What I did just now is setting to a strong circuit.

我刚才所做的，就是设置了一个强电路。

If the voltage source is replaced with a short circuit, there's no voltage. there's no voltage anymore. And for the current source, we set it to open circuit. So once the current source is open source, there's no current anymore. That's the reason we set a voltage source to short circuit. and the current source to open circuit.

如果将电压源替换为短路，就没有电压了。不再存在电压。而对于电流源，我们将其设置为开路。所以，一旦电流源处于开路状态，就没有电流了。这就是为什么我们要将电压源设置为短路的原因。而将电流源设置为开路。

And once we set all sources to zero, we find a really hard find the resultant resistance. We find the resultant resistance between the two marked terminals.

一旦我们将所有电源都设为零，就会发现非常难求出等效电阻。我们找到了两个标记端子之间的等效电阻。

So this is very important. In the third step, we remove the sources. For example, if there's a voltage source, we set it to short circuit. This means we replace the voltage source with a wire. And if there's a current source, we set it to broken, right? set it to open circuit.

所以，这一点非常重要。在第三步，我们要移除电源。例如，如果有电压源，我们就将其设为短路。这意味着我们用一根导线来代替电压源。如果有电流源，我们就将其设为断开，对吧？也就是开路。

after we set all sources to zero, and then we compute the resultant resistance.

在将所有电源置零之后，我们就可以计算出等效电阻了。

It's very important. For example, we have a one ohm here, one ohm here. How can we compute the resultant resistance?

这一点非常重要。例如，这里有一个1欧姆，这里也有一个1欧姆。我们该如何计算它们的等效电阻？

We start from A. We start here. And how can we go back to B? Okay, we start from here. You can see these two resistor are connected in series. How can it be series?

我们从A点开始。我们从这里开始。那么，我们如何回到B点呢？好的，我们从这里开始。大家可以看到，这两个电阻是串联连接的。为什么说是串联呢？

So they are together is two ohm. Here is broken, here is broken, right? So it's open. So we don't have to consider it.

所以它们加在一起是2欧姆。这里断开了，这里也断开了，对吧？所以这里是断路。所以我们不需要考虑它。

And here you can see these two resistors are connected in series.

而在这里，大家可以看到这两个电阻也是串联的。

And then this two ohm resistor is connected in parallel. It's this one.

然后，这个2欧姆的电阻是与前面的串联部分并联的。就是这一个。

So the total resistance is

所以，总电阻是

two ohms.

2欧姆。

And we have one ohm here. These two are connected in parallel. And this total resistance is the same resistance.

这里还有一个1欧姆的电阻。这两个是并联的。而这个总电阻，就是等效电阻。

Here is important. You have to start from A, and how to go back to B. Okay, start from here. these two are connected in series. and then connect with this one in parallel.

这里很重要。你必须从A点出发，然后找到回到B点的路径。好的，就从这里开始。这两个是串联的。然后再和这个并联起来。

That's the reason we have to use this

这就是为什么我们必须使用这种

equation to calculate the result.

公式来计算结果。

and also state, we return all sources to their original position.

另外还要说明一点，我们已经将所有电源都恢复到了原来的位置。

so instead of what you saw here, you put it back. sorry, what you saw should be used this symbol. and there is a current source, we put it back.

所以，不要按照你刚才看到的这样放着，要把它放回去。抱歉，你刚才看到的应该用这个符号。这里还有一个电流源，我们也把它放回去。

and then

然后，

we find the opposite case.

我们再来看相反的情况。

what is the voltage here?

这里的电压是多少？

the case is open, so there is no flow. so current flowing is from

电路是断开的，所以没有电流。因此，电流是从

this branch.

这条支路流过的。

the open circuit voltage, open circuit voltage Vab, is actually the voltage of this resistor.

开路电压Vab，实际上就是这个电阻两端的电压。

because there is no voltage drop. it is open.

因为这里没有电压降。因为它是断开的。

it's actually equal to this resistor.

它实际上等于这个电阻的电压。

you can use different methods. you can use Kirchhoff's laws. and you can get two equations. and based on Kirchhoff's current law and voltage law.

你可以用不同的方法来计算。比如基尔霍夫定律。这样就能得到两个方程。基于基尔霍夫电流定律和电压定律。

the voltage of this resistor.

这个电阻的电压。

so here is the important part here is that you have to compute the open-circuit voltage. of the two marked terminals.

所以，这里有一个关键的部分，那就是你必须计算开路电压。也就是这两个标记端点之间的开路电压。

and finally you have to draw the equivalent circuit.

最后，你需要画出等效电路。

in the first year, the students are just computing school. so they have to compute these two values, the Rth and Vth. don't forget to draw the circuit. it's also important.

因为在第一年，学生们只是在学习计算机。所以他们必须计算这两个值，即Rth和Vth。别忘了画出电路。这也很重要。

you have to draw it.

你必须把它画出来。

so these are the five steps. of Thevenin's theory. and when you compare it with Norton, the first three steps are exactly the same.

