN’ represents the instantaneous value of v to the scale chose.
New Words & Expressions:
steady direct current 恒稳直流电

Let us establish the relationship between the r.m.s. and peak values of a sinusoidal current, I and Im


New Words & Expressions:
sinusoidal time function正弦时间函数 complex number 复数 vector 矢量 magnetic flux磁通 sinusoidal quantity 正弦量
A.C. circuit=alternating current circuit 交流电路
complex plane 复平面
modulus 模
complex number 复数
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 proportional 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。

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，同时将限定词“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 complex 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）

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 steady 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。