So this is a typical closed-loop system. And in a closed-loop system, the output will be given to the feedback system. Here is the H. It has gains H. The output will be given to the feedback system.

所以，这是一个典型的闭环系统。而在闭环系统中，输出会被反馈回来。输入到反馈系统中。这里是H。它有一个增益H。输出将被送入反馈系统。

and then to compute the error. It is the controller. Once you know the error, the error will be given to the

然后计算误差。这就是控制器。一旦知道了误差，误差就会被送入

I thought, And afterwards, we're just given the feedback. and it computed the error. You are getting these two equations. And based on these two equations, you can, again, compute the transfer function for the global system.

放大器。也就是控制系统。这个控制系统有一个增益G。所以，输入就是误差。我想，之后，我们得到了反馈。系统计算出了误差。你得到了这两个方程。基于这两个方程，你可以再次计算出整个系统的传递函数。

And the global system usually depends on how you design the controller. Sometimes the output is very similar.

而全局系统通常取决于你如何设计控制器。有时候，输出结果非常相似。

Sometimes the output is jumping up and down.

有时候，输出会上下跳动。

Different control system have different damping values. If the system has very high damping, its output will look like like this.

不同的控制系统具有不同的阻尼值。如果系统的阻尼非常高，它的输出看起来会像这样。

It doesn't have a very high damping. So you probably go over the state, under the state, over the state, under the state. So this is the property of the system.

它的阻尼并不高。所以它可能会在稳态上下波动，一会儿超过，一会儿低于。这就是该系统的特性。

And we have a regulator and a servos. The reference is the cancel value.

我们有一个调节器和一个伺服系统。参考值就是目标值。

The output is the remaining angle, depends on this property. When a servo, which means the reference is changing.

输出是剩余的角度，这取决于上述特性。如果是伺服系统，就意味着参考值是在变化的。

And the objective is try to keep this small error.

我们的目标是尝试将误差保持在较小的范围内。

Okay, great. That's all we had to introduce in our next step.

好的，很好。这就是我们下一步要介绍的全部内容。

And now we would like to begin our lecture, lecture six.

现在，我们开始第六讲的课程。

so we look at the title, it's social regulation.

大家可以看到标题，是“社会规制”。

you probably have known what social regulation is. so the same thing, same thing, a northern theory. It's about the problem of nature. You must understand what the theory and the northern theories are.

大家可能已经知道，什么是社会规制。同样，诺德理论也是关于自然问题的。大家必须理解什么是诺德理论。

because of energy, if you only know energy, you can use the symbol tau.

因为关于能量，如果你只知道能量，就可以用符号tau来表示。

we have used the energy for many times in our future exercises.

我们在后面的练习中会多次用到能量这个概念。

you know energy is the power times the time. power has unit of watts. and time is second. power times the time is the energy.

大家知道，能量等于功率乘以时间。功率的单位是瓦特。时间的单位是秒。功率乘以时间就是能量。

the energy also other common units such as kilowatt hours. kilowatt hours is the 1,000 kilo times one hour. that we call the unit.

能量还有其他常见的单位，比如千瓦时。千瓦时就是1000千瓦乘以1小时。这就是我们所说的单位。

kilowatt hour is also the unit of energy.

千瓦时也是能量的单位。

and there are different types of energy. kinetic energy, potential thermal, gravitational, and some, and etc.

而且，能量有不同的类型。比如动能、势能。还有热能、引力能、等等。

and energy for battery. for example, the lightning is also

还有电池中的能量。比如，闪电也是一种

of the energy.

能量。

and we also have introduced the electric charge, right? the unit is the coulomb, we use C. to represent the unit of electric charge. and you know electric charge has property. positive and negative. and you can understand similarity. they will attract each other. If have different similarity, they will repair each other.

我们还介绍了电荷，对吧？它的单位是库仑，我们用C表示。用来表示电荷的单位。大家知道，电荷具有属性。有正负之分。你们应该能理解其中的相似之处。它们会相互吸引。如果带有不同的电荷，它们就会相互排斥。

and then is the reason when you have current, if the charge is moving, you have current. so current is the time rate of change of charge. we already know, we have introduced this equation.

这就是为什么会有电流。当电荷移动时，就形成了电流。所以，电流就是电荷随时间的变化率。我们已经知道了，也介绍过这个公式。

time rate change of charge.

电荷随时间的变化。

current is dq and time rate is dt.

电流就是dq，时间变化率就是dt。

so you can get current. current has unit.

这样你就能得到电流。电流是有单位的。

the charge has unit coulomb. so one coulomb divided by one second, one ampere.

电荷的单位是库仑。所以，一库仑除以一秒，就是一安培。

and dc, dc is direct current. which means the current is constant.

还有直流电，也就是直接电流。这意味着电流是恒定的。

so it's a normal line.

所以它是一条直线。

and for the ac, alternating current.

而对于交流电，就是交流电流。

the current is changing. it's changing with the time.

电流是变化的。它会随着时间而变化。

we also use this for multiple times. so we know the movement of electron. that is current. How can we make the electron move? It needs at work or transfer energy.

我们也多次使用过这个。所以我们知道电子的运动。这就是电流。那么我们如何让电子运动起来呢？它需要做功或传递能量。

to make the electron move.

才能让电子运动。

And the work or the energy is usually performed by electromotive force.

而这种做功或能量，通常是由电动势来提供的。

we also have seen this symbol for multiple times. EMF is electromotive force. It's also a source.

我们也多次见过这个符号。EMF就是电动势。它也是一种电源。

It's also a source of current. That's the reason why the electron move. And once the electron move, you will get current.

它也是电流的来源。这就是电子会运动的原因。一旦电子开始运动，就会产生电流。

It's a source, right? It's an energy source.

它是一种电源，对吧？是一种能量来源。

Load, also load.

负载，也是负载。

Again, it's also a load.

同样，它也是一个负载。

So this electromotive force can also be defined as a voltage. or potential difference.

所以，这个电动势也可以被定义为电压。或者说是电势差。

And the voltage difference between A and B is the energy needed to move a unit charge from A to B. So in order to move a charge from A to B, you must apply the energy. That's the reason we have the movement. of the electron.

而A和B之间的电压差，就是能量推动单位电荷从A移动到B所需要的能量。所以，要想把电荷从A移动到B，就必须施加能量。这就是为什么会产生移动的原因。也就是电子的移动。

So we know W is the energy, it's a symbol for energy, right? and Q is the symbol for the electric charge.

我们知道，W代表能量，它是能量的符号，对吧？而Q代表电荷。

And once you apply the energy for the electric charge, you will get the voltage.

一旦你对电荷施加了能量，就会得到电压。

And the energy has unit joules, and the electric charge has unit coulomb.

能量的单位是焦耳，电荷的单位是库仑。

And the power is the time rate of change.

而功率则是变化的速率。

of energy. Change of energy is dW. W is energy.

也就是能量的变化率。能量的变化就是dW。W代表能量。

dw means time rate, time rate is dt. so the power can be expressed by dt divide dW. dw divided by dt.

dw表示时间速率，时间速率就是dt。所以，功率可以用dt除以dW来表示。也就是dW除以dt。

and you can change this a little bit. so you can also use dw divided by dt. and dq divided by dt. We know dw divided by dq is the voltage, right?

你可以稍微调整一下这个表达式。所以，你也可以用dW除以dt。还有dq除以dt。我们知道，dW除以dq就是电压，对吧？

and dt is the current.

而dt就是电流。

so finally you will get the we have power is equivalent to the voltage times the current. so this is the final form. you can compute the power. Once you know the current, once you know the voltage, you can apply it to get the power.

所以最后，你会得到功率等于电压乘以电流。这就是最终的公式。你可以用它来计算功率。只要知道电流和电压，就能算出功率。

and so in order to draw a circuit, and a circuit usually includes several elements. so first, let's have a look at the first element. it's a voltage source. you already know this. this symbol in your circuit. so you can use this symbol to represent a source, a voltage source in a circuit. and sometimes we also use this symbol.

那么，为了绘制电路图，一个电路通常包括几个元件。首先，让我们来看看第一个元件。它是一个电压源。这个你们已经知道了。这是电路图中的符号。所以，你可以用这个符号来表示电路中的电压源。有时候，我们也会用这个符号。

this symbol represents a voltage source.

这个符号也代表电压源。

and here you can see there are different types of symbols. that can be used to represent a voltage source. and we also know there is an ideal. ideal voltage source.

在这里，你可以看到有不同的符号类型。都可以用来表示电压源。我们还知道，存在一种理想的情况。那就是理想电压源。

It is which remain the same voltage across its terminal. The amount of current is from its terminals.

它的特性是，其两端的电压始终保持不变。而流过的电流大小则取决于外部电路。

It doesn't matter how big the load is. The voltage is maintained the same value.

无论负载有多大，这都不会影响它。电压始终保持恒定。谢谢。

This requires the voltage source has zero internal resistance. This requires the voltage source has internal resistance.

这就要求电压源的内阻为零。这要求电流源具有内阻。

because if there's no internal resistance, there's no voltage drop, right?

因为如果没有内阻，就不会有电压降，对吧？

And for this one, I also want to basically it has introduced the ideal ammeter, right?

另外，关于这一点，我也想简单提一下，它介绍了理想电流表。

What is the requirement for the resistance?

那么，对它的电阻有什么要求呢？

can you still remember the ideal ammeter? I think in our last lecture, we also introduced the ideal ammeter. and ideal voltmeter.

大家还记得理想电流表吗？我记得在上一节课里，我们也介绍过理想电流表。还有理想电压表。

Ammeter and voltmeter are used to measure current and voltage. And we also introduced the ideal ammeter and ideal voltmeter.

电流表和电压表是用来测量电流和电压的。我们还介绍了理想电流表和理想电压表。

And in that case, we also have to define

在这种情况下，我们还需要定义

what the internal resistance should be. should be zero or should be infinite.

内阻应该是多少。应该是零，还是无穷大。

so everybody can see it.

这样大家都能看到了。

so in our last lecture, we have introduced the ideal ammeter, so if you still remember,

在上一节课中，我们介绍了理想电流表，如果大家还记得的话，

what is the structure? inside of the ammeter look like. looks like this.

它的结构是怎样的？电流表的内部是什么样子的？看起来就是这样。

it's the inside structure of ammeter.

这就是电流表的内部结构。

and you have to have idea. so nobody not have idea, nobody know have idea.

大家必须有个概念。可是没人知道，没人有概念。

because normally it's not an idea.

因为通常情况下，这确实没什么概念。

and there will be a requirement. there will be a requirement on this resistor. this is the internal resistance, right?

但是，这里有一个要求。就是对这个电阻有要求。这就是内阻，对吧？

and this is the resistor that can be connected in parallel with ammeter. in order to have an ideal ammeter.

而这个电阻是可以与电流表并联的。这样才能构成一个理想的电流表。

and you will get zero total resistance. then there's no voltage drop.

这样，总电阻就会变成零。也就没有电压降了。

to make a current in your circuit, right?

这样就能在电路中产生电流，对吧？

so the ammeter should not affect.

所以，电流表不应该对电路产生影响。

should not affect the original circuit.

不应该改变原来的电路状态。

so it should have no influence on the circuit.

也就是说，它应该对电路没有影响。

and similarly for the voltmeter, right? you have a resistor here. and this is the internal resistance.

同样地，电压表也是如此，对吧？这里有一个电阻。这就是内阻。

This resistor is used to extend the range. of the measuring. Because if you don't have this resistor, you probably have only, say, for example, microvolt. But if you connect with a resistor, you probably can measure 50 volts. That's the reason we have the resistor here. to extend the measuring.

这个电阻是用来扩展量程的。用于测量。因为如果没有这个电阻，你可能只能测量，比如说，微伏级别的电压。但如果你接上这个电阻，就能测量50伏了。这就是为什么这里要加电阻的原因。为了扩展测量范围。

And for the ideal, so this is the voltmeter.

对于理想情况来说，这就是电压表。

for the ideal voltmeter,

理想的电压表，

what is the requirement? of its resistance?

它的要求是什么？就是它的电阻。

because this voltmeter is connected in parallel. it's the object you want to measure, right?

因为这个电压表是并联连接的。也就是你要测量的那个对象，对吧？

For example, you want to measure the voltage of this resistor. And you connect your voltmeter in parallel.

比如，你想测量这个电阻两端的电压。然后你把电压表接上去，也是并联的。

it's the subject you want to measure. in order to not affect the original circuit. or in order not to influence the original circuit. and there should be no current.

这就是你要测量的对象。这样做的目的，是为了不影响原来的电路。或者说，是为了不干扰原电路。而且，不应该有电流通过。

if there's current flowing in this branch, it will be inaccurate.

如果这个支路有电流流过，结果就会不准确。

because the current is what we want to avoid. so there should be no current flowing in this branch. in order to make no current flow in this branch, so this resistor should have infinity.

因为我们正是要避免电流的影响。所以，这个支路里不应该有电流。为了让这个支路没有电流，这个电阻应该是无穷大。

and also the source also has internal resistance. and for the ideal current source,

另外，电源也有内阻。而对于理想电流源来说，

why it has internal resistance? infinity.

它为什么会有内阻呢？也是无穷大。

so for ideal current source, we use this symbol. it provides current for a circuit. for example, there is a load here.

所以，对于理想电流源，我们使用这个符号。它能为电路提供电流。比如，这里有一个负载。

so the current source provide current. for example, one ampere.

那么电流源就会提供电流。比如，一安培。

for the circuit. and for the current source, normally it also has internal resistance.

在电路中。通常，电流源也有内阻。

and the internal resistance is connected in parallel. this whole part is

而且这个内阻是并联连接的。这一整部分，就是

a current source. not only this one, these two part. together is the current source.

电流源。不仅仅是这一部分，这两部分都是。合起来才是一个电流源。

so the ideal current source, there should be no current flowing.

