They found that for small changes in temperature, if the temperature has a change, cause small value.

他们发现，对于温度的微小变化，温度的变化会导致一个较小的数值。

The change in resistance is proportional. with the change in temperature.

电阻的变化是成比例的。与温度的变化成正比。

The change in resistance is proportional. with the change in temperature.

电阻的变化是成比例的。与温度的变化成正比。

So when temperature is changed, the resistance is also changed. They have linear relation.

所以，当温度发生变化时，电阻也会随之改变。它们之间是线性关系。

And they introduce the temperature coefficient, alpha. It's defined as the ratio of the change in resistance per degree. change in resistance per degree of temperature.

他们还引入了温度系数，即α。它被定义为每度电阻变化的比率。也就是电阻随温度的变化率。

And they define more different temperature.

他们还定义了不同的温度。

And here is the definition. expressed by equation. So the change in resistance. change in resistance per degree of temperature.

这里是定义。用公式表示。所以，电阻的变化。就是每度温度的电阻变化。

And here's per degree of temperature divided by the reference resistance. and get the numerical coefficient.

而这里的“每度温度”，是除以参考电阻得到的。这样就得到了一个数值系数。

The initial resistance is R0. and current resistance is R1. So R1 minus R0 is the change in resistance.

初始电阻是R0。而当前的电阻是R1。所以，R1减去R0就是电阻的变化量。

and same about the current temperature. if we use 0 degree as the reference, so the change in temperature should be T1 minus 0. because 0 is defined as the reference temperature.

同样的，还有当前的温度。如果我们以0度作为参考，那么温度的变化量就是T1减去0。因为0被定义为参考温度。

so this is the change in temperature. And the reference resistance is R0. So you can get this equation to express the temperature coefficient.

所以，这就是温度的变化量。而参考电阻是R0。所以，你可以得到这个公式来表示温度系数。

by changing the form of the image, you can get this expression. But pay attention, so this expression is only

通过改变图像的形式，你可以得到这个表达式。但是要注意，这个表达式仅

holds. when the gradient of the strain rate is zero. this equation is only true when the different temperature is zero. you will get the following equation.

成立。当应变率的梯度为零时。这个公式只有在参考温度为零时才成立。你会得到下面的公式。

holds. when the gradient of the strain rate is zero. this equation is only true when the different temperature is zero. you will get the following equation.

成立。当应变率的梯度为零时。这个公式只有在参考温度为零时才成立。你会得到下面的公式。

here, theta zero is a reference temperature.

这里，θ0是参考温度。

So if theta zero is zero, you will get the equation above.

所以，如果θ0等于零，你就会得到上面的公式。

So based on this equation, we can compute the unload resistance. at a given temperature. What's the temperature? Given zeta one, given you can compute. So why should we know reference temperature and theta zero?

所以，基于这个公式，我们可以计算卸载电阻。在给定的温度下。温度是多少？给定θ1，就可以计算出来。那么，为什么我们需要知道参考温度和θ0呢？

reference temperature is theta zero and reference resistivity is r zero. Or if you know the resistance at a certain temperature, you can use this equation to compute the corresponding temperature theta one. r one is given. you can use this equation to compute theta one. so what is the corresponding temperature for this resistance?

参考温度是θ0，参考电阻率是R0。或者，如果你知道某个特定温度下的电阻，就可以用这个公式来计算出对应的温度θ1。R1是给定的。你可以用这个公式来计算θ1。那么，这个电阻对应的温度是多少呢？

i'll let you try in the class.

我让大家在课堂上试一试。

so you have higher temperature, you probably have higher resistance.

所以，温度越高，电阻可能也越大。

and temperature coefficient is also dependent on the material. so different material have different temperature coefficient. so you don't have to memorize.

而且，温度系数也取决于材料。不同的材料有不同的温度系数。所以你不需要去死记硬背。

and here's something different. As I mentioned before, sometimes people use derivative. and sometimes people use change degree. when you use the 20 degree as reference, so the change in resistance, is just 20 degree. so same up here.

这里还有一点不同。正如我之前提到的，有时候人们会使用导数。有时候人们也会使用变化率。当你以20度作为参考时，电阻的变化，就是20度。这里也是一样的。

and alpha 0, alpha 20 is the temperature coefficient. and r20 is the resistance at temperature 20.