以上就是这五个步骤。也就是戴维南定理。当你把它与诺顿定理进行比较时，前三个步骤是完全一样的。

that's the reason the Thevenin resistance is equal to Norton resistance. So they have the same resultant resistance. All the first three steps are

这就是为什么戴维南电阻等于诺顿电阻的原因。所以它们的等效电阻是相同的。前三个步骤都是

exactly the same.

完全一样的。

And the fourth step is we also have to return all circuits to their original positions. But here we found a short circuit.

第四步是我们还需要返回所有电路到它们原来的位置。但是在这里，我们发现了一个短路。

we found the short circuit current.

我们找到了短路电流。

Short circuit current, this means we just connect a wire. so here the current can flow. It can flow from A to B. It's short circuit current. We want to compute the current here.

短路电流，意思就是我们直接用一根导线连接起来。这样电流就可以流过了。它可以从A流向B。这就是短路电流。我们想计算这里的电流。

And also the another step

另外，还有一个步骤，

you have to draw the Norton equivalent circuit. And the Norton circuit should draw like this. You have a current source.

就是画出诺顿等效电路。诺顿电路应该画成这样。这里有一个电流源。

I connect in parallel.

我是并联连接的。

and the Norton resistance.

还有诺顿电阻。

These two circuit are the equivalent each other.

这两个电路是等效的。

they are the same.

它们是一样的。

and they have the same resistance. So you can also convert Norton current. it will not the same voltage. and you know the same resistance, you can just use the Ohm's law. and this is the Norton current.

而且它们的电阻也相同。所以，你也可以将诺顿电流进行转换。但电压不会相同。而且你知道电阻是相同的，所以你可以直接用欧姆定律。这就是诺顿电流。

any questions?

有什么问题吗？

Yes.

有。

so at the first step, you can build the short circuit current. so this is the Norton current.

那么，第一步，你可以把短路电路的电流求出来。这就是诺顿电流。

and here is the current we want to compute.

这就是我们想要计算的电流。

so you go back to the circuit. How can you compute the current here?

好的，那我们回到电路。那么，你怎么计算这里的电流呢？

you can't, even though this is a resistor, because here is the wire. this resistor is short-circuited. you don't have to consider it. The current must flow from here. from a to b. and not flow through this resistor.

你不能这么做，尽管这里有个电阻，但这里是一根导线。这个电阻被短路了。你不需要考虑它。电流必须从这里流过。从A到B。而不是通过这个电阻。

any question?

还有问题吗？

these two series are very important. i hope everybody can understand. how can you calculate the current? the three values. we have series voltage. we have voltage and current. and these two parameters actually one parameter, because they are the same.

这两个概念非常重要。希望大家都能理解。那么，如何计算电流呢？就是这三个值。我们有串联电压。还有电压和电流。其实这两个参数算是一个，因为它们是相同的。

so how can we calculate these three important parameters?

那么，我们该如何计算这三个重要的参数呢？

and draw the equivalent circuit.

并画出等效电路。

great. There's no any other questions?

很好。还有其他问题吗？

the northern parameter, you have the short circuit current, right? and you have voltage and resistance. just the series parameters.

关于那个参数，你有短路电流，对吧？还有电压和电阻。就是串联参数。

so the original here variable, they are also the series parameter. because the northern resistance is series resistance. and northern current can be expressed by ohm's law. using series parameters.

所以这里的原始变量，也是串联参数。因为那个电阻是串联电阻。而短路电流可以用欧姆定律来表示。也就是利用串联参数。

and we can easily convert a linear network from series to northern. and the other way around, from northern to series.

我们可以很容易地将线性网络从串联形式转换为并联形式。反之亦然，从并联转换为串联。

look at the equivalent. They are equivalent.

看看等效电路。它们是等效的。

if i convert a linear network from series to northern and also from northern to series.

如果我把一个线性网络从串联转换为并联，然后再从并联转换回串联。

yes, so it does not near.

是的，所以它并没有改变。

it has no near at the current.

它对电流没有影响。

it would not be different from original northern current.

它和原来的并联电流不会有区别。

and by definition, the series resistance is measured. it's measured from a and b. It is the node that is connected. and on any sources, you can check by your known resistance.

根据定义，串联电阻是可以测量的。它是从A和B两点测量的，也就是那个连接点。在任何电源上，你都可以用已知的电阻来检测。

this is the third stage, but for the series resistance, it's not from a.

这是第三阶段，但对于串联电阻来说，它不是从A点开始的。

and all the sources should be removed. and then you can get the resulting resistance. it's too challenging in series and like connecting is this one in parallel.

所有的电源都应该被移除。这样你就能得到等效电阻。串联太复杂了，而并联就像这个一样简单。

and for the voltage sources, it means ideal. we set it to a short circuit. there's no voltage drop.

至于电压源，这意味着是理想的。我们把它设置为短路。这样就没有电压降了。

so this is the reason we set voltage source to short circuit. As for current source, we set it as open circuit.

这就是为什么我们把电压源设为短路的原因。至于电流源，我们则将其设为开路。

so there is no current.

这样就没有电流了。

and for the ideal voltage sources, the initial internal resistance is zero. and for ideal current sources, the resistance of current source is infinite.

对于理想电压源，其内阻为零。而对于理想电流源，其电阻是无穷大的。

any questions?