那么，理想的电流源，应该没有电流流过。

the internal resistance should be ideal has very large value. so there will be no current flowing from

理想情况下，内阻应该非常大。这样就不会有电流从

and all the current are flowing through the load.

电源流出，所有的电流都会流过负载。

this is what we want to achieve. and here we introduce another very important concept.

这就是我们想要达到的效果。在这里，我们引入另一个非常重要的概念。

but before I introduce this, I want to define the voltage source. we have used this before. This is a voltage source, right?

但在介绍这个之前，我想先定义一下电压源。我们之前已经用过了。这是一个电压源，对吧？

and you have a load.

这里还有一个负载。

actually there is an internal resistance.

实际上，它有一个内阻。

these two parts together is the voltage source.

这两部分合在一起，就是电压源。

so for the ideal voltage source,

那么，对于理想电压源来说，

internal resistance should be zero.

内阻应该为零。

because if it's zero, there will be no voltage drop. and all the voltage are being given to the load.

因为如果内阻为零，就不会有电压降。所有的电压都会施加到负载上。

so that's the reason we must have the internal resistance.

所以，这就是为什么我们必须要有内阻的原因。

and we have dependent sources. but we should first this is a new concept.

还有受控源。不过，我们首先应该了解一个新概念。

probably haven't heard that in before.

大家以前可能没听说过。

so dependent source, which means the source, normally, for example,

受控源的意思是，这个源，通常情况下，比如

for independent sources,

对于独立源来说，

we have 4 bywords. for the voltage source, and we have two ampere.

有四个组成部分。对于电压源，我们有四个部分；而对于电流源，我们有两个安培。

right? This is an independent source. But what a dependent source, which means the source

对吧？这是一个独立源。那么什么是受控源呢？也就是说，这个源

is dependent.

是受控的。

Here's an example. So the voltage here, is dependent on the current. in a certain case.

这里有一个例子。那么这里的电压，取决于电流。在某种情况下。

So in the circuit, for example, has one ampere.

比如，在这个电路中，有一个安培。

In the circuit has the voltage source will produce 10 volts.

这个电路中的电压源会产生10伏特。

The value of the source is changed.

但是，这个源的数值会发生变化。

different current. The source will also produce different voltage.

取决于不同的电流。这个源也会产生不同的电压。

It's dependent.

这就是受控源。

And sometimes the source produce the power. to the outside. But sometimes the source also observe. absorb power from the outside.

有时候，这个源会提供功率。输出到外部。但有时候，源也会吸收功率。从外部吸收功率。

For example, you want to charge. you charge your phone, charge your laptop. The battery in your phone or laptop is absorb power. But if you don't need to charge your laptop or your phone, it produce power. to the device.

比如，你想给电池充电。给手机或笔记本电脑充电。你手机或笔记本电脑里的电池，就是在吸收功率。但如果你不需要给笔记本电脑充电，或者手机，它就是在提供功率。输出给设备。

How can we define the corresponding sign?

那么，我们如何确定相应的符号呢？

for absorbing power and supplying power.

也就是对于吸收功率和提供功率的情况。

And here is the definition. So if the power is assigned a positive sign, then it's entering the positive current of the voltage.

这里有一个定义。如果功率被赋予正号，那么它就是电流从电压的正极流入。

A positive current of voltage across an element.

也就是元件两端的电压为正，电流从正极流入。

So here you can see the current enters the positive polarity of the voltage.

大家可以看到，这里的电流是流入电压的正极的。

So here for the left figure, the voltage source is

那么，在左边的这张图中，电压源是

providing

在提供

current.

电流。

to the circuit. This resistor, this load, is absorbing. it's absorbing the power.

流向电路。这个电阻，也就是这个负载，正在吸收电流。它在吸收功率。

And here, so this, okay, the absorbing and supplying is for the resistor.

在这里，所以，这里的吸收和供应都是针对这个电阻而言的。

and there's the positive polarity of the voltage.

这里还有电压的正极性。

So in this figure, the current is in this direction.

那么，在这张图中，电流的方向是这样的。

and the current is leaving. It's leaving the positive polarity of this element.

电流是流出的。它是从这个元件的正极性端流出的。

So you have to make it right.

所以，你必须把它弄对。

And for the left figure, the current is reversed. it's the positive polarity of the element.

而对于左边的图，电流方向是相反的。它是从该元件的正极性端流出的。

So you have positive sign.

所以，这里有一个正号。

And why this has positive sign? this element is absorbing the power.

那为什么这里是正号呢？因为这个元件是在吸收功率的。

and for the right figure, the element is supplying.

而对于右边的图，这个元件是在提供功率。

Is it clear?

大家清楚了吗？

So, from my understanding, this is not a load. it is not considered as a resistance. It's an element. I don't know what exactly it is. It's just an element.

那么，根据我的理解，这并不是一个负载。它不能被视为一个电阻。它只是一个元件。但我不知道它具体是什么。它只是一个元件。

Here is the power view.

这里是功率视图。

Let me just draw it here.

我把它画在这里。

Okay, this is one element. in a circuit. So what's the current? It looks like this.

好的，这是一个元件。在电路里。那么电流是什么样的呢？就像这样。

If the current direction is to the left,

如果电流方向是向左的，

then the current is entering. Here is the positive, you know, this is the positive polarity of this element, right? this is negative. So if the current is entering the positive, of this element,

那么电流就是流入的。这里是正极，你知道，这是这个元件的正极性，对吧？这里是负极。所以，如果电流流入正极，那么这个元件

has a positive sign.

就是正号。

if the current enters the positive polarity, this is the direction of the current, and this is positive polarity. This is just for one element.

如果电流流入正极，这就是电流的方向，而这里是正极。这只是一个元件的情况。

If the current enters the positive polarity of elements, it will have positive sign.

如果电流流入元件的正极，它就会是正号。

And for the second case,

至于第二种情况，

here we have a here negative. so in this case, this is still one element.

这里是负号。所以在这种情况下，这仍然是一个元件。

Current is leaving the positive polarity, right? Here is the positive polarity, negative polarity. So it has negative sign.

电流是从正极流出的，对吧？这里是正极，这里是负极。所以，它是负号。

And when the current is entering, it's absorbing current. this element is absorbing. the power.

当电流流入时，它就是在吸收电流。这个元件就是在吸收。功率。

And when the current is leaving this element, this element is supplying power.

而当电流流出这个元件时，它就是在提供功率。

Here is an example.

这里有一个例子。

So let's just go over this example. I think you have done this similar exercise for multiple times. You just use the Ohm's law to get the current. and then you can compute the power. Once you know the current and you know the voltage, you can compute the power. And the power times the time. Here you know six hours, right?

那么，让我们来看一下这个例子。我想你们已经做过很多次类似的练习了。你们只需要用欧姆定律就能算出电流。然后就可以计算出功率。一旦知道了电流和电压，就能计算出功率。然后功率乘以时间。这里知道是六个小时，对吧？

And once you know the power and the time, you will get energy. And energy is one pound per watt hour.

一旦知道了功率和时间，就能得到能量。而能量的单位是瓦时。

Then you can get the total cost.

这样就能算出总成本。

And here you should pay attention. The watt hour, the watt hour is also a unit. It's also a unit for energy.

这里大家需要注意一下。瓦时也是一种单位。它也是能量的单位。

Energy, we normally use the joules, right?

通常我们用焦耳来表示能量，对吧？

But sometimes we also use watt hour.

但有时候也会用瓦时。

Because energy is equivalent to power times time. So here has the unit work.

因为能量等于功率乘以时间。所以这里就有功的单位。

And again, for example, a watt hour is also a unit.

再举个例子，瓦时也是一种单位。

for energy. Not only joules.

用于表示能量。不仅仅是焦耳。

Okay, here is the solution. You know the voltage, right? And you know the resistance for each resistor. And based on the Ohm's law, you can get the current. And based on, you know, the power is equal to the voltage. times the current. so you can get the power.

好的，这是解题过程。你知道电压，对吧？也知道每个电阻的阻值。根据欧姆定律，你可以算出电流。另外，你知道功率等于电压乘以电流。这样就能算出功率了。

for each resistor.

对于每个电阻来说。

And once you know the power for each resistor,

一旦知道了每个电阻的功率，

and times the time,

再乘以时间，

you will get the energy.

就能得到能量。

and the energy, you know the cost, right? cost is 100 more. per hour. So you can get the total cost.

而能量，你知道成本，对吧？成本是100多。每小时。所以你可以算出总成本。

so basically, almost all, yeah, just those rules is no big deal. so almost all they can use voltage across a resistor. it's directly proportional to the current. i is equal to v over r. so you can get this equation right?

所以基本上，几乎所有，是的，这些规则都没什么大问题。也就是说，它们都可以利用电阻两端的电压。它与电流成正比。I等于V除以R。所以你能得到这个公式，对吧？

and we also have introduced this equation. because the conductor or the material has a certain length. and also has certain cross-sectional area. cross-sectional area a. and rho is the resistivity. Rho is the resistivity and nearly given.

而且我们还引入了这个公式。因为导体或材料有一定的长度。同时也有一定的横截面积。横截面积A。而ρ是电阻率。电阻率是给定的。

so you don't have to remember it.

所以你不需要记住它。

and area, you can get the resistance of this material.

结合面积，你就可以得到这种材料的电阻。

and to represent the resistance. okay, new definition. here is important. three completely new definition. branches, nodes, and loops.

用来表示电阻。好的，这是一个新的定义。这一点很重要。这是三个全新的定义。分别是支路、节点和回路。

a section of circuit which is located between two junctions. you must have first of all a few junctions.

电路的一部分，位于两个节点之间。首先，你必须有几个节点。

and there is an element in between.

中间还有一个元件。

here is a branch. but the second one is not branch because there is no element.

这就是支路。但是第二个不是支路，因为里面没有元件。

there's an element in between. The element can either be a resistor, or a source. this is a current source. this is a branch. also contains one element in between.

中间有元件。这个元件可以是电阻，也可以是电源。这是一个电流源。这也是一个支路。中间也包含一个元件。

although the element is a current source. it doesn't matter whether it's a current source or a resistor.

只不过这个元件是电流源。无论是电流源还是电阻，都没关系。

only if the element is included in between.

只有中间包含元件，才能算作支路。

okay, nodes. A point or junction where two or more circuit elements

好的，节点。是指两个或更多电路元件连接在一起的点或 junction。

the elements can be, for example, resistor, capacitor, inductor or even source.

这些元件可以是电阻、电容、电感，或者甚至是电源。

which is called a node.

这就叫做节点。

So when two elements meet together,

所以，当两个元件连接在一起时，

in other words, a point of connection. and two or more branches is known as a node.

换句话说，就是一个连接点。而两个或更多的支路汇聚于此，就称为节点。

So once two elements meet together, you will get one node.

所以，只要两个元件连接在一起，就会形成一个节点。

Okay, such definition, too. we continue the definition of nodes. if there is no element between two or more connections, it's known as a node. This node can be recombined. as a single node. You know the node is two elements meet together, right? so you have one node here. and you have one node here. They meet two elements meet together. So, nodes below. put the nodes at bottom.

好的，这也是一个定义。我们继续来讲解节点的定义。如果两个或多个连接点之间没有任何元件，那么它们就被称为节点。这个节点可以重新组合。成为一个单一的节点。大家知道，节点就是两个元件连接在一起，对吧？所以这里有一个节点。这里也有一个节点。它们都是由两个元件连接而成的。那么，下面的节点。把节点放在底部。

There's no, okay, loops. Loop is any closed path. This is an important concept. in electrical circuit. That starts and ends. and the same node.

这里没有回路。所谓回路，就是任何闭合的路径。这是一个重要的概念。在电路中就是这样。它有一个起点和一个终点。而且起点和终点是同一个节点。

without passing through any node.

而且在这个过程中不经过任何其他节点。

How many loops we have? in this circuit.

那么，我们有多少个回路呢？在这个电路里。

Let me draw the circuit here.

让我在这里画一下这个电路。

Okay, a loop is a closed path. So the path should be closed. It starts and ends at the same node.

好的，回路就是一个闭合的路径。所以，这条路径必须是闭合的。它从同一个节点出发，并最终回到该节点。

This is one loop, right? And this is three. This three is actually one loop.

这是一个回路，对吧？而这里有三个。这三个实际上是一个回路。

There's no element different there. So they can be combined as one loop.

那里没有任何不同的元素。所以它们可以合并成一个回路。

And the follows at bottom is also one loop.

下面的这个也是一个回路。

Let's have a look at the definition. First, it should be a closed path. and then it starts and ends at the same node. So let's start from here. It's a closed path.

好的，让我们来看一下定义。首先，它必须是一条闭合的路径。而且它必须从同一个节点出发并回到该节点。那么，我们从这里开始。这是一条闭合的路径。

and we go through this node, go through this node. and then this node.

我们经过这个节点，再经过这个节点。然后是这个节点。

and go back here. So it's a closed path. and we pass every node just once.

然后回到这里。所以，这是一条闭合路径。而且我们只经过每个节点一次。

So this is the first. And similarly, you can have a look here. or you can look here.

所以，这符合第一个条件。同样地，大家可以看一下这里。或者看这里。

And you can also draw a bigger loop. for example, this one here. and then go here.

你也可以画一个更大的回路。比如这里的这个。然后走到这里。

and you go back. So you have a bigger loop.

然后再返回。这样你就有了一个更大的回路。

So hopefully you can get the solution like this. Keep in the corners. Keep in the corners, it's different loops.

希望大家能得出这样的解。注意角落的位置。角落对应的是不同的回路。

Here's something interesting.

这里有个有趣的地方。

For example, branch represent a single element.

比如，分支代表一个单独的元素。

The branch should contain one element.

一个分支应该只包含一个元素。

And we have a node.

然后我们还有节点。

And here, this tree can be combined together. and the other branch is combined here.

在这里，这棵树可以组合在一起。而另一个分支则组合在这里。

And we have the loops. It should be a closed path and pass every node just once. And there's an interesting conclusion.