而α0，也就是α20，是温度系数。而R20则是20度时的电阻。

so you should change three values. if you use a different reference. First, you have change the resistance temperature, right? and second, you have change the temperature coefficient. and third, you have change the

所以你需要改变三个值。如果你使用不同的参考值的话。首先，你需要改变电阻温度，对吧？其次，你需要改变温度系数。第三，你需要改变

the initial resistance.

初始电阻。

and there is another table about the temperature coefficient. at temperature 20 degree.

这里还有一个表格，是关于温度系数的。是在20度时的。

here we use 20 degree as the reference. by looking up this table, we can also get the temperature coefficient.

这里我们使用20度作为参考值。通过查阅这个表格，我们也可以得到温度系数。

alpha 20, alpha 20, alpha 20.

这里是α20，α20，α20。

but we also have introduced a conductance, right? Conductance is a basic model. so it's the inverse. inverse of resistance. so conductance equals to 1 divided by R.

但是，我们还介绍了电导，对吧？电导是一个基本模型。所以它是电导的倒数。也就是电阻的倒数。所以，电导等于1除以R。

and the resistance of a given smoking depends on two factors. one is the material.

而给定 Smoking的电阻取决于两个因素。一个是材料。

beside the resistivity, the material decides the resistivity and the shape. shape decides the length. and also the cross-sectional area. So based on these three values, you can get the resistance.

除了电阻率之外，材料决定了电阻率，还有形状。形状决定了长度。还有横截面积。所以，基于这三个值，你就可以得到电阻。

here again, the resistance is inversely proportional. the cross-sectional area. So a thicker copper wire has lower resistance than an otherwise identical thin copper wire.

这里再次强调，电阻与电导成反比。也就是横截面积。所以，一根更粗的铜线，其电阻比一根其他条件完全相同的细铜线要低。

because a thick copper has larger cross-sectional area. so the resistance is lower.

因为粗铜线的横截面积更大。所以电阻更低。

And also the resistance is proportional to the length. The longer the copper wire, the higher the resistance.

此外，电阻还与长度成正比。铜线越长，电阻就越大。

and conductance is the inverse resistance. so it was one divided by r.

而电导是电阻的倒数。也就是1除以R。

and here we use another unit.

这里我们使用了另一种单位。

called as ampere.

叫做安培。

conductivity is also the inverse resistivity. so it was one divided by rho.

电导率也是电阻率的倒数。所以它是1除以ρ。

this is sigma.

这就是西格玛。

conductivity is one divided by the rho.

电导率等于1除以电阻率。

so based on the definition, you can get these two.

所以，根据定义，你可以得到这两个公式。

and this the one on top is very famous, you know, resistivity, length and cross section area. and we can establish resistance. and g is the inverse of the resistance. so g is the inverse of the resistance.

上面的这个非常有名，就是电阻率、长度和横截面积。我们可以由此得出电阻。而电导G就是电阻的倒数。所以，g就是电阻的倒数。

you can define as conductivity.

你可以把它定义为电导率。

okay, here's some concept, electrical breakdown.

好的，这里有一个概念，那就是电击穿。

in some microwaves, you can see the lightning. the lightning is kind of electrical breakdown. in bad weather, there's not only rain, but also lightning. lightning is kind of electrical breakdown.

在一些微波中，你可以看到闪电现象。闪电其实就是一种电击穿。在恶劣天气下，不仅有雨，还有闪电。闪电也是一种电击穿。

so it's a process that never works. and electrical insulating material. some people might not know what is some insulance. and electrical conductor. and electricity always goes through it.

所以，这是一个不断重复的过程。还有绝缘材料。有些人可能不知道，什么是绝缘体。还有导体。电流总是通过它。

so initially the material is not conductive. but if you apply a very high voltage, to the material, the material suddenly becomes conductive. it's known as electric breakdown.

所以，一开始，这种材料并不是导电的。但是，如果你施加很高的电压，作用在材料上，它就会突然变成导电的。这被称为电击穿。

and what happens when you apply voltage? If you apply voltage, next is the material, I mean, dielectric constant. So when the voltage is too high and exceeds the material's dielectric constant, you are get the electric breakdown.

