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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。
Charge and
Current
The
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
1.60
210
×
10
?
19C,
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<
/p>
在数值上等于
1.602100
×
10-12C
，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
(l706
～
l790),
the
American
scientist
and inventor.
Although we now know that current in metallic
conductors
is due to negatively charged
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
, charge
q
, and time
t
1
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
1
－
1
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
dq
i
< br>?
??????????????????????????????
间的关系是：
dt
The
charge
transferred
between
time
t
0
and
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（
1
－
1
）两边积分求得。我们算得：
< br>
t
q
?
?
idt
???????????
?????????????????
??
t
0
The way we
define current as
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
（
1
－
1
）
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
dw
in Fig.l-1. This emf is
also known as voltage or potential difference.
u
ab
?
?????
???????????????????????
??
The
voltage
u
ab between two
points a and b in an electric circuit is the
dq
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
1
－
< br>1
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
is
energy
in
joules
(J)
and
q
is
charge
in
coulombs
(C).
The
voltage
u
ab is
measured in volts (V), named in honor of the
Italian physicist
Alessandro Antonio
Volta (l745
～
l827), 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).
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
V
olta
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<
/p>
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
and
b
.
The
plus
(+)
and
minus
(-)
signs
are
used to define reference
direction or voltage polarity. The
u
ab can be
2
interpreted in two ways:
①
point
a
is at a
potential
of
u
ab volts
higher
than point b;
②
the potential at
point
a
with respect to point
b
is
u
ab.
It follows
logically that in general
图
1
－
2
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
<
/p>
u
ab
?
-
u
ba
????????????????
???????????
??
Although current and voltage are the
two basic variables in an electric
circuit, they are not sufficient by
themselves. For practical purposes,
we
need to know
power
and
energy. To relate power and energy to voltage
and
current,
we
recall
from
physics
that
power
is
the
time
rate
of
expending or absorbing energy, measured
in watts (W).
We write this
relationship as
虽然电流和电压是电路的
两个基本变量，
但仅有它们两个是不够的。
从实际应用
来说，我们需要知道功率和能量。为了把功率和能量同电压、电流联系起来，我
< br>们重温物理学中关于功率是消耗或吸收的能量的时率，
它是以瓦特为单位来度量<
/p>
的。我们把这个关系式写成：
dw
p
?<
/p>
???????????????????????????
??
dt
Where
p
is power in watts (W),
w
is energy in joules (J),
and
t
is time
in
seconds
(s).
From
Eq.
(1-1),
Eq.
(1-3),
and
Eq.
(1-5),
it
follows
that
式中
p
< br>是以瓦特为单位的功率，
w
是以焦耳为单位的能量，
t
是以秒为单位的时
间，从方程（
1
－
1
）
、
（
1
－
< br>3
）和（
1
－
< br>5
）可以推出
p
?
ui
????????????????????
??????
??
Because
u
and
i
are generally function of
time, the power
p
in Eq.
(1-6)
is a time-varying quantity and is
called the instantaneous power. The
power absorbed or supplied by an
element is the product of the voltage
across the element and the current
through it. If the power has a plus
sign, power is being delivered to or
absorbed by the element. If, on the
other hand, the power has a minus sign,
power is being supplied by the
element.
But how do we know when the power has a negative
or a positive
sign
？
由于
u
和
i
通
常是时间的函数，
方程
（
1
－
6
）
中的功率
p
是个时间变量于是被称
为瞬时功率，
某一元件吸收或提供的功率等于元件两端电压和通过它的电流的乘
积。<
/p>
如果这个功率的符号是正的，
那么功率向元件释放或被元件吸收。
另一方面，
如果功率的符号是负的，
那
么功率是由元件提供的。
但我们如何得知何时功率为
正或为负？
Current direction and
voltage polarity play a major role in determining
the
sign
of
power.
It
is
therefore
important
that
we
pay
attention
to
the
relationship
between
current
i
and
voltage
u
in
Fig.1-3(a). The
voltage
polarity
and
current
i
direction
must
conform
with
those
shown
in
Fig.1-3(a) in order for the power to
have a positive sign. This is known
3
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