还有循环结构。它应该是一条闭合的路径，并且只经过每个节点一次。这里有一个有趣的结论。

So, T is a branch.

所以，T是一个分支。

It's the loops.

它就是循环。

It's the number of the loops. L is the number of the nodes. So actually they have this relation. So for circuit, what do you know? the number of loops. and you know the number of the nodes. and you can get the branch. or if you know the number of branch and the number of loops, you can get the number of the nodes.

这是循环的数量。L是节点的数量。所以实际上，它们之间存在这种关系。那么对于电路来说，你知道什么？循环的数量。你也知道节点的数量。这样你就能算出分支的数量。或者，如果你知道分支和循环的数量，就能算出节点的数量。

So this is the equation that we get.

这就是我们得到的公式。

Once we have the three equations.

一旦我们有了这三个方程。

And let's look at this circuit again. So in this circuit, we have how many nodes we have?

让我们再来看一下这个电路。那么在这个电路中，有多少个节点呢？

We have branches. Let's look at how many branches. The branch can be one in the branch. So how many elements do we have? one resistor. second resistor. third resistor and a voltage source. So we have five branches. And how many nodes?

我们有分支。让我们来看看有多少个分支。一个分支可以是一个分支。那么，我们有多少个元件呢？一个电阻。第二个电阻。第三个电阻和一个电压源。所以，我们有五个分支。那有多少个节点呢？

We have three nodes. So these three, I'm lying. Well, we will also combine. So we also have three nodes.

我们有三个节点。所以这三个，我说错了。不过，我们也会把它们合并起来。所以我们也有三个节点。

Once you use this equation, you can get

一旦你使用这个方程，就可以得到

the number of the loop is three. The number of the nodes is three. When you count the number here, it's not three, right? It's more than three. We have a one, two, three, four, five, six. We have six loops here. But here we only get three. This is because the three here means independent loops.

回路的数量是三个。节点的数量也是三个。但是当你在这里数的时候，并不是三个，对吧？是超过三个的。我们有：一、二、三、四、五、六。这里一共有六个回路。但这里我们只得到了三个。这是因为这里的三个指的是独立回路。

independent loops. So what is independent loops?

独立回路。那么，什么是独立回路呢？

A loop that contain at least one branch.

一个至少包含一条支路的回路。

That is one part, not a part. any other independent loop. It is not a part of any other independent loops. That's the reason.

也就是说，它包含至少一个部分，而不是一个部分。任何其他独立回路也是如此。它不属于任何其他独立回路的一部分。这就是原因。

For example, the blue one. The blue one is a part of the green one. That's the reason they are not independent.

比如，蓝色的这个。蓝色的这个是属于绿色的那个的。这就是它们不独立的原因。

The small blue loop is a part of the green one. That's the reason it's not independent loop.

那个小的蓝色回路是绿色回路的一部分。所以，它不是一个独立回路。

The three small loops in the middle is exactly our independent loops. This is also independent. There's no loop inside, right? It's not a part of any other.

中间的三个小回路，正是我们的独立回路。这个也是独立的。里面没有其他的回路，对吧？它不属于任何其他回路。

for each independent loop, you can obtain one equation.

对于每一个独立回路，你都可以得到一个方程。

so the first loop is a here is a b c a, right? so this first independent loop. The second is b e c. this is the loop in the middle.

那么第一个回路是a，这里是a-b。c-a，对吧？所以这是第一个独立回路。第二个是b-e-c。这是中间的那个回路。

and this loop is r2 and r3. oh, r2 and r3 is the middle. this r1 source and r3 is the loop at the right.

而这个回路包含R2和R3。哦，R2和R3就是中间的那个。这是R1电源，而R3是右边的回路。

so here it has three loops.

所以这里总共有三个回路。

and because these three loops can be joined together, and this whole loop can be joined together. so the circuit can be simplified. The circuit can be simplified to this version.

而且因为这三个回路可以合并在一起，整个回路也可以合并。所以这个电路可以简化。电路可以简化为这个版本。

finally, you will see the voltage source with r1 is connected in series. and r2 and r3 are in parallel.

最后，你会看到电压源与R1是串联连接的。而R2和R3是并联的。

with the current source.

也就是电流源。

i've mentioned it before. so actually all the sources are long ideal. because they have internal resistance. so this is the actual case. the real source we are in the real world. every source has an internal resistance. so they are non-ideal. but the voltage source is an internal resistance connected in series. this is the source.

我之前已经提到过了。所以实际上，所有的电源都是理想的。因为它们都有内阻。所以，这才是实际情况。现实世界中的电源就是这样的。每个电源都有内阻。所以它们都是非理想的。但是，电压源的内阻是串联连接的。这就是电源。

and for the current source, it has internal resistance connected in parallel. so these two circuits represent the real sources.

而对于电流源，它的内阻是并联连接的。所以，这两个电路分别代表了实际电源。

okay, what is the regulation? voltage regulation is actually very similar. similar to the efficiency. you know, the efficiency is the definition of the efficiency is the output power. divided by the input power, right? the voltage regulation is exactly have similar definition. this means in reality, the load, the load cannot get full voltage. from the voltage source. because of the internal resistance. there's always a voltage drop. It can be very small. Even though it's very small, but still there's a voltage drop. so for the ideal source, there's no voltage drop. so the voltage regulation is zero. because the load can get completely from the source. for the ideal source is.

好的，那么什么是调节呢？电压调节其实非常相似。类似于效率。大家知道，效率的定义就是输出功率。除以输入功率，对吧？电压调节的定义也完全类似。这意味着，在现实中，负载，无法获得全额电压。也就是说，无法从电压源那里获得全部电压。这是因为存在内阻。总会存在电压降。这个压降可能非常小。尽管它很小，但确实存在电压降。所以对于理想电源来说，是没有电压降的。因此，电压调节率为零。因为负载可以获得全部电压。来自电源的电压。这就是理想电源的特性。

That means voltage regulation is zero. But in the reality,

这意味着电压调节率为零。但在现实中，

the load will get less voltage.

负载获得的电压会减少。

And we have introduced before, for the voltage source is there's a voltage connect in series with an internal resistance.

我们之前已经介绍过，对于电压源来说，它相当于一个电压源与一个内阻串联。

And here you connect the source with a load. You have load here. This is load.

而在这里，你将电源与负载连接起来。这里有一个负载。这就是负载。

But because of this internal resistance, you cannot

但是，由于存在这个内阻，你无法

transfer the full voltage to the load. there's always a little smaller. voltage drop here.

将全部电压传输给负载。总会有一点点损失。这里会有电压降。

So if the internal resistance is smaller, and you will get more V out.

所以，如果内阻越小，输出电压就会越高。

So a smaller internal resistance, you will get smaller voltage regulation. and you will get more V out.

因此，内阻越小，电压调节效果就越好。而且输出电压也会更高。

That's the reason for ideal voltage source. It should be the internal resistance should be zero.

这就是理想电压源的原因。它的内阻应该为零。

How can we come with the voltage regulation?

那么，我们该如何实现电压调节呢？

So voltage regulation is the voltage without the load.

电压调节是指空载时的电压。

minus the voltage with the load. divided by the voltage with the load. So this is the definition here. Oh, this is unclear, right? you have vt. vt is the primary load. t is the primary load. so vt is the primary voltage.

减去带负载时的电压。再除以带负载时的电压。这就是这里的定义。哦，这一点可能不太清楚，对吧？这里有Vt。Vt是初级负载。T代表初级负载。所以Vt是初级电压。

after voltage. If there is no load, here, what is the voltage? of the primary load. this is the no-load voltage. and we connect the primary load with the load. what is the voltage here? you will get the voltage is followed. divided by the voltage with no load. you will get the voltage regulation. so the voltage regulation is between full load and no load.

这是空载电压。如果没有负载，这里的电压是多少？也就是初级电压。这就是空载电压。现在我们给初级负载接上负载。这里的电压是多少？你会得到，电压会下降。除以空载电压。这样就能得到电压调节率。所以，电压调节率就是满载和空载之间的差值。

of our power supply.

也就是我们电源的电压调节率。

and the difference between the no load and full load. the difference between the voltage no load and voltage full load is because of the internal resistance.

也就是空载和满载之间的差异。空载电压和满载电压之间的差异，是因为存在内阻。

so

所以，

you can get this equation. the voltage of no load minus the voltage for load.

你可以得到这个公式。空载电压减去满载电压。

is the current times the internal resistance.

等于电流乘以内阻。

and finally you can get the voltage regulation is actually the internal resistance divided by no load.

最后，你可以得到电压调整率的公式是内阻除以空载电压。

times 100. For the ideal voltage source, internal resistance is zero.

再乘以100。对于理想电压源来说，内阻为零。

so you will get voltage regulation also zero.

所以，电压调整率也是零。

Okay, for the voltage regulation, if you talk voltage, y-axis is the voltage, x-axis is the current.

好的，关于电压调整率，如果你看这张图，y轴是电压，x轴是电流。

and you can get a slope. The actual voltage of the load or the terminal is the

你可以得到一条斜率。负载或端子的实际电压是

voltage source. minus the internal.

电压源的电压。减去内阻上的压降。

voltage drop.

也就是电压降。

You kind of study some of this voltage drop. It's because of the internal resistance, you have more voltage drop.

你大概已经了解了一些关于电压降的内容。这是因为内阻的存在，导致了更大的电压降。

And when you draw the figure, the x-axis is the voltage. y-axis is the voltage, x-axis is the current.

当你绘制图表时，横轴代表电压。纵轴是电压，横轴是电流。

so you will get the curve like this, right?

所以你会得到像这样的曲线，对吧？

so when r is zero, you will get this is the what we saw.

那么，当R为零时，你会得到就是我们之前看到的那个结果。

and the slope is minus the internal resistance.

而这条直线的斜率就是负的内阻。

The voltage regulation has some applications. For example, if there's a very large machine, if the machine is turning off, the demand of power is suddenly a lot higher. because the machine is turned on. So what regulator compensate? compensate for the current in the load. for the change in the load.

电压调节有一些应用。例如，如果有一台非常大的机器，当它关闭时，对电力的需求会突然大幅增加。因为机器已经启动了。那么，电压调节器是如何进行补偿的呢？它会对负载中的电流进行补偿。以应对负载的变化。

to make sure the output voltage remains constant.

确保输出电压保持恒定。

And voltage regulator are used in devices such as air conditioner,

电压调节器被用于空调等设备中，

television, etc. protecting from fluctuating input voltage.

电视等等。用于防止输入电压波动。

So we know here is a voltage source, right? it has the internal resistance.

那么，我们知道这里是一个电压源，对吧？它有一个内阻。

And you can connect this voltage source with any load. It can be an air conditioner.

你可以将这个电压源连接到任何负载上。比如空调。

or can be a television. Because different devices have different loads. Or different devices have different resistance. So the output voltage will be changed.

也可以是电视。因为不同的设备有不同的负载。或者说，不同的设备有不同的电阻。所以输出电压会发生变化。

or be changed depending on how big the resistance here.

或者会根据这里电阻的大小而变化。

Because the current is changed. So the final output will also change. And what is the purpose? The exact is to protect the air conditioner or television from operating input voltage.

因为电流发生了变化。所以最终的输出也会改变。那么，它的目的是什么呢？就是为了保护空调或电视，使其免受工作电压的影响。

Make sure that this final output voltage remain constant. It's very similar to what we have in the open-loop control, right? or actually in the closed-loop control.

确保最终的输出电压保持稳定。这和我们开环控制中的情况非常相似，对吧？或者更准确地说，是在闭环控制中。

you have comparator here, you have the control system. the control system in this case is the regulator.

这里有一个比较器，还有一个控制系统。在这种情况下，控制系统就是稳压器。

this is the control system, the voltage regulator. and you have output voltage.

这就是控制系统，即电压调节器。这里还有输出电压。

once you can connect the output voltage with a load. it's an air conditioner or television. so the output voltage is changing. if the voltage is 220 volt, right? but you connect the output with the air conditioner. it may drop to 180. so what we want is to keep output voltage 220. okay, now you can see the error. and click on this button here. it found 40 difference. that issue, we should use the regulator. to control output, make sure output is always 220.

现在，我们可以把输出电压连接到负载上。比如空调或电视机。所以输出电压会发生变化。如果电压是220伏，对吧？但是你把输出端连接到了空调上。电压可能会降到180伏。所以我们希望保持输出电压在220伏。好的，现在大家可以看到错误了。然后点击这里的这个按钮。它发现相差40。这个问题，我们应该使用稳压器。来控制输出，确保输出电压始终为220伏。

so the voltage regulator is kind of close-loop control system. that we have introduced.

所以，电压稳压器其实是一种闭环控制系统。我们之前已经介绍过了。

regulators in the real world, in our real life, the regulators usually consist of a relay. so we use relay in the voltage regulator. that's also a major problem. the relay can response quite fast, which result in faults in the product.

在现实世界中，在我们的日常生活中，稳压器通常由继电器组成。所以我们在这个电压稳压器中使用了继电器。这也是一个主要问题。因为继电器的响应速度非常快，这会导致产品出现故障。

now is the important knowledge, I would say.

我想说，现在这是一个非常重要的知识点。

the first is the theory, 70 theory.

首先是理论，70理论。

the main purpose of 70 theory is trying to

70理论的主要目的是试图

replace our media, the true communist politics. it's an implement circuit.

取代我们的媒体，也就是真正的共产主义政治。这是一个实现电路。

the main purpose of 70 theory is trying to replace a linear two-terminal circuit with an equivalent circuit. and the equivalent circuit consists of a voltage source. vth, th is the 70.

70理论的主要目的是用一个等效电路来取代线性二端电路。而这个等效电路由一个电压源组成。Vth，th就是70。

a voltage source in series with a rth

这是一个与一个Rth串联的电压源。

so if you, for example, if you have a very complex circuit, it can be very big, very big, I don't know.

所以，举个例子，如果你有一个非常复杂的电路，它可能会非常大，非常大，我也不确定。

and if you want to compute, for example, the voltage or source, or voltage or current for each resistor, it's very difficult. it can be very time consuming.