那么，当你施加电压时会发生什么呢？接下来要讲的是材料的介电常数。当电压过高，超过了材料的介电常数时，就会发生电击穿。

You know, the applied voltage will produce electric field strength. when you apply voltage for materials, the material will produce electric field. So if the electric field is too large, and exceed the material's dielectric constant, you are get the electric breakdown.

大家知道，施加的电压会产生电场强度。当你给材料施加电压时，材料会产生电场。所以，如果电场强度过大，超过了材料的介电常数，就会发生电击穿。

And the voltage at which a given insulation object becomes conductive, is called breakdown.

而使得某个绝缘物体变成导体的那个电压，就称为击穿电压。

And the voltage you will find when the breakdown happens, is defined as breakdown voltage. When electrical breakdown happens, the current voltage defined as breakdown voltage.

当击穿发生时，你所测得的电压，就被定义为击穿电压。当发生电击穿时，此时的电压就是击穿电压。

The breakdown voltage depends on the size and the shape of the material. So different material requires different breakdown voltage.

击穿电压取决于材料的尺寸和形状。因此，不同的材料需要不同的击穿电压。

Some material you must apply a very, very high voltage. in order to get breakdown. And some material you don't have to apply very much. You can just apply very small voltage. and still you can get breakdown.

有些材料必须施加非常高的电压，才能发生击穿。而有些材料则不需要施加太大的电压。只需施加很小的电压即可。同样也能实现击穿。

And breakdown can happen in different materials. It can be either in a solid material or or liquid material. or gas material. Different kinds of material both have breakdown.

击穿现象可以发生在不同的材料中。它既可以发生在固体材料中，也可以发生在液体材料中。或者气体材料中。不同类型的材料都会发生击穿。

Here's the image to illustrate the breakdown. So even though it's a glass, it actually is not a bad case. But if you apply very, very large,

这里有一张图来说明击穿现象。所以，尽管这是玻璃，它实际上并不是一个绝缘体。但是，如果你施加非常大的电压，

the glass can become conductive.

玻璃就会变成导体。

And we know the voltage, when you apply voltage, and you know the distance between two plates. and get the electrical density.

我们知道电压，当你施加电压时，也知道两个极板之间的距离。就可以得到电场强度。

And this is also known as electrical breakdown.

这也被称为电击穿。

And this is also known as electrical field. So the breakdown strength or dielectric strength.

这也称为电场。所以，这就是击穿强度，或者说是介电强度。

It's the maximum electrical field that material can withstand under ideal conditions. without undergoing electrical breakdown.

它是材料能够承受的最大电场强度。在理想条件下。而不会发生电击穿。

When the electric field is applied to the dielectrics, it produces dipoles. And next, the material will become conductive.

当电场施加在电介质上时，就会产生偶极子。接下来，材料就会变成导电的。

And also we have a light dependent resistor. At the beginning, you need to use the different signal. for mixing, right? So we have pass the light. So the resistance will not change.

此外，我们还有光敏电阻。一开始，你需要使用不同的信号。用来混合，对吧？这样光线就通过了，所以电阻不会改变。

But some resistance has light dependent. For example,

但有些电阻是光敏的。比如，

here is a conductive resistor for the auto. or light dependent. And light dependent resistor, LDR.

这是一个汽车用的导电电阻。或者是光敏的。光敏电阻，简称LDR。

So it's a very important resistor. That is controlled by the intensity of light. When the intensity of light is increased, the resistance will be decreased.

所以这是一种非常重要的电阻。它的阻值是由光的强度控制的。当光的强度增加时，电阻会减小。

When the light of intensity decreased, the resistance will be higher.

当光的强度减弱时，电阻会增大。

so that's a very special resistor.

所以，这是一种非常特殊的电阻。

And it shows a photoconductivity. And when you use it to low-power materials, it's very used in low-power materials or semi-conductors. So the photoresistor, photoresistor, use the material for semiconductors.

它表现出光导效应。当你用它来检测低功率材料时，它广泛应用于低功率材料或半导体领域。那么，光敏电阻就是利用半导体材料制成的。

And semiconductors is kind of a low-power material.

而半导体属于低功率材料的一种。

And this kind of resistors also have special spectral responses. similar to that of human eyes.

