电路基础 - 第五版 | Wener Live & Life

所有学习电路基础(Foundation of Electric Circuit 5th ed)的笔记.

笔记

An electric circuit is an interconnection of electrical elements.

六个基础 SI(International System of Units) 定义单位

量	基础单位	符号
Length/长度	meter	m
Mass/重量	kilogram	kg
Time/时间	second	s
Electric current/电流	ampere/安倍/安	A
Thermodynamic temperature/热度	kelvin/开尔文/开	K
Luminous intensity/发光强度	candela/坎德拉/坎	cd
Charge/电量/电荷	coulomb/库仑	C

单位前缀

Multiplier	前缀	符号
10¹⁸	exa	E
10¹⁵	peta	P
10¹²	tera	T
10⁹	giga	G
10⁶	mega	M
10³	kilo	k
10²	hecto	h
10¹	deka	da
10^-1	deci	d
10^-2	centi	c
10^-3	milli	m
10^-6	micro	μ
10^-9	nano	n
10^-12	pico	p
10^-15	femto	f
10^-18	atto	a

Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C).

一个原子有电子,质子和中子组成.电子携带电荷 $e = 1.602 \times 10^{-19} C$ , 电子电荷为负点.质子携带等量的正电.等量的电子和质子使原子电荷处于中和状态.

库伦是一个较大的电量单位.1 C 电量为 $1/(1.602 \times 10^{-19}) = 6.24\times 10^{18}$ , 在实际中大多使用 pC, nC 或 μC.
根据试验观察,自然中发生的电荷均为电子电荷 $e = -1.602 \times 10^{-19}$ 的整数倍
电荷守恒定义说明,电荷不能被创建和摧毁,只能被传输.因此一个系统的电子电荷总量不会改变.

当导线(由原子组成)连接到电池两端(电动势/electromotive force 来源),正电荷往一个方向移动,负电荷往相反方向移动,这样就形成了电流.

Electric current is the time rate of change of charge, measured in amperes (A).

电流 $i$ , 电荷 $q$ , 时间 $t$

i_{ = }^{ \triangle }{ \frac { dq }{ dt } }

1 ampere 1 coulomb/second

A direct current (dc) is a current that remains constant with time. An alternating current (ac) is a current that varies sinusoidally with time

使用 $I$ 表示恒量电流, $i$ 表示变量电流.

练习 1.1

Ex 1.1: How much charge is represented by 4,600 electrons?

text

4600 C * e

= 4600 * 1.60210^-19 = 7369.210^-19 = 7.3692*10^-16 C = 73.692 fC

Practice 1.1: Calculate the amount of charge represented by six million protons.

text

6MC * e

=6 * 1.602*10^-13 =9.612*10^-12 C =9.612 pC

Ex 1.2: The total charge entering a terminal is given by $q=5t sin{4 \pi} t$ mC. Calculate the current at $t=0.5s$ .

i=dq/dt =(d/dt)(5tsin4Pit)mC/s

sin4 = 4 sum cos4Pidt

=5 t sin4 Pi t + 20Pi t cos 4 Pi t mA

Practice 1.2: If in Example 1.2, find the current at s.

两点之间的外部电动势(external electromotive force - emf) 也表示为 voltage 或 potential difference.电路上两点之间的电压 $v_{ab}$ 表示从 a 移动一个电荷到 b 需要的能量(或工作).

符号	单位	含义
p	W/watts	电功率
w	J/joules	能量
t	s/seconds	时间
v	v/volt	电压

v_{ab} {_{ = }^{ \triangle }} { \frac { dw }{ dq } }

text

1 volt  1 joule/coulomb  1 newton-meter/coulomb

v_{ab} = -v_{ba}

Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V).

$V$ 表示恒量电压, $v$ 表示变量电压.恒量电压一般由电池提供,变量电压一般是发电器.

Power is the time rate of expending or absorbing energy, measured in watts (W).

符号	单位	含义
p	W/watts	电功率
w	J/joules	能量
t	s/seconds	时间

p {_{ = }^{ \triangle }} { \frac { dw }{ dt } }

p= \frac{dw}{dt} = \frac{dw}{dq} \cdot \frac{dq}{dt} = vi

p=vi

Passive sign convention is satisfied when the current enters through the positive terminal of an element and p=+vi. If the current enters through the negative terminal, p=-vi.

因为能量守恒定义,总电量实际为 0

\sum p = 0

一个原件从 t0 到 t 消耗或提供的电量为

w = \int _{ t_0 }^{ t }{ p dt } = \int _{ t_0 }^{ t }{ vi dt }

Energy is the capacity to do work, measured in joules (J).