如果你想计算电压或电流源，或者计算每个电阻上的电压或电流，那就会非常困难。这会非常耗时。

So in this case, we can replace

所以在这种情况下，我们可以用

this circuit. It's an equivalent circuit.

这个电路来替代。这是一个等效电路。

And the equivalent circuit only include a voltage source. it is the same. connect in series with the resistor.

而这个等效电路只包含一个电压源。这是一样的。它与电阻串联。

So the main purpose of this Thévenin's theorem is used to simplify. a circuit, a very complex and long circuit.

所以，戴维南定理的主要目的就是用来简化电路。也就是那些非常复杂和冗长的电路。

this is our terminal.

这就是我们的端子。

you can be connected to a load.

你可以把它连接到一个负载上。

so a very complex circuit can be replaced by a very simple circuit. And this simple circuit includes a voltage source and a resistor. and they are connected in series.

这样，一个非常复杂的电路就可以被一个非常简单的电路所替代。这个简单电路包括一个电压源和一个电阻。它们是串联在一起的。

now the key problem is how can we obtain

好的，现在关键的问题是：我们如何获得

the equivalent voltage? how can we obtain the equivalent resistance? this is the key point here.

等效电压？又如何获得等效电阻？这就是这里的关键点。

how can you get these two value? Because if you can get these two value, any linear two-terminal circuit can be simplified. it's a very simple circuit.

你怎么得到这两个值？因为如果你能得到这两个值，任何线性二端电路都可以简化。这是一个非常简单的电路。

here is a linear two-terminal. Linear means the circuit obeys ohm's law. Ohm's law is expressed in linear.

这里是一个线性二端网络。“线性”指的是电路遵循欧姆定律。欧姆定律就是用线性方程表达的。

there should be no diodes or transistor.

电路中不应该有二极管或晶体管。

okay, this figure exactly shows the simplification. you have very large linear two-terminal circuit. and it can be replaced just with one voltage connected in series with a resistor.

好的，这张图正好展示了简化过程。这里有一个非常大的线性双端电路。它可以被替换为一个电压源与一个电阻串联的电路。

this is our equivalent circuit.

这就是我们的等效电路。

okay, now, this takes to obtain. how can we compute this one? How can we compute the voltage? the equivalent voltage and equivalent resistance. kind of key steps. The first one, you remove the load.

好的，现在，这就是获得等效电路的步骤。我们如何计算这个电压呢？等效电压和等效电阻。关键步骤如下。第一步，你要移除负载。

remove the load across which the same equivalent is to be found.

也就是要移除那些需要求等效电路的两端之间的负载。

here is load. it can be an air conditioner or i don't know. you remove the load.

这里就是负载。它可以是一台空调，或者其他任何东西。所以，你要先把负载去掉。

and second, you mark the terminals. you mark the terminals of the remaining two-terminal network.

第二步，你要标记出端子。标记出剩余这个二端网络的端子。

okay, remove the load and you mark. you make a mark here. this is the two terminals, right?

好的，去掉负载，然后标记端子。在这里做个标记。这就是那两个端子，对吧？

and the terminal's name is same or associated terminal.

这个端子的名称是“相同”或者“关联”端子。

there's one current source here and one voltage source here. we set all sources to zero. how can we set them to zero?

这里有一个电流源，还有一个电压源。我们将所有源都设为零。那我们怎么把它们设为零呢？

for voltage source, we set it to short circuit. short circuit is replace the voltage source with a wire. so it's just connected.

对于电压源，我们把它短路。短路的意思就是，用一根导线来代替电压源。所以，它们就直接连起来了。

and for the current source, we set it to open circuit. open circuit, which means

而对于电流源，我们把它设置为开路。开路的意思是，

the current source is broken. there's a gap here. it's open. so this is the third state. It's set all sources to zero. we set the voltage source to short circuit, and we set current source to open circuit.

电流源被断开了。这里有一个缺口。它是开路的。所以，这就是第三种状态。我们将所有电源都设为零。我们把电压源短路，电流源开路。

and after we set all sources to zero, and we find the result. the resistance. it turned out to be 15 ohms.

在将所有电源设为零之后，我们就得到了结果。也就是电阻。结果发现是15欧姆。

we found the resultant resistance between the two marked terminals. we set all sources to zero, right? and then we start from here.

我们找到了这两个标记端子之间的等效电阻。我们把所有电源都设为零了，对吧？然后我们从这里开始。

okay, this is our circuit.

好的，这就是我们的电路。

and how can we compute the equivalent resistance? okay, we start from here. okay, this resistor these two are connected in series. in parallel. actually it's three.

那么我们该如何计算等效电阻呢？好的，我们从这里开始。这个电阻，这两个是串联的。而是并联的。实际上，有三个。

connected in parallel. because this is a short circuit, right?

它们是并联连接的。因为这是一个短路，对吧？

so for this circuit,

所以对于这个电路来说，

even though these three resistors are connected in parallel, because there's a short circuit in here, so we can just ignore these three. so the final resultant resistance is just this one.

尽管这三个电阻是并联的，但这里有一个短路，所以我们可以直接忽略这三个电阻。所以最终的等效电阻就是这个。

this is R1. and Rth. should equal to R1.

这是R1。还有Rth。应该等于R1。

here is open. and here is short circuit. so we don't have to consider these three. It's short circuit.

这里是开路。而这里是短路。所以我们不需要考虑这三个。它们是短路。

so the final resistance is R1.

所以最终的电阻就是R1。

before you take the exam, you return all sources to the original position. okay, we return.

在考试之前，请把所有电源都恢复到原来的位置。好的，我们已经恢复了。

In the first step, we've removed them, right? Now we put them back.

第一步，我们把它们都拆掉了，对吧？现在我们把它们装回去。

Here is a current source, and here is a voltage source. So we put them back.

这里是一个电流源，这里是一个电压源。所以我们把它们装回去了。

and find the open circuit voltage. Here is open. This is the terminal. We want to find the voltage here.

然后求开路电压。这里是开路状态。这是端子。我们要求这里的电压。

Here is open. So there is no current. No in this branch. It's open circuit. So the voltage here is actually the voltage here. There is no current flow in this branch. So the voltage of these two terminals is also the voltage on this resistor. R2.

这里也是开路。所以没有电流。这条支路里没有电流。这是开路。所以这里的电压，其实就是这里的电压。这条支路没有电流流过。所以这两个端子之间的电压，也等于这个电阻上的电压。也就是R2。

So what's the source of bank? How can you get the voltage of R2?

那么，电源电压是多少？你怎么得到R2的电压？

We just use what we have learned before.

我们只需要用之前学过的知识。

We can get the voltage of R2.

我们可以求出R2的电压。

This is the first step. The main step is input the source bank. and then you find the open source.

这是第一步。主要的步骤就是输入电源电压。然后找到开路电压。

open circuit. Because this is open, so there's no current. there's no voltage drop. And the voltage of the terminal is equivalent the voltage of this resistor.

也就是开路。因为这里是开路，所以没有电流。也就没有电压降。而端子的电压等于这个电阻上的电压。

And once you know the voltage, the same voltage is equivalent the voltage of R2. And once you know these two values,

一旦你知道了这个电压，那么它也就等于R2上的电压。一旦你知道了这两个值，

the complex circuit can be just replaced by this one.

这个复杂的电路就可以用这个来代替。

Any questions?

有什么问题吗？

Okay, we have more examples.

好的，我们还有更多的例子。

The same parameters are related and identically to it are obtained by measuring voltage and current.

这些相同的参数是相互关联的，并且可以通过测量电压和电流来获得。

Okay, let's have a look at an example.

好的，让我们来看一个例子。

Okay, we have to show this example together.

好的，我们必须一起展示这个例子。

And here we have some results, right? And here, channel a little resistor.

这里我们有一些结果，对吧？还有这里，是一个小电阻。

Okay, here should be connected with a load, right? Here is a load. And here we have two terminals.

好的，这里应该连接一个负载，对吧？这里就是一个负载。这里有两个端子。

The first step is we move the load. Okay, the load is already removed.

第一步是移动负载。好的，负载已经移除了。

Second is, in mind,

第二步是，记住，

we mark the terminals.

我们要给端子做标记。

Okay, this is terminal, for example, this is terminal A. this is terminal B, right? We removed the load and marked two terminals.

好的，比如说，这是端子A。这是端子B，对吧？我们移除了负载，并标记了两个端子。

Third one is, we calculate. Rth.

第三步是计算。Rth。

How can we calculate Rth?

我们该如何计算Rth？

The step is we set all sources to zero. And here we have current source, right?

步骤是，我们将所有电源置零。这里有一个电流源，对吧？

Current source, which means we set it to open circuit.

电流源意味着我们要把它开路。

Power source, set it to open circuit.

电压源也要置零，也就是开路。

This means we have the circuit like this.

这意味着电路变成了这个样子。

A and B.

A和B。

Okay, here is open.

好的，这里是开路。

So there's no, there's cannot flow through this branch. And then you can get the resultant resistance. Okay, we start from here. So we start from here, from A. And we find there's only one resistor here. So the equivalent resistance is exactly equals to this one.

所以没有电流可以流过，这条支路。然后你就可以得到等效电阻了。好的，我们从这里开始。所以我们从A点开始。我们发现这里只有一个电阻。所以等效电阻就是等于这个。

R1.

R1。

So this is the equivalent.

这就是等效电阻。

This is the equivalent resistance. It's the circuit here.

这就是这里的等效电阻。

Okay, the first step.

好的，第一步。

The first step is we have to compute the equivalent voltage source.

第一步是计算等效电压源。

We put the source back. Okay, let's draw it again. We put the source back, should look like this, right? we are get the original circuit.

我们把电源放回去。好的，我们再画一遍。把电源放回去后，应该就是这个样子，对吧？我们就得到了原始电路。

And then we can use the open circuit. open circuit voltage. between A and B. So the open circuit voltage of this two terminal.

然后，我们可以使用开路法。也就是开路电压。在A和B之间。那么，这个两端口的开路电压就是多少呢？

Because this is open, so there's no current.

因为这里是开路，所以没有电流。

And the voltage

那么电压

the equivalent voltage is actually equals to Vab. This is exactly the open circuit voltage of the two terminals. The Vab is exactly the voltage of this resistor. And we know the current is V.

实际上就等于Vab。这正是这两个端口的开路电压。Vab实际上就是这个电阻上的电压。我们知道电流是I。

The resistor is 4, so we have we get volts.

这个电阻是4欧姆，所以我们得到4伏特。

Is the first step clear?

第一步清楚了吗？

Okay, don't forget the last step. draw the circuit. You should draw the equivalent circuit.

好的，别忘了最后一步。画出电路图。你应该画出等效电路。

Here is a 12 volt. Here is 4 ohm. So for this circuit, you have some series points. So you can find the equivalent series circuit.

这里是12伏特。这里是4欧姆。那么对于这个电路，有一些串联的点。所以你可以找到等效的串联电路。

This is called the first step. because the circuit is already removed. And you mark the terminals A and B.

这被称为第一步。因为电路已经被简化了。然后标记A和B两个端子。

This is called the first step. because the circuit is already removed. And you mark the terminals A and B.

这被称为第一步。因为电路已经被简化了。然后标记A和B两个端子。

And set all sources to zero. Here we only have current source. So we still need to open circuit. And then we find the resultant resistance. It's 12 ohm. The first step, we turn all sources. and find the open circuit voltage. Open circuit voltage is here.

将所有电源置零。这里我们只有一个电流源。所以我们仍然需要开路。然后我们找到等效的电阻。是12欧姆。第一步，我们将所有电源置零，然后求出开路电压。开路电压在这里。

And always remember to draw the equivalent circuit.

一定要记住，要画出等效电路。

Let's go back.

我们回到前面。

Here is another very important point. of Thevenin's theorem.

这里还有一个非常重要的点。就是戴维南定理。

As we know, based on the Thevenin's theorem, we can get the the equivalent voltage and equivalent resistance, right? But here they are ohms. If you have these two items, based on Ohm's law, you can get the corresponding voltage. and current.

我们知道，根据戴维南定理，我们可以得到等效电压和等效电阻，对吧？但在这里，它们的单位是欧姆。如果你有这两个量，根据欧姆定律，就能算出相应的电压。还有电流。

This means once you know the current here,

这意味着，一旦你知道这里的电流，

you know the voltage. you can get the third one.

你就知道电压了。这样就能求出第三个量。

And the third one is, in this equation, the current is defined as charge per second.

第三个量是：在这个公式中，电流被定义为每秒的电荷量。

short-circuit current.

这就是短路电流。

So if you know two parameters, you can find the third one.

所以，如果你知道两个参数，就能求出第三个。

Short-circuit current means you replace the load with a wire.

短路电流的意思是，用一根导线代替负载。

so they are connected together. it's not open.

这样它们就连接在一起了。电路不是断开的。

and the short-circuit current is actually

而短路电流实际上

what we explain or what we introduce in the open circuit.

就是我们在开路部分所解释或介绍的内容。

and the open circuit is exactly the current is zero.

而开路时，电流正好为零。

here you can see the open circuit.

这里可以看到开路的情况。

this is the open circuit. is this equal to the short-circuit?

这就是开路。这等于短路吗？

is the current connected in parallel with a resistance. it's the Norton. It's the first character of Norton.

电流是与电阻并联的。这就是诺顿等效电路。这是诺顿的第一个特征。

and IN is the short-circuit current.

而IN就是短路电流。

and RN is the equivalent resistance. and the current sources are turned off.

而RN是等效电阻。此时，电流源被置零。

you should remove the sources. in independent sources. We have introduced the dependent sources, right? but dependent sources shall not be removed. when you calculating the equivalent resistance.

你应该把电源去掉。这是独立电源。我们之前已经介绍过受控源了，对吧？但是，受控源是不能去掉的。在计算等效电阻时，这一点很重要。

it's a very important point. You must turn off independent sources.