好的，有什么问题吗？

here is something important.

这里有一点很重要。

we can convert a linear two-terminal circuit. it's a voltage source in series.

我们可以将线性二端电路进行转换。也就是串联一个电压源。

with R. This is a very circuit, right? And we can also replace it by a current source in parallel with R. This is another circuit.

和一个电阻R。这是一个非常简单的电路，对吧？我们也可以用一个与电阻R并联的电流源来替代它。这是另一个电路。

So these two circuit can be converted to each other.

所以，这两个电路是可以相互转换的。

And here is something different. Here we have independent source.

而这里则有所不同。这里有一个独立电源。

We have dependent source. Most of the source are independent. And here we have a very special case. Here source are dependent.

这里有一个受控源。大多数电源都是独立的。而这里有一个非常特殊的情况。这里的电源是受控的。

So for the dependent source, source transformation should be be after the load.

那么，对于受控源来说，电源变换应该在负载之后进行。

Yeah, this is true. because the first thing is always to remove the load.

是的，确实如此。因为第一步总是先移除负载。

and the third stage, we have to remove all the sources, right? but we only remove the independent source.

而第三步，我们必须移除所有的电源，对吧？但我们只移除独立电源。

if there's a dependent source in the circuit, it's not removing.

如果电路中有受控源，则不需要移除。

and let's go back to the third stage. set all sources zero. this means we set independent sources to zero.

让我们回到第三步。将所有电源置零。这意味着，我们要把独立电源设为零。

if there's a dependent source, we should not set it to zero.

如果有受控源，就不能将其置零。

there is a dependent source.

这里有一个受控源。

we should not set it to zero, which means we keep it. we keep it there. let me have an example to explain how can we handle the case with dependent source.

所以我们不能把它置零，也就是说要保留它。我们就把它留在那里。我举个例子，来说明一下如何处理含有受控源的情况。

and the source transformation is not possible when we have ideal sources.

当我们遇到理想电源时，电源变换法就不适用了。

ideal sources, which means for the ideal voltage source, we have zero resistance. and for the ideal current source, we have infinity.

理想电源意味着，对于理想电压源，我们有零电阻。而对于理想电流源，则是无穷大。

but normally we don't have such kind of ideal sources. all the sources in the reality have internal resistance.

但实际上，我们并不存在这种理想的电源。现实中的所有电源都有内阻。

great. Maximum power transfer.

很好。接下来是最大功率传输。

i think we have already covered this aspect in our previous lectures. but here we just repeat it.

我想我们在之前的课程中已经讲过这方面了。不过这里我们再复习一下。

so what time can we get maximum power transfer?

那么，在什么情况下才能实现最大功率传输呢？

this case happens

这种情况发生在

when the resistance is equal to the source resistance of the network.

电阻等于网络的源电阻时。

in this situation happens, the maximum power is transferred.

在这种情况下，就能实现最大功率传输。

when the maximum power is transferred to load, when the load resistance is equivalent to the source resistance. so if they have the same resistance, we will have the maximum power transferred.

当负载电阻等于源电阻时，最大功率就会传输到负载上。所以，如果它们的电阻相等，就能实现最大功率传输。

this is the conclusion.

这就是结论。

but we will have some theory analysis.

不过，我们还会进行一些理论分析。

okay, here is a brief summary. and we have defined the resistance, right? we use this equation to define the resistance. It depends on the resistivity, the length of the conductor and also the cross the cross-sectional area. And we have introduced the definition of branches. nodes and loops.

好的，这里是一个简要的总结。我们已经定义了电阻，对吧？我们用这个公式来定义电阻。它取决于电阻率、导体的长度，以及横截面积。我们还介绍了支路的定义。还有节点和回路。

And we have voltage regulations.

我们还学习了电压定律。

We can simplify the voltage regulation with the resistance. It's the internal resistance divided by the load resistance.

我们可以用电阻来简化电压定律。也就是内阻除以负载电阻。

And we have introduced the Norton's theory. and Thevenin's theory.

我们还介绍了诺顿定理。和戴维南定理。

They have the same resistance. but the open-circuit voltage.

它们的电阻是相同的。但是开路电压不同。

We can build the open-circuit voltage. And for the Norton parameter, we can build the short-circuit current.

我们可以计算出开路电压。而对于诺顿参数，我们可以计算出短路电流。

And for the maximum power transfer, when the load resistance is equivalent to the Thevenin resistance,

至于最大功率传输，当负载电阻等于戴维南电阻时，

maximum power is transferred. Any questions? Otherwise, we have finished the lecture today.

就能实现最大功率传输。有什么问题吗？如果没有的话，今天的课就到这里。

But if there are no questions, let's do this exercise first. for some minutes.

不过，如果没有问题的话，我们先来做一下这个练习。花几分钟时间。

I will actually convert this circuit to Norton circuit.

我实际上会把这个电路转换成诺顿电路。

这是一个并联和一个这个串联，它的电阻还一样。

这是一个并联，还有一个串联，它们的电阻是一样的。

这啥也问不到

这根本问不到什么。

Yeah, so we want our research to be applicable.

是的，所以我们希望我们的研究能够具有实际应用价值。

So our research step is remove the logo.