1 Wh = 3600 J

Ex 1.4 An energy source forces a constant current of 2 A for 10 s to flow through a light bulb. If 2.3 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb.

An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit elements.

An ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current.

four possible types of dependent sources

A voltage-controlled voltage source (VCVS).
A current-controlled voltage source (CCVS).
A voltage-controlled current source (VCCS).
A current-controlled current source (CCCS).

电子原件分为

被动元件（Passive components）是一种电子元件，在使用时它们没有任何的增益或方向性。[1]在电路分析（Network analysis）时，它们被称为电力元件（Electrical elements）。
主动元件（Active components）是一种电子元件，相对于被动元件所没有的，在使用时它们有增益或方向性。它们包括了半导体器件与真空管。

R=\rho \frac{\ell }{A}

$\rho$ 为物质抗阻性,单位为欧姆每米.

R 为电阻阻值,电阻是最简单的 passive element.

材质	抗阻率( $\Omega \cdot m$ )	Usage
Silver/银	1.64 x 10⁸	Conductor/导线
Copper/铜	1.72 x 10⁸	Conductor
Aluminum/铝	2.8 x 10⁸	Conductor
Gold/金	2.45 x 10⁸	Conductor
Carbon/碳	4 x 10⁵	Semiconductor/半导体
Germanium/锗	47 x 10²	Semiconductor
Silicon/硅	6.4 x 10²	Semiconductor
Paper/纸	10¹⁰	Insulator\绝缘体
Mica/云母	5 x 10¹¹	Insulator
Glass/玻璃	10¹²	Insulator
Teflon/聚四氟乙烯	3 x 10¹²	Insulator

Ohm’s law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor.

v\propto i

欧姆定律定义 R 为常量电阻.因为电阻阻值可能受内部或外部环境改变.

v=iR

The resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms ( $\Omega$ ).

R=\frac{v}{i}

1 \Omega = 1 V/A

以上公式需要保证电流和电压是同向的,如果电流为相反,则为 -i.

由于电阻可以是从0到无限大,因此,对于一个小电路而言

v = iR = 0

电压为0,电流为任意,因此在实际中一个小的电路中认为导线是完美的,没有电阻率.

A short circuit is a circuit element with resistance approaching zero. 短电路电路原件电阻趋于零.

原件 $R=\infty$ 成为开合电路(open circuit).

i=\lim _{ R \rightarrow \infty } \frac v R = 0

即电流为0,电压为任意值.

An open circuit is a circuit element with resistance approaching infinity.

遵循欧姆定律的电阻成为线性电阻,非线性电阻的 v-i 图是非线性的.所有的电阻在特定环境下都是非线性的,但是实际使用时都假设为是线性电阻.

G=\frac 1 R=\frac i v

原件电导(conductance)用于衡量电流导性,单位为 mho, 反过来的 ohm, IS 单位为 S(siemens)

1 S = 1 \mho = 1 A/V

Conductance is the ability of an element to conduct electric current; it is measured in mhos ( $\mho$ ) or siemens (S).

同样的电阻率可以表示为欧姆和西门子. 10 $\Omega$ = 0.1 $\mho$ = 0.1 S

i = Gv

p=vi=i^2R=\frac {v^2} R

p=vi=v^2G=\frac {i^2} G

上述两个公式需要注意

The power dissipated in a resistor is a nonlinear function of either current or voltage.
Since R and G are positive quantities, the power dissipated in a resistor is always positive. Thus, a resistor always absorbs power from the circuit. This confirms the idea that a resistor is a passive element, incapable of generating energy.

A branch represents a single element such as a voltage source or a resistor.

A node is the point of connection between two or more branches.

A loop is any closed path in a circuit.

b = l + n - 1

Two or more elements are in series if they exclusively share a single node and consequently carry the same current. Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

where N is the number of branches connected to the node and is the nth current entering (or leaving) the node.

N 个连接到节点的分支, in 为第 n 个元件进入或离开该节点的电流.

\sum_{i=0}^{N} i_n = 0

KCL 和欧姆定律是电路基础理论.

The sum of the currents entering a node is equal to the sum of the currents leaving the node.

Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.

M 循环中的电压数

\sum_{v=0}^{M} v_m = 0

Sum of voltage drops Sum of voltage rises

The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

R_{eq} = R_1 + R_2 + R_3 + \cdots + R_N = \sum_{n=1}^N R_n

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resistors, capacitors, and inductors.generators, batteries, and operational amplifiers

电路基础 - 第五版

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