这是一个非常重要的要点。你必须将独立电源置零。

and we also have introduced the dependent sources. dependent sources we use this symbol, right?

同时，我们也介绍了受控电源。受控电源我们用这个符号，对吧？

for example, this voltage is five times the current of the circuit. this is the dependent sources.

比如，这个电压是电路中电流的五倍。这就是受控源。

so for dependent sources, you should not remove. that's the thing.

所以对于受控源，你不能把它去掉。就是这样。

when you look at the source of the circuit, the first three are actually identical.

当你分析电路时，前三个其实是一样的。

it's for the same thing. you set all our source to be zero. voltage source set it to short circuit and current source set it to open circuit. and you find the result of this is this.

它们是相同的。你把所有的源都设为零。电压源要短路处理，电流源要开路处理。然后得到的结果就是这个。

so the first three steps are identical. because the first three steps are identical, so you will get the same resistance. actually, it's the same as the total resistance.

所以前三个步骤是一样的。因为前三个步骤相同，所以你会得到相同的电阻。实际上，这和总电阻是一样的。

as all the first three steps are identical.

因为前三个步骤完全相同。

so you will get the same resistance.

所以你会得到相同的电阻。

and the fourth step is different. and similarly, you return all sources to their original position. and here is different. you find the short-circuit current. not the open-circuit voltage.

而第四步是不同的。同样地，你把所有的电源都恢复到原来的位置。而这里则不同。你需要求出短路电流。而不是开路电压。

open-circuit voltage is the principle or is the first step in the series. but in a Norton's theorem, you find the short-circuit current.

开路电压是串联分析中的第一步或基本原则。但在诺顿定理中，你需要求出短路电流。

and the final step is the same. you should draw the equivalent circuit.

最后一步是一样的。你需要画出等效电路。

Maybe let's do one example.

也许我们举个例子吧。

Okay, here.

好的，这里。

That's the finishing example that we can end the class today. So here we have a 10 volts.

这是今天的最后一个例子，讲完这个我们就可以结束这节课了。这里有一个10伏的电源。

voltage source, right? and there is two ohm.

这是一个电压源，对吧？还有一个2欧姆的电阻。

Okay, for the Norton's theorem, at first, we remove the load.

好的，对于诺顿定理，首先，我们要把负载去掉。

the load is already removed. so we don't have to do it. second, we mark terminal. we mark it A and B.

负载已经去掉了。所以我们不需要再做这一步了。第二，我们标记端子。我们把它标记为A和B。

third step is, we set all sources to zero. for the voltage source, we set it to short circuit.

第三步是，将所有电源置零。对于电压源，我们将其设为短路。

this is for voltage source.

这是针对电压源的。

sorry, below should be no.

抱歉，下面应该是“不”。

it's short circuit like this. then we calculate the resistance. what are the resistance?

就像这样短路。然后我们计算电阻。电阻是多少？

actually they are identical. because the first and the second are identical.

实际上，它们是相同的。因为第一个和第二个是一样的。

so the equivalent resistance is just the resistor, 2 ohm. and the first step is we return the source to the original position. and we can build a short circuit current.

所以等效电阻就是2欧姆。第一步，我们回到电源的原始位置。然后我们可以计算短路电流。

so the short circuit current of this terminal. we connect them together. They are short circuit. and what is the current here?

也就是这个端口的短路电流。我们把它们连接在一起。这就是短路。那么这里的电流是多少？

so i n, if we connect them together, the current is the voltage it times. divided by 2 ohm. so we will get current.

所以In，如果我们把它们连接起来，电流是电压乘以时间。除以2欧姆。这样我们就能得到电流。

and finally, don't forget to draw the circuit. you have a current source and you connect in parallel.

最后，别忘了画出电路图。这里有一个电流源，并且是并联连接的。

this is Norton's theory.

这就是诺顿定理。

five ampere.

5安培。

and two ohm.

还有2欧姆。

okay, so the practice. Any questions?

好的，这就是练习部分。有什么问题吗？

okay, no question. so that's for today.

好的，没有问题。那么今天就到这里。

This is a typical closed-loop system. In a closed-loop system, the output is fed back through a feedback path with gain h.

这是一个典型的闭环系统。在闭环系统中，输出通过增益为 h 的反馈路径进行反馈。

Once you know the error, the error will be given to the amplifier or controller system. This controller system has a gain of G. So the input is the error, and the gain is G, so you will get E times G as output. The output is given to the feedback system, and then calculate the error. So you will get these two equations, and based on these two equations, you can again calculate the transfer function for the closed-loop system.

一旦知道了误差，该误差将被送入放大器或控制器系统。这个控制器系统的增益为G。因此输入是误差，增益是G，所以你会得到E乘以G作为输出。输出被送入反馈系统，然后计算误差。这样你就得到了这两个方程，基于这两个方程，你可以再次计算闭环系统的传递函数。

Different control systems have different damping values. If the system has very high damping, its output will converge to the reference value. But if the plant has very...

不同的控制系统具有不同的阻尼值。如果系统具有很高的阻尼，其输出将收敛到参考值。但如果被控对象具有很……

This is a property of the system. We have a regulator and a servo. The regulator represents the cancelled output, so the output is zero.

这是系统的一个性质。我们有一个调节器和一个伺服机构。调节器代表被抵消的输出，因此输出为零。

There is a reference model which is changing over time, and the objective is to try to input with more error. For S4B, we had a new vector. Now we are at the beginning of iteration six.

存在一个随时间变化的参考模型，其目标是尝试以更大的误差进行输入。对于S4B，我们得到了一个新的向量。现在我们已经进入第六次迭代的开始。

When you look at the title, it is social regulation. You probably have not heard of social regulation, but for the same thing, normative theory—these are formal in nature. You must understand what normative theory is. In terms of energy, we already know energy; energy can be sustainable or not.

当你看到这个标题时，它是社会规制。你可能没有听说过社会规制，但与此相关的是规范理论——这些在性质上是正式的。你必须理解什么是规范理论。就能源而言，我们已经知道能源；能源可以是可持续的，也可以不是。

There are different types of energy. Energy is power times time. Power has a unit of watts, and time is in seconds. Power times time gives us energy.

能量有不同的类型。能量等于功率乘以时间。功率的单位是瓦特，时间的单位是秒。功率乘以时间即为能量。

Energy can also be measured in kilowatt-hours. One kilowatt-hour equals one thousand watts times one hour—that is, power times time. Another unit for energy is the kilocalorie. There are different types of energy: kinetic energy, potential energy, thermal energy, chemical energy, and electrical energy.

能量也可以用千瓦时报来衡量。一千瓦时报等于一千瓦乘以一小时，即功率乘以时间。能量的另一个单位是千卡。能量有多种类型：动能、势能、热能、化学能和电能。

For example, polarity is also a kind of flow of energy. We have also introduced electric charge. The unit is called coulomb, represented by C, to denote the unit of electric charge. Electric charge has two types: positive and negative. If they have different polarity, they will attract each other; if they have the same polarity, they will repel each other.

例如，极性也是一种能量的流动。我们还介绍了电荷。电荷的单位叫做库仑，用C表示。电荷有两种类型：正电荷和负电荷。如果极性不同，它们会相互吸引；如果极性相同，它们会相互排斥。

An electric charge is the reason we can have current. If an electric charge is moving, we will have current. So current is the time rate of change of charge. We have already introduced this equation: current is dq over dt, where dq is the change of charge and dt is the time rate.

电荷是产生电流的原因。如果电荷在移动，就会产生电流。因此，电流是电荷随时间的变化率。我们已经引入了这个公式：电流等于 dq 除以 dt，其中 dq 是电荷的变化量，dt 是时间变化率。

Current has the unit ampere. Charge has the unit coulomb divided by second, so one ampere equals one coulomb per second. DC stands for direct current. Direct current means the current is constant—it does not change over time. That is in contrast to alternating current.

电流的单位是安培。电荷的单位是库仑除以秒，因此一安培等于一库仑每秒。DC代表直流电。直流电意味着电流是恒定的——它不随时间变化。这与交流电形成对比。

Voltage—we also use this term multiple times. The movement of electrons will produce current. But how can we make the electron move? We need to add work or transfer energy.

电压——这个术语我们也多次使用。电子的运动将产生电流。但我们如何让电子运动呢？我们需要对电子做功或传递能量。

This work or energy is needed to make an electron move. The work or energy is, in theory, performed by electromotive force, or EMF. We have also seen this symbol for EMF. Electromotive force is also a source—it can be a voltage source or a current source. That is the reason why, once an electron moves, you get current.

使电子运动需要做功或消耗能量。从理论上讲，这个功或能量是由电动势（EMF）提供的。我们也已经见过电动势的符号表示。电动势本身也是一种电源——它可以是电压源，也可以是电流源。这就是为什么一旦电子开始运动，就会产生电流的原因。

Electromotive force is typically from a battery. A battery is an energy source. Electromotive force is also known as voltage or potential difference.

电动势通常来自电池。电池是一种能量源。电动势也称为电压或电势差。

The potential difference, the voltage difference between A and B, is the energy needed to move a unit charge from A to B. In order to move a charge from A to B, you must apply an energy. That's the reason we have the movement of the electron.

A与B之间的电势差，即电压差，是将单位电荷从A移动到B所需的能量。为了将电荷从A移动到B，你必须施加能量。这就是电子发生移动的原因。

W is the symbol for energy, and Q is the symbol for electric charge. Once you apply energy to an electric charge, you get voltage. The unit of voltage is Volt, the unit of energy is Joule, and the unit of charge is Coulomb. So when you divide Joule by Coulomb, you get Volt.

W 是能量的符号，Q 是电荷的符号。一旦对电荷施加能量，就得到电压。电压的单位是伏特（Volt），能量的单位是焦耳（Joule），电荷的单位是库仑（Coulomb）。因此，将焦耳除以库仑，就得到伏特。

Power is the time rate of change of energy. W is energy, so dW represents the change of energy. The time rate is dt. Therefore, power can be represented as dW divided by dt.

功率是能量对时间的变化率。W 表示能量，因此 dW 代表能量的变化量。时间变化率为 dt。所以功率可以表示为 dW 除以 dt。

V divided by Z gives us the current I. So V over Z is the voltage, and I equals V over Z is the current. The power P equals voltage times current. This is the final formula for power. Once you know the current and once you know the voltage, you can multiply them together to get the power.

电压V除以阻抗Z得到电流I。V除以Z是电压，I等于V除以Z是电流。功率P等于电压乘以电流。这就是功率的最终公式。一旦知道了电流和电压，就可以将它们相乘得到功率。

In the other tutorial, you will draw a circuit. A circuit usually includes several elements. Let us first look at the first element: a voltage source. You already know this symbol. You can use this symbol to represent a voltage source in your circuit. Sometimes we also use this symbol to represent a voltage source.

在另一节习题课中，你们将会绘制电路。一个电路通常包含若干元件。我们先来看第一个元件：电压源。你们已经认识这个符号了。你们可以用这个符号来表示电路中的电压源。有时我们也用这个符号来表示电压源。

We represent what is stored. At the end, you can see there are different types of symbols that can be used to represent what is stored. We also know there is an ideal what is stored. Ideally, the voltage should remain the same across these terminals, no matter how much current is drawn from these terminals.

我们表示所存储的内容。最后可以看到，有不同类型的符号可以用来表示所存储的内容。我们还知道存在一种理想的存储表示。理想情况下，无论这些端子抽取多少电流，其两端电压都应保持不变。

No matter how deep the load is, the voltage is maintained at the same value. This requires the voltage source to have zero internal resistance. Because if there is no internal resistance, there will be no voltage drop.

无论负载多深，电压都保持在同一值。这要求电压源具有零内阻。因为如果没有内阻，就不会有电压降。

There will be no potential drop for the internal resistance. And for this part, I also want to mention that it has been produced as an ideal ammeter. What is the…

内阻上不会有电势降落。对于这一部分，我还想提到它被当作理想电流表来处理。什么是……

Resistance. Ideal ammeter. Can you still remember the ideal ammeter? In our last lecture, we also introduced the ideal ammeter and the ideal voltmeter.

电阻。理想电流表。你们还记得理想电流表吗？在上一次课中，我们也介绍了理想电流表和理想电压表。

An ammeter and a voltmeter are used to measure current and voltage. We also introduce the ideal ammeter and the ideal voltmeter. In that case, we also have to define whether the internal resistance should be zero or should be infinite.

电流表和电压表分别用于测量电流和电压。我们还引入了理想电流表和理想电压表的概念。在这种情况下，我们还需要定义其内阻应为零还是应为无穷大。

[No substantive lecture content detected in this segment. The audio consists primarily of non-speech sounds including shuffling, movement, throat clearing, and breathing.]

[该时间段内未检测到实质性讲课内容。音频主要由非语音声音组成，包括翻动声、移动声、清嗓子和呼吸声。]

[No intelligible lecture content detected in this segment; only background noise, shuffling, and non-verbal sounds.]

[该时间段内未检测到可辨识的授课内容；仅有背景噪音、翻动声及非语言声音。]

Our notes are on Blackboard so everybody can see it together. We are about to begin the lecture.

我们的笔记在Blackboard上，这样大家都能一起看到。我们即将开始讲课。

We have introduced the ideal ammeter. Do you still remember what the structure inside of an ammeter looks like? It looks like this. This is the inside structure of an ammeter. Normally, we do not have an ideal ammeter because…

我们已经介绍了理想电流表。大家还记得电流表内部的结构是什么样的吗？就是这样的。这是电流表的内部结构。通常我们并没有理想电流表，因为……

In order to have an ideal ammeter, there will be a resistor connected in parallel with the internal resistance.

为了得到一个理想电流表，需要在内阻上并联一个电阻。

This resistor should be zero. Because this resistor is zero, you will get zero total resistance when there is no voltage drop. There is no voltage drop when you connect the ammeter with the circuit, because you use this ammeter to measure current in the circuit.

