1第一章第一篇 sectiong Two variables u(t) and i(t) are the most basic concepts in an electric circuit, they characterize the various relationships in an electric circuit u(t)和 i(t)这两个变量是电路中最基本的两个变量，它们刻划了电路的各种关 系。 ChargeCharge andand CurrentCurrentThe concept of electric charge is the underlying principle for explaining all electrical phenomena. Also, the most basic quantity in an electric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). 电荷和电流电荷的概念是用来解释所有电气现象的基本概念。也即，电路中最基本 的量是电荷。电荷是构成物质的原子微粒的电气属性，它是以库仑为单位来度 量的。 We know from elementary physics that all matter is made of fundamental building blocks known as atoms and that each atom consists of electrons, protons, and neutrons. We also know that the charge e on an electron is negative and equal in magnitude to 1.602101019C, while a proton carries a positive charge of the same magnitude as the electron. The presence of equal numbers of protons and electrons leaves an atom neutrally charged. 我们从基础物理得知一切物质是由被称为原子的基本构造部分组成的， 并且每个原子是由电子，质子和中子组成的。我们还知道电子的电量是负的并 且在数值上等于 1.60210010-12C，而质子所带的正电量在数值上与电子相等。 质子和电子数量相同使得原子呈现电中性。 We consider the flow of electric charges. A unique feature of electric charge or electricity is the fact that it is mobile; that is, it can be transferred from one place to another, where it can be converted to another form of energy 让我们来考虑一下电荷的流动。电荷或电的特性是其运动的特性，也就是，它 可以从一个地方被移送到另一个地方，在此它可以被转换成另外一种形式的能 量。 When a conducting wire is connected to a battery (a source of electromotive force), the charges are compelled to move; positive charges move in one direction while negative charges move in the opposite direction. This motion of charges creates electric current. It is conventional to take the currentflow as the movement of positive charges, that is, opposite to the flow of negative charges, as Fig.l-1 illustrates. This convention was introduced by Benjamin Franklin (l706l790), the American scientist and inventor. Although we now know that current in metallic conductors is due to negatively 2charged electrons, we will follow the universally accepted convention that current is the net flow of positive charges. Thus, Electric current is the time rate of charge, measured in amperes (A). Mathematically, the relationship among current i i, charge q q, and time t t is 当我们把一根导线连接到某一电池上时(一种电动势源)，电荷被外力 驱使移动；正电荷朝一个方向移动而负电荷朝相反的方向移动。这种电荷的移 动产生了电流。我们可以很方便地把电流看作是正电荷的移动，也即，与负电 荷的流动方向相反，如图 11 所示。这一惯例是由美国科学家和发明家本杰明 富兰克林引入的。虽然我们现在知道金属导体中的电流是由负电荷引起的， 但我们将遵循通用的惯例，即把电流看作是正电荷的单纯的流动。于是电流就 是电荷的时率，它是以安培为单位来度量的。从数学上来说，电流 i、电荷 q 以及时间 t 之间的关系是：The charge transferred between time t t0 and t t is obtained by integrating both sides of Eq. (1-1). We obtain 从时间 t0 到时间 t 所移送的电荷可由方程（11）两边积分求得。我们算得：The way we define current as i i in Eq. (1-l) suggests that current need not be a constant-valued function, charge can vary with time in several ways that may be represented by different kinds of mathematical functions 我们通过方程（11）定义电流的方式表明电流不必是一个恒值函数，电荷可 以不同的方式随时间而变化，这些不同的方式可用各种数学函数表达出来。 电压，能量和功率To move the electron in a conductor in a particular direction requires some work or energy transfer. This work is performed by an external electromotive force (emf), typically represented by the battery in Fig.l-1. This emf is also known as voltage or potential difference. The voltage u uab between two points a and b in an electric circuit is the energy (or work) needed to move a unit charge from a to b; mathematically 在导体中朝一个特定的方向移动电荷需要一些功或者能量的传递，这个功是由 外部的电动势来完成的。图 11 所示的电池就是一个典型的例子。这种电动势 也被称为电压或电位差。电路中 a、b 两点间的电压等于从 a 到 b 移动单位电荷 所需的能量（或所需做的功） 。数学表达式为：where w w is energy in joules (J) and q is charge in coulombs (C). The voltage u uab is measured in volts (V), named in honor of the Italian physicist Alessandro Antonio Volta (l745l827), who invented the first voltaic battery. Thus, Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V). dqidt0ttqidtabdwudq3式中 w 是单位为焦耳的能量而 q 是单位为库仑的电荷。电压 Uab 是以伏特为单 位来度量的，它是为了纪念意大利物理学家 Alessandro Antonio Volta 而命名 的，这位意大利物理学家发明了首个伏达电池。于是电压（或电压差）等于将 单位电荷在元件中移动所需的能量，它是以伏特为单位来度量的。 Fig.l-2 shows the voltage across an element (represented by a rectangular block ) connected to points a a and b b. The plus (+) and minus (-) signs are used to define reference direction or voltage polarity. The u uab can be interpreted in two ways: point a a is at a potential of u uab volts higher than point b; the potential at point a a with respect to point b b is u uab. It follows logically that in general 图 12 显示了某个元件（用一个矩形框来表示）两端 a、b 之间的电压。正号 （）和负号（）被用来指明参考方向或电压的极性，Uab 可以通过以下两 种方法来解释。1）在 Uab 伏特的电位中 a 点电位高于 b 点，2）a 点电位相对 于 b 点而言是 Uab，通常在逻辑上遵循Although current and voltage are the two basic variables in an electric circuit, they are not sufficient by themselves. For