所以我们的研究步骤是移除标志。

And the logo is already removed. So we don't have to do anything. Second step, we must something else.

而且标志已经被移除了。所以我们什么都不用做。第二步，我们需要做点别的。

Okay, the logo is already removed. And we come back with Airbnb. And third step is set all source to zero.

好的，标志已经移除了。现在我们回到Airbnb。第三步是将所有源设置为零。

And here we have current source. Right?

这里有一个电流源。对吧？

How do we set current source to zero?

那我们怎么把电流源设为零呢？

Should it be open circuit or short circuit?

应该是开路还是短路呢？

For the current source, the current source is set to open circuit.

对于电流源来说，应该将其设为开路。

Right?

对吗？

So for the circuit, you can get a certain like this.

所以，对于这个电路，你可以得到这样的结果。

We set it to open circuit.

我们把它设为开路。

So here is open. So there's no current flowing. in this branch. And then, you can get the resultant resistance. this time from a. and then go back to b. here we can also compute. you cannot close this branch because it's broken. you can go here and here. you don't have to do this. so how do you find the resistance?

所以这里就是开路。这样就没有电流流过。在这个支路里。然后，你就可以得到等效电阻。这次是从a点看的。然后再回到b点。这里我们也可以计算出来。你不能闭合这个支路，因为它是断开的。你可以从这里走到这里。没必要这样做。那么，你怎么求电阻呢？

so the same thing resistance, it's just this resistance. it's 4 ohm.

其实是一样的，电阻就是这个电阻。是4欧姆。

and the fourth step is you put the source back.

第四步是把电源放回去。

you put the source back. it's 3 ampere. and then you can compute the the open circuit voltage. so we want to compute the voltage here.

把电源放回去。这里是3安培。然后，你可以计算开路电压。所以我们想计算这里的电压。

open circuit voltage.

开路电压。

it's open. so the current just flowing is the resistance. so you have three ampere there. and you have four ohm. so i get 12.

这里是断开的。所以电流只流过这个电阻。所以那里有3安培。还有4欧姆。所以得到12。

and finally the third step. okay, just to draw the equivalent circuit.

最后，第三步。好的，画出等效电路。

don't forget to draw the equivalent circuit. you have a resistance here, you have a voltage.

别忘了画等效电路。这里有一个电阻，还有一个电压。

and here is the four ohm.

这里是4欧姆。

don't forget the direction of the voltage. don't forget the direction.

别忘了电压的方向。别忘了方向。

okay, the question is you also have to complete the voltage regulation, right?

好的，问题是，你还必须完成电压调节，对吧？

so the current is ac. if we connect this circuit with a load, here is a load.

那么，电流是交流电。如果我们把这个电路连接一个负载，这里就是一个负载。

and now the current is 213. micro ampere.

现在的电流是213。微安。

okay, based on the voltage regulation.

好的，基于电压调节。

the equation is the voltage with four loads, right?

公式是四个负载下的电压，对吧？

minus the voltage without load.

减去空载时的电压。

divided by the voltage with four loads.

再除以四个负载时的电压。

or you can use the simplified equation, it's the internal resistance.

或者你可以使用简化公式，那就是内阻。

it's the saving resistance divided by the load resistance. you can also use this simplified version.

就是串联电阻除以负载电阻。你也可以使用这个简化版本。

but here we know the saving resistance is 4. and how can we get the load resistance?

但是在这里，我们知道串联电阻是4。那么我们怎么得到负载电阻呢？

you know the total voltage is 4, right?

你知道总电压是4，对吧？

divided by the current, you will get the total load. it's the total resistance minus 4.

除以电流，就能得到总负载电阻。也就是总电阻减去4。

this is load resistance.

这就是负载电阻。

so this is the r load, it should be

所以这就是R负载，它应该是

14, right?

14，对吧？

so the load resistance is r load, which is 40 ohm.

所以负载电阻R负载是40欧姆。

so 44 ohm divided by 1.4, you are going to get 1.5 by 0.

那么44欧姆除以1.4，你会得到1.5乘以0。

any questions?

有任何问题吗？

okay, it should be these are what did you get? what did you get with four load?

好的，应该是这些。你们算出来是多少？那四个负载呢？

any questions?

还有问题吗？

if there's no questions, we can continue to the exercise.

如果没有问题，我们可以继续做练习了。

for certain exercise, also five minutes, have a check the answer.

对于某些练习，也有五分钟的时间，大家可以检查一下答案。

how can we find the seven to five minutes?

我们怎么找到这七到五分钟的时间呢？

because we come back to the circle. so just following five steps.

因为我们要回到圆圈这里。所以，只需要按照五个步骤来做。

For a voltage source, we set it to a short circuit. If the voltage source is replaced with a short circuit, there is no voltage anymore. And for a current source, we set it to an open circuit. Once the current source is an open circuit, there is no current anymore. That is the reason we set a voltage source to a short circuit and a current source to an open circuit.