这种电阻还具有特殊的光谱响应特性。与人眼相似。

And here is the property of this resistor. When the light intensity is higher, you will get lower resistance. When the light intensity is lower, you will get higher

这里展示了这种电阻的特性。当光强较高时，电阻会降低。当光强较低时，电阻会升高。

resistance. Okay, let's look at the figures. this is the area of light dependent. When the light intensity, x-axis is the light intensity, y-axis is the resistance. When the light intensity is increased, you will get lower when the light intensity is lower, you will get higher resistance. It has a curve like this.

电阻。好的，让我们来看一下图表。这是光敏电阻的示意图。横轴代表光强，纵轴代表电阻。当光强增加时，电阻会降低。当光强降低时，电阻会升高。它的曲线是这样的。

And so this image shows that

这张图展示了，

the real LDR. So it looks like this. This is the real product. A real LDR, light-dependent resistor. And also we use these two symbols. to represent LDR. And there you can see two arrows.

实际的光敏电阻。它看起来就是这样。这是实物产品。也就是光敏电阻。另外，我们还使用了这两个符号。用来表示光敏电阻。大家可以看到这里有两个箭头。

Arrows, right? Arrows is the light.

箭头，对吧？箭头代表光。

It represents the light. When the light is applied,

它表示光。当有光照射时，

you will get a different resistance depending on the light intensity.

它的电阻值会发生变化，具体取决于光的强度。

Two different symbols to represent LDR. And the LDR has different applications. It can be used to detect

用两种不同的符号来表示光敏电阻。光敏电阻有不同的应用。它可以用来检测

whether it's light if there's no light, the resistance will be high. if there's light, the resistance will be low. So you can use this function. to detect whether the light is present. or absent.

是否有光。如果没有光，电阻会很高。如果有光，电阻就会很低。所以，你可以利用这个特性。来检测光是否存在。或者不存在。

And you can measure the light intensity, depending on how how big the resistance have changed.

你还可以测量光的强度，这取决于电阻变化的幅度。

For example, you can use this resistor, LDR, as for a fire detector, right? Because fire produce light. If there's a fire, okay, this resistor has changed. Then it will call the fire fighter. You can use this function to design a warning system. If fire happens, the resistance will be changed. So we can activate the warning system and call the fire fighter.

例如，你可以用这个光敏电阻作为火灾探测器，对吧？因为火会发光。如果有火，这个电阻就会发生变化。这样就会触发消防警报。你可以利用这个原理来设计一个报警系统。一旦发生火灾，电阻就会改变。这样我们就能启动报警系统，并通知消防员。

And here's another application of the LDR. Depending on the light. The resistance will be changed. So once the resistance change, you can have different applications.

这是光敏电阻的另一个应用。它取决于光线。电阻也会随之变化。所以，一旦电阻发生变化，就能实现不同的应用。

You don't have to remember these concrete examples. These concrete examples just used to explain the possible applications.

你不需要记住这些具体的例子。这些例子只是为了说明可能的应用场景。

Okay, that's all for lecture eight, right? So it's not complex. It's just a set of definitions. We repeat the knowledge that we have introduced at the beginning.

好的，这就是第八讲的全部内容了，对吧？所以并不复杂，只是一系列定义而已。我们只是重复了一下开头介绍过的知识。

So we introduce the resistance. depending on the light, and also the cross-sectional area. And also we know the resistance. It depend on temperature.

我们介绍了电阻。它会根据光线的变化而变化。还有横截面积。而且我们也知道电阻的公式。它还取决于温度。

Based on the reference temperature, you can get the new resistance at a certain temperature. And finally, we have introduced the electrical strength. breakdown. So when the voltage is too high,

根据参考温度，你可以计算出在特定温度下的新电阻值。最后，我们介绍了电强度。也就是击穿。当电压过高时，

it will not conduct if a current.

电流就无法导通了。

Yeah, just the three aspects.

是的，就是这三个方面。

Okay, that's the result. This is just from lecture 6 and lecture 7, right?

好的，这就是结果。这仅仅来自第6讲和第7讲的内容，对吧？

After we use the simulation, we have the seven parameters.

经过模拟之后，我们得到了七个参数。

for this circuit.

对于这个电路来说。

For the world TV source,

对于世界电视信号源，

it's set to short circuit. so there's no voltage drop. There is no voltage drop anymore. And then for the tolerance source, it's set to open circuit. so there's no current flowing.