这个电阻应该为零。因为这个电阻为零，当没有电压降时，总电阻为零。当你将电流表接入电路时，没有电压降，因为你是用这个电流表来测量电路中的电流。

The ammeter should not affect the original circuit. It should have no influence on the circuit. In this case, there should be no voltage drop by the ammeter. This means we should have an ideal ammeter with zero resistance inside. And similarly for the voltmeter: you have a resistor here, and this is the internal resistance. And this resistor should be infinite.

电流表不应影响原电路，它对电路不应产生任何影响。在这种情况下，电流表上不应有电压降。这意味着我们应该使用一个理想电流表，其内部电阻为零。类似地，对于电压表：这里有一个电阻，这就是内阻。而这个电阻应为无穷大。

This is to extend the range of the measuring instrument. Because if you don't have this resistor, you probably can only measure, for example, 30 microvolts. But if you connect with this resistor, you probably can measure 30 volts. That's the reason we have the resistor here—to extend the measuring range. And for the ideal case, this is the voltmeter.

这是为了扩展测量仪器的量程。因为如果没有这个电阻，你可能只能测量例如30微伏。但如果你接上这个电阻，你可能就能测量30伏。这就是我们在这里放这个电阻的原因——扩展测量量程。对于理想情况，这就是电压表。

For an ideal voltmeter, why is its resistance infinite? Because the voltmeter is connected in parallel with the object you want to measure. When you want to measure the voltage of a resistor, you connect your voltmeter in parallel with the subject you want to measure.

对于理想电压表，为什么其电阻为无穷大？因为电压表是与被测对象并联连接的。当你想要测量一个电阻的电压时，你需要将电压表与被测对象并联连接。

In order not to influence the original circuit, there should be no current flowing in this branch. If there is current flowing in this branch, you will get an inaccurate voltage, because the current is used by that branch. This is what we want to avoid. So there should be no current flowing in this branch. In order to make no current flow in this branch, this resistor should have infinite impedance.

为了不影响原始电路，该支路中不应有电流流过。如果该支路中有电流流过，你将得到一个不准确的电压，因为电流被该支路所消耗。这正是我们要避免的情况。因此，该支路中不应有电流流过。为了使该支路中没有电流流过，这个电阻应具有无穷大的阻抗。

An ideal current source has infinite internal resistance. Why should it have infinite internal resistance?

理想电流源具有无穷大的内阻。为什么理想电流源的内阻应该是无穷大？

For an ideal current source, we use this symbol. This current source provides current for the circuit. For example, there is a node here. The current source provides, for example, one ampere for the circuit. Normally, a current source also has internal resistance, and the internal resistance is…

对于理想电流源，我们使用这个符号。该电流源为电路提供电流。例如，这里有一个节点。电流源为电路提供例如一安培的电流。通常，电流源也具有内阻，而内阻是……

This whole part — these two parts together — is a current source. For an ideal current source, there should be no current flowing through this resistance.

这一整部分——这两个部分合在一起——是一个电流源。对于理想电流源，不应有电流流过这个电阻。

No resistance would be idealized as very large. One is already thin; one is flowing below, current flowing in front, and all currents are flowing through the node. This is what we want to achieve. So for internal—internal to be... And here we introduce another very important concept.

零电阻可理想化为极大值。其中一个已经很薄；一个在下方流动，电流在前方流动，所有电流都流经该节点。这正是我们要实现的目标。因此对于内部——内部而言……在这里我们引入另一个非常重要的概念。

Before I use this slide, I want to define the voltage source. This is the symbol for the voltage source. If you have a load, this is the load. There is an internal resistance — this is the internal resistance of the source. These two parts together constitute the voltage source.

在使用这张幻灯片之前，我想先定义电压源。这是电压源的符号。如果你有负载，这就是负载。存在一个内阻——这是电源的内阻。这两部分共同构成了电压源。

If we want to get an ideal voltage source, the internal resistance should be zero. Because if it is zero, there will be no voltage drop, and all the voltage will be given to the load. So that's the reason it must have zero internal resistance.

如果我们想要得到一个理想电压源，其内阻应为零。因为如果内阻为零，就不会有电压降，所有电压都将施加到负载上。这就是它必须具有零内阻的原因。

We have dependent sources, but we should first discuss a new concept, which I will refer to later in this book. A dependent source means the source is not attached to the model; it depends on a parameter of the circuit. Normally, for example, for independent...

我们有受控源，但首先需要讨论一个新概念，我会在本书后面再提及。受控源意味着该电源不依附于模型本身，而是取决于电路中的某个参数。通常，例如对于独立……

For independent sources, for example, we have a 4–5 V for the voltage source, and we have 2 A for the current source. This is an independent source. But for a dependent source, it means the source is dependent on a parameter of the circuit. Here is an example: the voltage here is dependent on the current in the circuit. So if the circuit, for example, has 1 A current—

对于独立源，例如，电压源为4到5伏，电流源为2安培，这就是独立源。但对于受控源，意味着该源依赖于电路中的某个参数。这里有一个例子：这里的电压取决于电路中的电流。所以如果电路中，例如，有1安培的电流——

Then the voltage source will produce 5 volts. But if the circuit has 2 ampere current, the voltage source will produce 10 volts. So the value of the source changes depending on the parameter of the circuit. Once the circuit has different currents, the source will also produce different voltages. This is a dependent source.

那么电压源将产生5伏特。但如果电路中有2安培电流，电压源将产生10伏特。因此，电源的值取决于电路的参数而变化。一旦电路中的电流不同，电源也将产生不同的电压。这就是受控源。

Sometimes the source produces power to the outside load. Sometimes the source absorbs power from the outside.

有时电源向外负载输出功率，有时电源从外部吸收功率。

When you charge your phone or laptop, the battery is absorbing power. But if you don't use the charger, your laptop or phone will produce power for the device. How can we define the corresponding sign for absorbing power and supplying power?

当你给手机或笔记本电脑充电时，电池在吸收功率。但如果你不使用充电器，笔记本电脑或手机会向设备提供功率。我们如何定义吸收功率和提供功率的对应符号？

Here is the definition. If we assign a positive sign to the voltage, the current enters the positive polarity of the voltage across an element.

以下是定义。如果我们对电压赋予正号，则电流从元件两端电压的正极性端流入。

For the left figure, the voltage source is providing current to the voltage drop. This means—

对于左图，电压源正在向电压降提供电流。这意味着——

This means this resistor, this node is absorbing power. The current enters here. The absorbing and supplying is for the resistor.

这意味着这个电阻，这个节点正在吸收功率。电流从这里流入。吸收和供给是针对电阻而言的。

Under the output polarity of the voltage, in this figure, the current is in this direction, to the right, and the current is leaving the output polarity of this element. So you have a negative sign.

在电压的输出极性下，在这张图中，电流方向是向右的，而电流是从该元件的输出极性端流出的。因此你得到一个负号。

The left figure: the power series enters the positive parity of x, so it has a positive sign. Once it has a positive sign, this element is absorbing power. For the right figure, the element is applying power. Is it clear?

左图：幂级数进入x的正奇偶性，因此它具有正号。一旦具有正号，该元件吸收功率。对于右图，该元件施加功率。清楚了吗？

From my understanding, this is not a load. It is not classified as resistance. It is an element. I do not know exactly what it is, but it is just an element. Here is a box beam.

据我理解，这不是一个荷载。它不被归类为阻力。它是一个构件。我不确定它具体是什么，但它就是一个构件。这里是一根箱梁。

This is one element in a circuit. Once the current looks like this, if the current direction is to the left, then the current is entering...

这是电路中的一个元件。当电流看起来像这样时，如果电流方向是向左的，那么电流正在进入……

Here is the positive polarity of this element; this is the negative polarity of this element. If the current is entering the positive polarity of this element, it has a positive sign according to the definition. This is the direction of the current, and this is the positive polarity. This is just one element. If the current enters the positive polarity—

这是该元件的正极性端，这是负极性端。如果电流从该元件的正极性端流入，根据定义，它取正号。这是电流的方向，这是正极性端。这只是一个元件。如果电流从正极性端流入——

For elements with a positive sign, and for the second case, here we have sphere one element. We know the current is leaving the positive polarity. Here is the positive polarity, here is the negative polarity. Since the current is leaving the positive polarity, it has a negative sign.

对于具有正号的元件，以及第二种情况，这里是球面一元件。我们知道电流从正极性端流出。这里是正极性，这里是负极性。由于电流从正极性端流出，因此它取负号。

When the current is entering this element, it is absorbing power. When the current is leaving this element, this element is supplying power. Here is an example.

当电流进入该元件时，该元件吸收功率。当电流离开该元件时，该元件提供功率。下面举一个例子。

Let's just go over this example quickly. I've done similar exercises multiple times. You just use Ohm's law to get the current, and then you can compute the energy. Once you know the current and the voltage, you can compute the power. Power times the time — here you know six hours, right? Six hours is the time.

我们快速过一下这个例题。类似的练习我已经做过很多次了。你只需要用欧姆定律求出电流，然后就可以计算能量。一旦知道了电流和电压，就可以计算功率。功率乘以时间——这里已知是六小时，对吧？六小时就是时间。

Power multiplied by time gives you energy. Energy is measured in watt-hours. Then you can calculate the total cost. Here you should pay attention: the watt-hour is also a unit for energy. We normally use joules for energy, but sometimes we also use watt-hours.

功率乘以时间得到能量。能量的单位是瓦时。然后你可以计算总费用。这里需要注意：瓦时也是能量的一个单位。我们通常用焦耳来表示能量，但有时也用瓦时。

Watt-hour. Because energy is equivalent to power times time. Here you have the unit volt, and here you have seconds, for example. So watt-hour is also a unit for energy, not only joules. Now for the solution: you know the voltage across each resistor, and you know the resistance for each resistor. Based on Ohm's law, you can get the current. And since power is equivalent to voltage times current, you can get the power for each resistor.

瓦时。因为能量等于功率乘以时间。这里单位是伏特，这里单位是秒，举例来说。所以瓦时也是能量的单位，不仅仅是焦耳。现在来求解：你知道每个电阻两端的电压，也知道每个电阻的阻值。根据欧姆定律，可以求出电流。又因为功率等于电压乘以电流，所以可以求出每个电阻的功率。

Multiply the power of each resistor and use the power times the time. You will get the energy. And the energy unit is cost, right? Cost is one kilowatt-hour. So you can get the total cost. Basically, Ohm's law states that the voltage across a resistor is directly proportional to the current flowing through the resistor.

将每个电阻的功率乘以时间，即可得到能量。能量的单位是度（cost），一度等于一千瓦时。因此可以算出总费用。基本上，欧姆定律指出：电阻两端的电压与流过该电阻的电流成正比。

From this equation, voltage is proportional to current because resistance is constant. We also have another equation: a conductor of a certain material has a certain length L and a certain cross-sectional area A. ρ is the resistivity, and it is given—you do not have to memorize it.

由该方程可知，电压与电流成正比，因为电阻是恒定的。我们还有另一个方程：某种材料的导体具有确定的长度 L 和确定的横截面积 A。ρ 是电阻率，它是已知的——你不需要去记忆它。

Different materials have different resistivities. Resistivity is denoted by ρ (rho). The law governing resistance states that resistivity determines the resistance of a material; given the cross-sectional area and the length, you can calculate the resistance of that material. There are two types of representations for resistance. Now, here are three different units—three completely new definitions: ohm·cm, ohm·m, and ohm·m². What is the difference among these three?

不同材料具有不同的电阻率。电阻率用符号 ρ（rho）表示。决定电阻的规律是：电阻率决定了材料的电阻；已知横截面积和长度，就可以计算该材料的电阻。电阻有两种表示方式。接下来介绍三种不同的单位——三个全新的定义：欧姆·厘米、欧姆·米和欧姆·平方米。这三者之间有什么区别？

A branch is a part or section of a circuit which is located between two junctions and contains a single element. To identify a branch, you must first find two junctions, and there is an element in between the two.

支路是电路中位于两个节点之间且仅包含一个元件的部分或区段。要确定一条支路，首先必须找到两个节点，两者之间存在一个元件。

This is a branch. Here is a branch. But the second one is not a branch because there is no element in between. This is the definition. Here you can also find a branch because there is an element. The element can either be a resistor or a source. Here is a current source. This branch also contains one element in between, so this is also a branch.

这是一条支路。这里也是一条支路。但第二条不是支路，因为中间没有元件。这就是定义。这里你也可以找到一条支路，因为中间有一个元件。该元件可以是电阻，也可以是电源。这里是一个电流源。这条支路中间也包含一个元件，所以这也是一条支路。

Even though an element is a current source, it doesn't matter whether it's a current source or a resistor. Only if the element is included in the branch reactions, it is a branch. Nodes: points or junctions where two or more circuit elements meet.

即使一个元件是电流源，它究竟是电流源还是电阻并不重要。只有当该元件包含在支路反应中时，它才构成一条支路。节点：两个或更多电路元件相交的点或连接处。

A node is where two or more elements meet. The elements can be, for example, resistors, capacitors, inductors, or even sources. When two elements meet together, you have one node. In other words, a point of connection between two or more branches is known as a node.

节点是两个或多个元件交汇之处。这些元件可以是电阻、电容、电感，甚至是电源。当两个元件交汇在一起时，就形成一个节点。换句话说，两条或多条支路之间的连接点称为节点。

Once two elements are knitted together, you get one node. Third definition: nodes. If there is no element between two or more adjacent nodes, these nodes can be combined as a single node. We know that a node is two elements knitted together. So you have one node here, and you have one node here, because two elements are knitted together. But for the nodes at the bottom...

两个元素编织在一起，就得到一个节点。第三个定义：节点。如果两个或多个相邻节点之间没有元素，这些节点可以合并为一个节点。我们知道，一个节点就是两个元素编织在一起。所以这里有一个节点，这里也有一个节点，因为两个元素编织在了一起。但是对于底部的节点……

If there are no elements between two nodes, they can be combined together. A loop is any closed path in an electrical circuit that starts and ends at the same node.