对于电压源，我们将其设为短路。如果电压源被替换为短路，则不再有电压。而对于电流源，我们将其设为开路。一旦电流源成为开路，则不再有电流。这就是我们将电压源设为短路、将电流源设为开路的原因。

We find the resultant resistance between the two terminals. This is very important. The first step is that we remove the sources. For example, if there is a voltage source, we set it to a short circuit. Short circuit means we replace the voltage source with a wire. And if there is a current source, we set it to an open circuit.

我们求两个端子之间的等效电阻。这一点非常重要。第一步是去除电源。例如，如果存在电压源，我们将其置为短路。短路意味着用一根导线替代电压源。如果存在电流源，我们将其置为开路。

After we set all sources to zero, we compute the resistance. This is important. For example, we have one ohm here, one ohm here, and one ohm here. How can we compute the resistance?

将所有电源置零之后，我们计算电阻。这一点很重要。例如，这里有一个一欧姆，这里有一个一欧姆，这里也有一个一欧姆。我们该如何计算电阻？

Starting from A, how do we reach B? You can see these two resistors are connected in series, and they combine to give 2 ohms. K is broken, so we do not consider it. And here you can see these two resistors are also connected in series, giving 2 ohms.

从A点出发，我们如何到达B点？可以看到这两个电阻串联，等效为2欧姆。K是断开的，所以我们不予考虑。这里也可以看到这两个电阻同样是串联的，等效为2欧姆。

These two resistors are connected in parallel — this one and this one. So the total resistance is two ohms. We have one ohm here. These two are connected in parallel, and this total resistance is the Thevenin resistance. Here is what is important: we start from A and come back to B. Starting from here, he finds these two are connected in series, and then connected with this one in parallel.

这两个电阻并联连接——这一个和这一个。所以总电阻是两欧姆。这里有一个欧姆。这两个并联连接，而这个总电阻就是戴维南电阻。这里重要的是：我们从A出发，回到B。从这里开始，他发现这两个串联连接，然后再与这一个并联连接。

To use this equation to calculate the resultant resistance, we also return all sources to their original position. If there is a voltage source here, you put it back. Note that the voltage source should use this symbol. If there is a current source, you put it back. There is R...

要使用这个方程计算等效电阻，我们还需将所有电源恢复到其原始位置。如果这里有一个电压源，就把它放回原位。注意电压源应使用这个符号。如果有一个电流源，也把它放回原位。这里有R……

What do you find? The open-circuit voltage. So what is the voltage here? There is an open circuit, so there is no current flowing through it. Therefore, the open-circuit voltage V_AB is actually the voltage across this resistor.

你们发现了什么？开路电压。那么这里的电压是多少？由于是开路，没有电流流过。因此，开路电压V_AB实际上就是这个电阻两端的电压。

It may appear difficult to compute the density of a body, but actually it is not difficult. You can use different methods. For example, you can use K, S, and S rules to obtain two equations, and then at least one particle and body can be determined.

计算物体的密度看似困难，但实际上并不难。你可以使用不同的方法。例如，你可以利用K、S和S规则得到两个方程，从而至少确定一个粒子和物体。

Here is the important part of Thevenin's theorem: you have to compute the open-circuit voltage of the two marked terminals. And finally, you have to draw the equivalent circuit — don't forget to draw the circuit.

这是戴维南定理的关键部分：你必须计算两个标记端口的开路电压。最后，你必须画出等效电路——别忘了画电路。

Students often just compute these two values, Rth and Vth, and skip the short-circuit step. The short circuit is very important. Once you know the equivalent voltage source, you must perform this short-circuit calculation. These are the first three steps of Thévenin's theorem. When you compare them with Norton's theorem, the first three steps are exactly the same.

学生往往只计算Rth和Vth这两个值，而跳过了短路这一步。短路是非常重要的。一旦你知道了等效电压源，就必须进行这个短路计算。这些是戴维南定理的前三个步骤。当你将其与诺顿定理进行比较时，前三个步骤是完全相同的。

That is why the series resistance equals the resultant resistance — we obtain the same resultant resistance. The first three states have their resistors in parallel. The fourth state also retains its resistances in their original positions. However, here we find a short circuit.

这就是为什么串联电阻等于总等效电阻——我们得到相同的等效电阻。前三种状态下电阻是并联的。第四种状态中，电阻仍保持在其原始位置。然而，在这里我们发现了短路。

Show the current between these two points. You just connect A and B with a wire; here the current can flow from A to B. This gives us some current here. And also there is another step which can be...

展示这两点之间的电流。你只需将A和B用一根导线连接起来，这里电流就可以从A流向B。这就给了我们这里的电流。另外还有一个步骤，它可以是……

You have a Norton equivalent circuit. The Norton circuit should look like this: you have an ideal current source, I_N, connected in parallel to the Norton resistance, R_N. These two circuits are equivalent to each other.

你有一个诺顿等效电路。诺顿电路应该长这样：一个理想电流源 I_N 与诺顿电阻 R_N 并联连接。这两个电路彼此等效。

They have a sandwich system. You can also consider the bottom tolerance. If you know the sandwich package and the sandwich system, you can use almost no bottom tolerance if you do not want to repeat the same steps.

它们具有三明治结构系统。你还可以考虑底部公差。如果你了解三明治封装和三明治系统，在不想重复相同步骤的情况下，几乎可以不使用底部公差。

Any questions? Yes. For the state, you can take a short circuit current here. This is the loading current.

有问题吗？好的。对于该状态，你可以在此取短路电流。这就是负载电流。

Here is the current; we do not need to consider it. If you go back to the circuit, how can you determine the current here? Because the resistor is open—it is a short circuit—you do not have to consider it. The current must flow from A to B. It cannot flow through this resistor.

这里是电流，我们不需要考虑它。回到电路中，如何确定这里的电流？因为电阻是断开的——它是短路——所以不需要考虑它。电流必须从A流向B，不能流过这个电阻。

These two theorems are very important. I hope everyone can understand how they can be applied. There are three values: voltage, current, and resistance. These three parameters are actually one parameter because they are the same.

这两个定理非常重要。我希望大家能理解如何应用它们。有三个值：电压、电流和电阻。这三个参数实际上是一个参数，因为它们是相同的。

No other questions? The short-circuit current, the voltage, the resistance—these are several parameters of the original network available. They are also the same.

没有其他问题了吗？短路电流、电压、电阻——这些是原始网络的几个可用参数。它们也是相同的。

Series parameters can be used because the Norton resistance is a series resistance. The Norton current can be expressed by Ohm's law using series parameters. We can use this to convert a linear network from series to Norton form, and the other way around, from Norton to series. They are equivalent. We can convert a linear network from series to Norton and also from Norton to series.

可以使用串联参数，因为诺顿电阻是一个串联电阻。诺顿电流可以用欧姆定律通过串联参数来表示。我们可以利用这一点将线性网络从串联形式转换为诺顿形式，反之亦然，从诺顿转换为串联。它们是等效的。我们可以将线性网络从串联转换为诺顿，也可以从诺顿转换为串联。

Yes, so if there is no load here, the current would not be different from the original current.

是的，所以如果这里没有负载，电流就不会与原始电流有所不同。

By definition, the semi-weak system is linear. A semi-weak system is linear for A if A and B are locally connected. On any source, you can log in systems. This is the source state for the semi-weak systems: B star for A. The source should be removed.

根据定义，半弱系统是线性的。若A与B局部连通，则半弱系统对A是线性的。在任意源上，可以记录系统。这是半弱系统的源状态：B星对A。该源应当被移除。

This equation has a voltage source in it. If you short-circuit the voltage source in this equation, there is no voltage drop. So this is the result for the short circuit. After the short circuit, we have the open circuit.

这个方程中有一个电压源。如果你将方程中的电压源短路，则没有电压降。所以这就是短路的结果。在短路之后，我们来看开路。

There is no current. For ideal voltage sources, the internal resistance is zero. For ideal current sources, the internal resistance is infinity. Now, here is something important.

没有电流。对于理想电压源，其内阻为零。对于理想电流源，其内阻为无穷大。接下来是一个重要的内容。

We know that a linear circuit can be converted to its Thevenin equivalent: a voltage source in series with a resistor R. This is the Thevenin circuit. We can also replace it by a current source in parallel with R. This is the Norton circuit. These two circuits can be converted to each other. And here is something different.

我们知道，线性电路可以转换为其戴维南等效电路：一个电压源与电阻R串联，这就是戴维南电路。我们也可以将其替换为一个电流源与R并联，这就是诺顿电路。这两种电路可以相互转换。接下来是一个不同的内容。

Here we have dependent sources. Most of the sources are independent, but here we have a very special case where sources are dependent. For dependent sources, source transformation becomes undesirable.

这里有受控源。大多数电源是独立的，但这里有一个非常特殊的情况，即电源是受控的。对于受控源，电源变换变得不可取。

The first step is always to remove the node. And the third step: we have to remove all sources, but we only remove the independent sources. If there is a dependent source, it is not removed. Let us go back to the third step. The third step is to set all sources to zero. This means we set independent sources to zero.

第一步始终是移除节点。第三步：我们需要移除所有源，但只移除独立源。如果存在受控源，则不移除。让我们回到第三步。第三步是将所有源置零。这意味着我们将独立源置零。

If there's an independent set, we should not set it to zero; we should use k. Let's give an example to understand how we can handle the case with an independent set.

如果存在一个独立集，我们不应将其设为零，而应使用 k。我们举一个例子来理解如何处理含独立集的情形。

Source transformation is not possible when we have ideal sources. By ideal sources, we mean that for an ideal voltage source we have zero resistance, and for an ideal current source we have infinite resistance.

当使用理想电源时，源变换是不可行的。所谓理想电源，是指理想电压源的内阻为零，而理想电流源的内阻为无穷大。

Normally we don't have such kind of ideal sources. All the sources in reality have internal resistance. It's great — maximum power transfer point. I think we have already covered this aspect in our previous lecture.

通常我们并不存在这种理想电源。现实中所有电源都具有内阻。很好——最大功率传输点。我想我们在之前的课程中已经讨论过这个内容了。

When can a load receive maximum power transfer? This occurs when the total resistance is equal to the internal resistance of the battery. In this situation, maximum power is transferred to the load.