如果两个节点之间没有元件，它们可以合并在一起。回路是电路中从同一节点出发并最终回到该节点的任意闭合路径。

A cycle does not pass through any node more than once. Let's have a look at how many nodes we have in this circuit. I will draw the answer here.

一个环不经过任何节点超过一次。我们来看看这个回路中有多少个节点。我把答案画在这里。

A loop is a closed path. First, it should be closed. It starts and ends at the same node. This is one node, right?

回路是一条闭合路径。首先，它必须是闭合的。它从同一个节点出发，又回到同一个节点。这是一个节点，对吧？

These three elements are actually one node. There is no element depending on them separately, so they can be combined as one node. The elements at the bottom are also one node. Now let us look at the definition. First, it should be a closed path, and then it should start and end at the same node. So let us start from here—it should be a closed path.

这三个元素实际上是一个节点。没有任何元素单独依赖于它们，因此可以将它们合并为一个节点。底部的元素也是一个节点。现在我们来看定义。首先，它应该是一条闭合路径，然后它应该在同一个节点处开始和结束。所以我们从这里开始——它应该是一条闭合路径。

Go to this node, and then this node, and go back again. So you start here, pass that, and you pass every node just once. You pass every node just once. So this is the first loop. And similarly, you can have a loop here, or you can loop here and loop here. It's also a loop. And you can also draw a bigger loop. For example, you start here and then go here.

到达这个节点，然后到这个节点，再返回。所以从这里出发，经过那个节点，每个节点只经过一次。每个节点只经过一次。这就是第一个环。类似地，你可以在这里有一个环，或者在这里绕一圈、在那里绕一圈。这也是一个环。你还可以画一个更大的环。例如，从这里出发，然后到这里。

Hopefully you can get the solution like this: given at corners of the elements and given at nodes. Great. Here is something interesting for the problem.

希望大家能理解这样的解：在单元角点处给定，在节点处给定。好，接下来是关于这个问题的一个有趣的内容。

Branches represent a single element. As we defined it, a branch should contain one element. And then we have a node. Here, these three can be combined together as part of a whole—six combined together.

分支代表单个元素。根据我们的定义，一个分支应包含一个元素。然后我们有一个节点。在这里，这三个可以组合在一起作为整体的一部分——六个组合在一起。

And we have the loops, which should be a closed path, and a task, every node, just one. And there is an interesting relation. So B is the number of branches, L is the number of loops, N is the number of nodes. They have this relation. So for a circuit, once you know the number of loops and you know the number of nodes, you can get the number of branches. Or if you know the number of branches and the number of loops, you can get the number of nodes.

我们有回路（loops），即闭合路径，以及任务（task），每个节点对应一个。它们之间存在一个有趣的关系。B是支路数，L是回路数，N是节点数。它们满足这个关系。因此对于一个电路，一旦你知道回路数和节点数，就可以求出支路数。或者如果你知道支路数和回路数，就可以求出节点数。

Once we have three equations, let's look at this circuit again. In this circuit, how many branches do we have? A branch contains one element. So how many elements do we have? One resistor, a second resistor, a third resistor, and a voltage source — that gives us five branches. And how many nodes? We have three nodes.

有了三个方程之后，我们再来看这个电路。在这个电路中，有多少条支路？一条支路包含一个元件。那么有多少个元件呢？一个电阻、第二个电阻、第三个电阻，再加上一个电压源——一共五条支路。那有多少个节点呢？我们有三个节点。

These three combine; all three nodes also combine, so we have three nodes. Once you use this equation, you can get the number of loops is three. But when you count the number here, it is not three—it is more than three. We have one, two, three, four, five, six. We have six loops here, but the equation only gives three. This is because the three here means independent loops.

这三个合并在一起；三个节点也全部合并，所以我们得到三个节点。一旦使用这个方程，就可以得到回路数为三。但是当你在这里手动计数时，并不是三——而是多于三。我们有一个、两个、三个、四个、五个、六个。这里共有六个回路，但方程只给出三。这是因为这里的三指的是独立回路。

What is an independent loop? An independent loop is a loop that contains at least one branch that is not a part of any other independent loop. For example, in this figure, the blue loop is a part of the green loop. That is the reason they are not independent.

什么是独立回路？独立回路是指至少包含一条不属于任何其他独立回路的支路的回路。例如，在这张图中，蓝色回路是绿色回路的一部分，这就是它们不独立的原因。

The small blue loop is a part of the green one. That is the reason it is not an independent loop. For the independent loops, the three small loops in the middle—this is exactly our independent loop. This is also independent because there is no loop inside; it is not a part of any other loops.

小蓝色回路是绿色回路的一部分，这就是它不是独立回路的原因。对于独立回路，中间的三个小回路正是我们的独立回路。它也是独立的，因为内部没有其他回路，它不是任何其他回路的一部分。

Three independent conditions you have. For each independent — this is one independent, this is the second independent — for each independent you can obtain one equation.

你有三个独立条件。对于每一个独立条件——这是一个独立条件，这是第二个独立条件——对每个独立条件你都可以得到一个方程。

The first loop is A-B-C-A; this is the independent loop. The second is D-E-C-D; this is the loop in the middle, containing R2 and R3, with R1 and R3 in the middle. The third, involving the R1 source and R3, is the loop at the right.

第一个回路是A-B-C-A，这是独立回路。第二个是D-E-C-D，这是中间的回路，包含R2和R3，中间有R1和R3。第三个涉及R1电源和R3，是右侧的回路。

These two R3s can be joined together, and these four can be joined together, so the circuit can be simplified to this version. Finally, you will see that R1 is connected in series with the voltage source, and R2 and R3 are in parallel with the current source.

这两个R3可以合并在一起，这四个也可以合并在一起，因此电路可以简化为这个版本。最后你会看到，R1与电压源串联，R2和R3与电流源并联。

As we have mentioned before, voltage sources are non-ideal because they have internal resistance. This is the actual case in the real world — every source has internal resistance, so they are non-ideal. The internal resistance can be modeled as being in series with the source.

正如我们之前提到的，电压源是非理想的，因为它们具有内阻。这是现实世界中的实际情况——每个电源都有内阻，因此它们都是非理想的。内阻可以建模为与电源串联。

A power source has internal resistance connected in parallel with the power source. These two circuits represent real sources in the real world. Voltage regulation is actually very similar to efficiency. The definition of efficiency is output power divided by input power. Voltage regulation has exactly a similar definition. This means in reality, the load cannot get full voltage from the source.

电源具有与电源并联的内阻。这两个电路代表了现实世界中的实际电源。电压调整率实际上与效率非常相似。效率的定义是输出功率除以输入功率。电压调整率具有完全相似的定义。这意味着在现实中，负载无法从电源获得全部电压。

In a real voltage source, because of the internal resistance, there is always a voltage drop. It can be very small, but there is still a voltage drop. For an ideal source, there is no voltage drop, so the voltage regulation is zero, because the load can get completely the voltage from the source.

在实际电压源中，由于内阻的存在，始终存在电压降。这个电压降可能非常小，但仍然存在。对于理想电源，没有电压降，因此电压调整率为零，因为负载可以从电源获得完整的电压。

But in reality, the load gets less voltage. We have introduced before that a voltage source is modeled as a voltage connected in series with an internal resistance. And here you connect...

但实际上，负载获得的电压会更低。我们之前已经介绍过，电压源可以建模为一个电压与一个内阻串联。而在这里你连接……

The source has no load. Because of this internal resistance, you cannot transfer the full voltage to the load. There is always a small voltage drop here. If the internal resistance is smaller, you will get more output, because the voltage drop is smaller. A smaller internal resistance gives a smaller voltage drop.

电源没有接负载。由于存在内阻，你无法将全部电压传输给负载，这里始终会有一个小的电压降。如果内阻更小，你就能获得更多的输出，因为电压降更小。更小的内阻意味着更小的电压降。

With voltage regulation, you get more reactive power. That is the reason why the internal resistance will be zero. How can we compute the voltage regulation? The voltage regulation is V no-load minus V full-load.

在电压调整率方面，你会得到更多的无功功率。这就是内阻为零的原因。我们如何计算电压调整率？电压调整率等于空载电压减去满载电压。

Voltage regulation is defined as the no-load voltage minus the full-load voltage, divided by the no-load voltage. This is the definition. For this circuit, you have Vt, which is the terminal voltage. If there is no load here, what is the voltage at this terminal? This is the no-load voltage. And if we connect a terminal with a load, what is the voltage here? You get the full-load voltage. Divided by the no-load voltage, you get the voltage regulation. So voltage regulation is between full load and no load of a power supply.

电压调整率的定义为空载电压减去满载电压，再除以空载电压。这就是其定义。对于这个电路，Vt 是端电压。如果这里没有接负载，该端子的电压是多少？这就是空载电压。如果我们接上负载，这里的电压是多少？得到的是满载电压。再除以空载电压，就得到电压调整率。因此，电压调整率反映的是电源在满载与空载之间的差异。

Power supply. The difference between the voltage of no-load and the voltage of full-load is because of the internal resistance. So you can get this equation: the voltage of no-load minus the voltage of full-load.

电源。空载电压与满载电压之间的差异是由内阻造成的。因此可以得到这个方程：空载电压减去满载电压。

The voltage drop is the current times the internal resistance. Finally, you can get that the voltmeter reading is actually the voltage measurement across the internal resistance divided by the internal resistance times 100. For the ideal voltmeter, the internal resistance is zero, so you will get...

电压降等于电流乘以内阻。最终可以得到，电压表读数实际上是内阻两端的电压测量值除以内阻再乘以100。对于理想电压表，内阻为零，因此你会得到……

For voltage regulation, the Y-axis is voltage and the X-axis is current.

关于电压调整率，纵轴为电压，横轴为电流。

The actual voltage of a load, or the terminal, is the voltage source minus the internal voltage drop. Because of the internal resistance, you have a small voltage drop.

负载（或端子）的实际电压等于电压源减去内部电压降。由于内阻的存在，会产生一个小的电压降。

The x-axis or y-axis is an eigenvector. When r = 0, the slope is minus infinity.

x轴或y轴是特征向量。当 r = 0 时，斜率为负无穷。

The voltage regulator has some applications. For example, if there is a very large machine, such as a motor, and the machine is turned on, the demand for power is suddenly a lot higher because of the machine. So the voltage regulator compensates for the change in load.

稳压器有一些应用场景。例如，如果有一台非常大的机器，比如电动机，当机器启动时，由于机器的缘故，对功率的需求会突然大幅增加。因此，稳压器会对负载的变化进行补偿。

To ensure the output voltage remains constant. Most regulators are used in devices such as air conditioners, refrigerators, etc., protecting them from fluctuating input voltage. We know here that a voltage source has internal resistance and a negative terminal. And you can connect…

以确保输出电压保持恒定。大多数稳压器用于空调、冰箱等设备中，保护它们免受输入电压波动的影响。我们知道，电压源具有内阻和负极端子。你可以连接……

Different devices have different loads or different resistances. So the output voltage will be changed depending on all the resistance, because the current changes, so the output voltage changes.

不同设备具有不同的负载或不同的电阻。因此，输出电压会根据总电阻的变化而改变，因为电流发生了变化，所以输出电压也随之改变。

The final outputs, or the final values of the system, are determined by the exact type of potential that air conditioners operate with—specifically, from creating input voltages. We need to make sure that the final output voltage remains constant. This voltage signal can be what you have in open-loop control, or more precisely, in closed-loop control.

系统的最终输出，即最终值，由空调运行所依赖的确切电位类型决定——具体而言，来自产生输入电压。我们需要确保最终输出电压保持恒定。这种电压信号可以出现在开环控制中，或者更准确地说，出现在闭环控制中。

In this system, you have a controller and a control system. The control system in this case is the regulator—the body serves as the regulator. You also have the output of the body. The controller adjusts the output of the body according to the load, which here is the air conditioner or ventilation. When the load changes, the output of the body changes accordingly. The input of the body is 224. The controller connects the output with the air conditioner, and the output drops to 220. Then you have the error, and there is a feedback system. If you find a difference of 40, then you should use the regulator.

在这个系统中，你有一个控制器和一个控制系统。此处的控制系统就是调节器——人体充当调节器。你还有人体的输出量。控制器根据负载来调节人体的输出量，这里的负载是空调或通风设备。当负载变化时，人体的输出量也随之变化。人体的输入量为224。控制器将输出量与空调相连接，输出量降至220。然后你就得到了误差，这里存在一个反馈系统。如果发现40的差值，那么就应当使用调节器。

A regulator can control the output, making sure the output is always 400 volts. So the voltage regulator is a closed-loop control system that we have introduced. In the real world, regulators usually consist of a relay. We use a relay in the voltage regulator, but the relay has also created a problem: the relay can create sparks when it is closed.

调节器可以控制输出，确保输出始终为400伏。因此，电压调节器是我们已经介绍过的闭环控制系统。在现实世界中，调节器通常由继电器组成。我们在电压调节器中使用继电器，但继电器也带来了一个问题：继电器在闭合时会产生火花。

Knowledge is important. The first theory is Savary's theory. The main purpose of Savary's theory is to try to replace—

知识是重要的。第一个理论是萨瓦里理论。萨瓦里理论的主要目的是试图取代——

The main purpose of Thévenin's theorem is to replace a linear two-terminal circuit with an equivalent circuit. The equivalent circuit consists of a voltage source, Vth, where 'th' stands for Thévenin, in series...

戴维南定理的主要目的是将一个线性二端电路替换为一个等效电路。该等效电路由一个电压源组成，记为Vth，其中'th'代表Thévenin（戴维南），串联……

is an RTH system. If you have a very complex circuit, it can be very large. And if you want to compute, for example, the voltage or current for each resistor, for each branch, it can be very time-consuming to solve. So in this case...