负载何时能获得最大功率传输？当总电阻等于电池内阻时，即发生最大功率传输。在这种情况下，最大功率被传输到负载上。

The load resistance is equivalent to the Thevenin resistance. If they have the same resistance, we have maximum power transfer to the load. This is the conclusion, but we might have some further analysis later on. Here is a brief summary. We have defined the resistance using this equation. It depends on the resistivity rho, the length of the conductor, and the cross-sectional area. We have introduced the definitions of branches, nodes, and loops.

负载电阻与戴维南电阻等效。若二者电阻相同，则可实现向负载的最大功率传输。这是结论，后续我们可能还会进行进一步分析。以下是简要总结：我们利用该公式定义了电阻，它取决于电阻率ρ、导体长度以及横截面积。我们还引入了支路、节点和回路的定义。

Voltage regulation can be simplified as the internal resistance divided by the load resistance. We have introduced Norton's theorem and Thevenin's theorem. They have the same resistance. For Thevenin voltage, we compute the open-circuit voltage. For the Norton parameter, we compute the short-circuit current. And for maximum power transfer, when the load resistance is equal to—

电压调整率可以简化为内阻除以负载电阻。我们已经介绍了诺顿定理和戴维南定理，它们具有相同的电阻。对于戴维南电压，我们计算开路电压；对于诺顿参数，我们计算短路电流。而对于最大功率传输，当负载电阻等于——

Remember that the total resistance is equivalent to the series resistance. Any questions? Otherwise, we have finished the lecture today. If there are no questions, let's do this exercise.

请记住，总电阻等于串联电阻。有什么问题吗？如果没有，我们今天的课就结束了。如果没有问题，我们来做一个练习。

Just like the total surface.

就像总表面积一样。

In a circuit with a single battery and resistors, the voltage across the resistor equals the electromotive force of the battery.

在一个由单一电源和电阻组成的电路中，电阻两端的电压等于电源的电动势。

[No discernible lecture content in this segment; only ambient noise and unintelligible fragments.]

[该片段无可辨识的授课内容；仅有环境噪音和无法辨认的碎片声音。]

[No discernible instructional content in this segment. The audio consists of indistinct background murmuring, movement noise, and fragmented speech that cannot be reliably transcribed into meaningful lecture material.]

【该片段无可辨识的教学内容。音频仅包含模糊的背景低语、移动噪音及碎片化语音，无法可靠转录为有意义的讲课材料。】

The group discusses obtaining cards from Longze Academy. One speaker mentions receiving cards valued at 170, while another references 150 and 155. There is uncertainty about what specific cards were received. The conversation then shifts to the material composition of an item: one speaker asks whether it is cloth or leather, noting that Yang Chen's item is made of cloth.

众人讨论从龙泽书院获取卡牌的事。一人提到拿到价值170的卡，另一人提及150和155。大家对具体拿到什么卡并不清楚。随后话题转向某件物品的材质：有人问是布还是皮，指出杨晨的那件是布的。

信部和院是平级的，有大有小。

The Information Department and the College are at the same hierarchical level; some are larger and some are smaller.

This math part is not very familiar. Union of high school level. Teacher, every day around four o'clock. Depends on the situation. Original. Right. One year.

这部分数学不太熟悉。高中水平的并集。老师，每天大概四点。看情况。原始的。对。一年。

You can reduce it to a very simple example. This problem is relatively straightforward; we can take a complex situation and simplify it down to a single, manageable case. The example we are working through now is sufficient to illustrate the point.

你可以把它化为一个非常简单的例子。这道题比较直观，我们可以把一个复杂的情形化归为一个单一、易于处理的案例。目前正在讨论的这个例子已经足以说明问题。

Look at the circuit diagram. You need to recognize it as a simplified circuit. In the simplified circuit, there is a load component. The load is connected to the source. For maximum power transfer, the load resistance must equal the source resistance. That is the condition for maximum power transfer.

看这个电路图。你需要把它识别为一个简化电路。在简化电路中，有一个负载部分。负载连接到电源上。要实现最大功率传输，负载电阻必须等于电源内阻。这就是最大功率传输的条件。

The conversation touches on high school experiences in Dalian, referencing distances of tens of kilometers and the number 182, though the exchange remains largely fragmentary and informal.

对话涉及在大连的高中经历，提到了几十公里的距离和数字182，但整体交流仍然零散且非正式。

This segment contains informal Chinese conversation among students, not an English lecture. The speakers discuss exam raw scores (裸分) and university tiers (二本, 一本). No coherent instructional content is present in this time range.

该时间段内为学生之间的非正式中文对话，并非英文课堂讲授。说话者讨论了高考裸分数及二本院校、一本院校等话题。此区间内无可整理的正式教学内容。

The first step is to put the source back. The second step involves the original source. Once we put it back, we recover the original source. After putting the source back, they found the...

第一步是将源放回。第二步涉及原始源。一旦将其放回，我们即可恢复原始源。将源放回之后，他们发现了……

The short-circuit current. This means we get a short circuit like this. We get the short-circuit current at phase A and phase B, and we want to get the current here—the short-circuit current here. How can you get the current in this circuit? Just one voltage source and one resistance of two ohms, so you get five amperes. That is the short-circuit current. Next step: we have to draw the equivalent circuit. Do not forget this. The equivalent is—you have a Norton current source connected in parallel with a Norton resistance of two ohms.

短路电流。这意味着我们得到这样一个短路。我们得到A相和B相的短路电流，我们要求这里的电流——即此处的短路电流。如何求该电路中的电流？只有一个电压源和一个两欧姆的电阻，因此得到五安培。这就是短路电流。下一步：我们必须画出等效电路。不要忘记这一点。等效电路是——一个诺顿电流源与一个两欧姆的诺顿电阻并联连接。

In the first stage, don't forget to draw the circuit and use another circuit. Any questions? We will now take a ten-minute break. So, we want our circuit to be equivalent — the same circuit.

在第一阶段，不要忘记画出电路并使用另一个电路。有问题吗？我们现在休息十分钟。那么，我们希望我们的电路是等效的——即同一个电路。

We follow the five steps. The first step is to remove the lock. Since the lock is already removed, we do not have to do anything. The second step is to terminate the lock. We must terminate the lock. The lock is already removed, and we can mark it as A and B. The third step is to set all sources to zero. Here we have the current source.

我们按照五个步骤进行。第一步是移除锁。由于锁已经被移除，我们无需做任何操作。第二步是终止锁。我们必须终止该锁。锁已经被移除，我们可以将其标记为A和B。第三步是将所有源置零。这里我们有电流源。

For the current source, when we set it to zero, should it be open-circuited or short-circuited? The current source is set to open-circuited. So for the circuit, you can get a result like this.

对于电流源，当我们将其置零时，应该开路还是短路？电流源应置为开路。因此对于该电路，可以得到如下结果。

We consider an open circuit. Since the branch is broken, no current flows through it. We then compute the resultant resistance from A back to B. We cannot pass through the broken branch; the only available path goes through this route and this route back to B. Therefore, only one resistor remains, giving the same resistance.

我们考虑一个开路。由于该支路断开，没有电流流过它。然后我们计算从A回到B的等效电阻。我们无法通过断开的支路；唯一可用的路径是经过这条路线和这条路线回到B。因此，只剩下一个电阻，得到相同的电阻值。

In terms of the resistance, it is measured in ohms. The first step is to put the source back. We place a three-amp source here. Then we compute the open-circuit voltage. So the question is: what is the voltage here? It is the open-circuit voltage.

关于电阻，其单位是欧姆。第一步是将电源放回。我们在此处放置一个三安培的电源。然后计算开路电压。所以问题是：这里的电压是多少？它就是开路电压。

In the open case, the current just flows through this resistor going back. You have 3 amps here and 4 ohms, so again 12 volts. Finally, the fifth case — don't forget to draw the equivalent circuit. You have a resistor here, you have a voltage.

在开路情况下，电流仅流过该电阻并返回。此处有3安培和4欧姆，因此再次得到12伏特。最后是第五种情况——别忘了画出等效电路。这里有一个电阻，还有一个电压。

AI is common to all of them. You also get the direction of the velocity. The only thing that changes is the magnitude. The question is whether it also has the velocity variation.

AI 对所有这些量都是共同的。你还能得到速度的方向。唯一改变的是大小。问题是它是否也具有速度变化。

What is regulation? If we connect this circuit with a load—here is a load—and now the current is 230 microamperes. Based on this, what is the regulation? The equation is the voltage...

什么是调整率？如果我们用一个负载连接这个电路——这里是一个负载——此时电流为230微安。在此基础上，调整率是什么？其方程是电压……

Voltage V_OL, that is, minus V_OL divided by V_OL, or…

电压V_OL，即负的V_OL除以V_OL，或者……

You can use the simplified version. It is the internal resistance, or the terminal resistance divided by the load resistance. You can also use this simplified version. But here we know the terminal resistance is 4 ohms. And how can we get the load resistance? We know the power is 4 watts, right?

你可以使用简化版本。它是内阻，或者端电阻除以负载电阻。你也可以使用这个简化版本。但这里我们知道端电阻是4欧姆。那么如何得到负载电阻呢？我们知道功率是4瓦特，对吧？

If I get a total resistance times rho, this is local resistance. So this is R naught should be...

如果我得到总电阻乘以ρ，这就是局域电阻。所以这个R₀应该是……

For n = 2, the expression is R₀ times 4 over 4². So 4 divided by 4². And 1 divided by ∞ equals 0.

对于 n = 2，表达式为 R₀ 乘以 4 除以 4²。即 4 除以 4²。而 1 除以 ∞ 等于 0。

Any questions? — What would be the result? What would be the final outcome?

还有问题吗？——结果会是什么？最终结果是什么？

Any questions? For some questions, we can continue the exercise. For certain exercises, have you ever taken the answer?

有什么问题吗？对于某些问题，我们可以继续做练习。对于某些练习，你们曾经做过答案吗？

How can we find the values? We convert to a certain form. So we just follow these five steps.

我们如何求值？我们将其转化为某种形式。因此我们只需遵循这五个步骤。

[No intelligible speech detected in this segment. The audio contains only ambient sounds such as movement, coughing, and shuffling.]

[该片段未检测到可辨识的语音内容。音频仅包含环境声音，如移动声、咳嗽声和翻动声。]