是一个RTH系统。如果你有一个非常复杂的电路，它可能非常大。如果你想计算每个电阻、每条支路的电压或电流，求解起来可能非常耗时。所以在这种情况下……

In this case, we can replace this circuit with an equivalent circuit. The equivalent circuit only includes a voltage source Vth, the Thevenin voltage, connected in series with a resistor Rth. The main purpose of Thevenin's theorem is to simplify a very complex and long circuit.

在这种情况下，我们可以将该电路替换为一个等效电路。该等效电路仅包含一个电压源Vth（即戴维南电压），与一个电阻Rth串联。戴维南定理的主要目的是简化一个非常复杂且冗长的电路。

This is all connected to the load. A current can flow through a closed circuit. This equivalent circuit includes a voltage source and a resistor, and they are connected in series.

这些全部连接到负载上。电流可以在闭合回路中流动。这个等效电路包含一个电压源和一个电阻，它们以串联方式连接。

Now the key problem is: how can we obtain the equivalent voltage? How can we obtain the equivalent resistance? These are the key points here. Because if you can get these two values, any linear two-terminal circuit can be simplified to a very simple circuit.

现在关键问题是：如何求得等效电压？如何求得等效电阻？这就是这里的要点。因为如果你能得到这两个值，任何线性二端网络都可以简化为一个非常简单的电路。

Here, linear two-terminal — linear means the circuit is almost always in class a linear two-terminal circuit. There should be no diode or transistor in the circuit. This figure exactly shows the simplification: you have a large linear two-terminal circuit, and it can be replaced by just one voltage connected in series with a resistor.

这里，线性二端——线性意味着电路在课上几乎总是线性二端电路。电路中不应有二极管或晶体管。这张图恰好展示了简化过程：你有一个大型线性二端电路，它可以被替换为一个电压源与一个电阻串联。

This is our equivalent circuit. How can we compute the equivalent voltage and equivalent resistance? Here are the key steps. The first one: you remove the load.

这是我们的等效电路。如何计算等效电压和等效电阻？以下是关键步骤。第一步：移除负载。

approach of network across which Thevenin equivalent is to be found. You remove the load. Here is load. It can be an air conditioner or a television. Suppose that you remove the load. Second, you mark the terminals of the remaining two-terminal network.

求戴维南等效电路的网络方法。首先，移除负载。这里是负载，它可以是空调或电视。假设你移除了负载。其次，标记剩余二端网络的端子。

You make a mark here. These are the two terminals. The terminals here. We set all sources to zero. There is one current source here and one voltage source here. We set all sources to zero. How can we set them to zero? For the voltage source, it is set to short circuit. Short circuit means we replace the voltage source with a wire, so it is just connected.

你在这里做一个标记。这是两个端子。这里的端子。我们将所有电源置零。这里有一个电流源，那里有一个电压源。我们将所有电源置零。如何将它们置零？对于电压源，将其设为短路。短路的意思是用一根导线替代电压源，即直接连接起来。

For the current source, we say it is an open circuit. Open circuit means the current source is broken—there is a gap here. This is the third statement: it says the voltage source is zero, meaning the voltage source is replaced by a short circuit, and the current source is replaced by an open circuit.

对于电流源，我们说它是开路。开路意味着电流源被断开——这里有一个间隙。这是第三条陈述：电压源为零，即电压源被短路替代，而电流源被开路替代。

We found the resistance between the two marked terminals. We set our source to zero, and then we start from here.

我们求出了两个标记端子之间的电阻。我们将电源置零，然后从这里开始。

This is not short-circuited. How can we compute the equivalent resistance? Let's start from here. These three resistors are connected in parallel, because this is short-circuited.

这里没有短路。我们如何计算等效电阻？从这里开始分析。这三个电阻是并联连接的，因为这条支路被短路了。

For this circuit, even though these three resistors are connected in parallel, because there is a short circuit here, we can just ignore these three. So the final resistance is just this one. If this is R1, then R_th should equal R1.

对于这个电路，虽然这三个电阻是并联连接的，但由于这里存在短路，我们可以直接忽略这三个电阻。因此最终电阻就是这一个。如果这是R1，那么R_th应该等于R1。

Here is an open circuit, and here is a short circuit. So we do not need to consider this resistor in the system; it is short-circuited. Therefore, the final resistance is R1. The first step is to return the voltage source to its original position.

这里是开路，这里是短路。因此我们不需要考虑系统中的这个电阻，它被短路了。所以最终电阻是R1。第一步是将电压源恢复到其原始位置。

We remove them, then put them back. There is a current source and there is a voltage source. We put them back and find the open-circuit voltage. Here is open — this is a terminal. We want to find the voltage here. What is the voltage here? Here is open, because...

我们把它们移除，再放回去。这里有一个电流源和一个电压源。把它们放回去，然后求开路电压。这里是断开的——这是一个端子。我们要求这里的电压。这里的电压是多少？这里是断开的，因为……

If it's open, there's no current flowing in this branch. There's no current flowing in this branch; it's open, it's open circuit. So the voltage here is actually the voltage here. It's equivalent to the voltage here. There's no current flow in this branch; it's open. So the voltage of these two terminals is also the voltage on this resistor R2. So what's the source applied? How can you get the voltage of R2? You just use—

如果这条支路是断开的，就没有电流流过它。没有电流流过这条支路；它是开路的，是开路状态。所以这里的电压实际上就等于这里的电压，等效于这里的电压。这条支路没有电流流过；它是断开的。所以这两个端子的电压也等于这个电阻R2上的电压。那么所加的电源是什么？你怎么求R2上的电压？你只需要用——

What we have learned before: we should get the voltage of R2. The main step in step four is you put the source aside and then you find the open-circuit voltage. Because this is open, there is no current, there is no voltage drop, and the voltage of the terminal is equal to the voltage of this resistor.

我们之前学过：要求出R2上的电压。第四步的主要操作是：将电源移除，然后求开路电压。因为电路是断开的，所以没有电流，没有电压降，端口的电压等于该电阻上的电压。

Once you know the voltage, the same voltage is equal to the voltage of R2. And once you know these two values, the complex circuit can be replaced by this one. Any questions?

一旦你知道电压，该电压等于R2上的电压。一旦你知道了这两个值，复杂电路就可以用这个来替代。有问题吗？

We have more examples. Several parameters are related, identified by varying…

我们还有更多例子。几个参数是相互关联的，通过改变……来识别。

Let's have a look at this example together.

我们一起来看这个例子。

We have a connected graph. Here it should be connected with the node. Here is a node. Here we have two terminals. The first step is to remove the node. The node is already removed.

我们有一个连通图。这里它应该与该节点相连。这里是一个节点。这里我们有两个终端。第一步是移除该节点。该节点已经被移除了。

Remove the load. The second step is input terminals — this is Terminal A, this is Terminal B. The third step is to calculate RTD.

移除负载。第二步是输入端子——这是端子A，这是端子B。第三步是计算RTD。

You set all sources to zero. Here we have a current source. Setting a current source to zero means an open circuit. So the given circuit becomes this, between terminals A and B.

将所有电源置零。这里有一个电流源。将电流源置零意味着开路。因此，给定电路变为这样，位于端子A和B之间。

It is open, so no current flows through this branch. And then we can compute the resistance of this path from A. There is only one resistor here. So the equivalent resistance is exactly equal to R1.

该支路是断开的，因此没有电流流过这条支路。然后我们可以计算从A点出发这条路径上的电阻。这里只有一个电阻。所以等效电阻恰好等于R1。

This is the equivalent resistance. This is the source-free KVL. The first step is to compute the equivalent voltage. The first step is to input the source. Let's draw it again. Inputting the source should look like this. We are at the original circuit. And then we compute the open—

这是等效电阻。这是无源KVL。第一步是计算等效电压。第一步是输入电源。我们再画一遍。输入电源应该看起来像这样。我们回到原始电路。然后我们计算开路——

Open-circuit voltage between A and B. The open-circuit voltage of these two terminals. Because this is open, there is no current here. The equivalent voltage is actually equal to V_AB. This is exactly the open-circuit voltage of the two terminals. V_AB is exactly the voltage of this resistor, and we know the current is zero.

A与B之间的开路电压。这两个端子的开路电压。因为此处是断开的，所以没有电流流过。等效电压实际上等于V_AB。这正是两个端子的开路电压。V_AB恰好等于该电阻上的电压，而我们知道电流为零。

The first step is to clear the circuit. Do not forget the last step: you should draw the equivalent circuit. For this circuit, you have successfully found the equivalent Thevenin circuit.

第一步是清除电路。不要忘记最后一步：你应该画出等效电路。对于这个电路，你已经成功找到了等效戴维南电路。

This is another approach to find Rth. Step one: since no independent sources are removed, mark the terminals A and B. There are also dependent sources; here we only have a dependent source. The dependent source is an open circuit. Then we find the resistance R_open. In the first step, we turn off all sources and find the open-circuit voltage at the terminals.

这是求 Rth 的另一种方法。第一步：由于没有移除独立源，标记端子 A 和 B。电路中还有受控源；这里我们只有一个受控源。该受控源相当于开路。然后求电阻 R_open。第一步中，关闭所有电源，求端子处的开路电压。

Based on Thevenin's theorem, you can get the equivalent voltage and the equivalent resistance. And here, with Ohm's law, given these two variables, you can get the corresponding current.

根据戴维南定理，可以得到等效电压和等效电阻。而在这里，利用欧姆定律，已知这两个变量，就可以得到对应的电流。

Once you know the current and the voltage, you can get the third one. In this equation, the current is defined as short-circuit current. So if you know two parameters, you can find the third one.

一旦你知道电流和电压，就可以求出第三个量。在这个方程中，电流被定义为短路电流。因此，如果你知道两个参数，就能求出第三个。

For the short circuit current, we replace the load with a wire. The source and the load are connected together; it is not open, just connected together. And the short circuit current equals what we introduced in the Norton theorem. In the Norton theorem, it is actually the current source.

对于短路电流，我们将负载替换为一根导线。电源和负载直接连接在一起，不是开路，而是短接。短路电流等于我们在诺顿定理中介绍的那个量。在诺顿定理中，它实际上就是电流源。

Here you can see the Norton circuit. The current source IN is in parallel with the resistance RN. IN is the Norton current, the first parameter of the Norton equivalent. And IN is the short-circuit current through terminals A and B.

这里可以看到诺顿电路。电流源 IN 与电阻 RN 并联。IN 是诺顿电流，即诺顿等效电路的第一个参数。而 IN 等于通过端子 A 和 B 的短路电流。

When finding Thevenin resistance, you must turn off independent sources. You should not remove the sources; they are important. For independent sources, we have introduced dependent sources, right? So dependent sources must not be removed. You can imagine it is called an equivalent resistance. Here is a very important point: you must turn off independent sources.

在求戴维南等效电阻时，必须将独立源置零。不应移除这些源，它们很重要。对于独立源，我们已经引入了受控源的概念，对吧？所以受控源不能被移除。你可以将其想象为一个等效电阻。这里有一个非常重要的要点：必须将独立源置零。

We also have introduced dependent sources. A dependent source uses this diamond symbol. For example, this voltage is five times the current of the circuit. This is a dependent source. For dependent sources, we should not remove the source; it must remain active in the circuit. When you look at the states, the first three are identical.

我们还介绍了受控源。受控源使用这个菱形符号。例如，这个电压是电路中电流的五倍，这就是一个受控源。对于受控源，我们不能将其移除，它必须在电路中保持激活状态。当你观察这些状态时，前三个是完全相同的。

For identical particles in the same state, all quantum numbers are zero. Both these states are symmetric under exchange, and the particles are identical. The four states are identical. Because the four states are identical, the exchange symmetry properties are the same as those of boson statistics, as all the four states...

对于处于同一态的全同粒子，所有量子数均为零。这两个态在交换下是对称的，且粒子是全同的。这四个态是全同的。由于这四个态全同，其交换对称性质与玻色统计相同，因为所有四个态……

The first three things are identical, so you can get the same resistance. The fourth thing is different. Similarly, if we turn all sources off into their original position, here it is different. If I am to short-circuit the current—not the open-circuit voltage—the open-circuit voltage is the principle.

前三个量是相同的，因此可以得到相同的电阻。第四个量则不同。类似地，如果我们将所有电源置零恢复到原始位置，这里就不同了。如果我要求的是短路电流——而非开路电压——那么开路电压才是其原理所在。

It is not a short circuit; it is an open circuit. If we want to find the current, the final step is to determine the total impedance. Here is a finished example, and then we can end the class today. So here you have 10 volts.

这不是短路，而是开路。如果我们想求电流，最后一步是确定总阻抗。这里有一个已完成的例题，然后我们就可以结束今天的课了。所以这里有10伏特。

For Norton's theorem, the first step is to remove the load. Here the load is already removed, so we don't have to do that again. Second, we mark the terminals—label them A and B. Third, we set all independent sources to zero. For a voltage source, we replace it with a short circuit.

对于诺顿定理，第一步是移除负载。这里负载已经被移除了，所以我们不需要再操作。第二步，标记端子——将其标注为A和B。第三步，将所有独立源置零。对于电压源，我们将其替换为短路。

Consider the short circuit case. We calculate the equivalent resistance. Since the resistors are identical and the power source is identical, the equivalent resistance is simply one resistor, which is 2 ohms. Then we return the source to its original position and compute the short circuit current.

考虑短路情况。我们计算等效电阻。由于电阻相同且电源相同，等效电阻就是一个电阻的值，即2欧姆。然后将电源恢复到原始位置，计算短路电流。

You connect these terminals together. You have a short circuit, and that is always the problem here. The voltage difference divided by two ohms will give this current. Don't forget to draw the circuit. You have a current source connected in parallel. This is Norton's theorem.

将这些端子连接在一起，就形成了短路，而这始终是一个问题。电压差除以两欧姆即可得到该电流。别忘了画出电路图。你有一个并联连接的电流源。这就是诺顿定理。

That's it. Any questions? No questions? That's all for today.

就这些。有问题吗？没有问题？那今天就到这里。