它被设置为短路。所以没有电压降。现在没有电压降了。然后是容差信号源，它被设置为开路。所以没有电流流过。

So if we redraw the circuit, actually here is the circuit. and here is the same.

那么，如果我们重新画一下这个电路，实际上这里就是电路。这里也是一样的。

The voltage is a short circuit and current is open circuit. so it's open.

电压是短路，电流是开路。所以它是断开的。

And current cannot flow through this branch.

电流无法流过这个支路。

And now we can build the Thevenin resistance.

现在，我们可以构建戴维南等效电阻了。

The Thevenin is start from A. And these two resistors are connected in series. You go back to B. So we just plus 6k with 2k.

戴维南等效电路是从A点开始的。这两个电阻是串联的。然后回到B点。所以我们直接把6k和2k相加。

So this is the Thevenin resistance.

这就是戴维南等效电阻。

And the fourth step is

第四步是

you put the source back. Then you can get the original circuit. And you have to compute the open circuit. Open circuit voltage of the terminals. Open circuit, Vab.

把电源放回去。这样你就能得到原始电路了。然后你需要计算开路电压。也就是端子的开路电压。开路电压，Vab。

Now we should use the superposition. Based on the question, we should use the superposition. Superposition is used to compute voltage or current. For the series resistance, you just follow the the normal process. You use only superposition to compute the voltage.

现在，我们应该使用叠加定理。根据题目要求，我们必须使用叠加定理。叠加定理用于计算电压或电流。对于串联电阻，你只需要遵循常规步骤即可。这里我们只使用叠加定理来计算电压。

or current. Now we want to compute the open circuit voltage. And based on the superposition, so every time we just keep one source. If we keep the voltage source, and we remove the current source. How to be removing?

或者电流。现在，我们要计算开路电压。根据叠加定理，每次我们只保留一个电源。如果我们保留电压源，而移除电流源。那么，该如何移除呢？

we set it to open circuit. there's no current.

我们将其设置为开路。这样就没有电流了。

So what is the voltage here? the voltage is Vab.

那么，这里的电压是多少？电压是Vab。

because it's open, right? so there's no, it's not a closed loop. so the voltage of ab is directly the source voltage.

因为是开路，对吧？所以没有闭合回路。因此，ab之间的电压是直接等于电源电压。

okay, this is situation one.

好的，这是第一种情况。

so there's no voltage drop, there's no current. there's no current in the circuit.

所以没有电压降，也没有电流。电路中没有电流。

so the Vab equals the voltage of the source.

所以Vab等于电源电压。

and for the second we remove the voltage source.

对于第二种情况，我们把电压源去掉。

how can we remove the voltage source?

那我们该如何移除电压源呢？

we replace the voltage source with a wire. so it's a short circuit. so it should look like this.

我们用导线来代替电压源。这样就形成了一个短路。所以它应该看起来像这样。

and this time you have a current source.

而这一次，我们有一个电流源。

a and b.

A和B。

and for this case, the open circuit, give the open circuit voltage there, the open circuit voltage here.

对于这种情况，开路时，这里会产生开路电压，也就是这里的开路电压。

a and b. This loop. this loop is open. so there's no voltage drop for this resistor. so the b and b is directly having

A和B。这个回路。这个回路是断开的。所以这个电阻上没有电压降。因此，B点的电压直接等于

this voltage. is directly the voltage of this resistor.

这个电压。也就是这个电阻两端的电压。

because the loop is not closed. so there's no current flowing here. so vab is directly the voltage of this resistor. so in this case, vab is the, you know, current is one.

因为回路没有闭合。所以这里没有电流流过。所以，Vab直接等于这个电阻的电压。在这种情况下，电流是1。

i know i'm here, the resistance is 6k.

我知道这里，电阻是6k。

so i get 6 volt.

所以得到6伏特。

but you should pay attention the direction.

但是，大家要注意方向。

so in the first case, it's okay. in the first case, a is positive value. a is the high potential, b is low potential. current is going from a to b.

在第一种情况下，是可以的。在第一种情况下，a是正值。a是高电位，b是低电位。电流是从a流向b的。

now to the second case. the current is flowing here.

现在我们来看第二种情况。电流在这里流动。

and the current is flowing from a to a, right? from b to a.

电流是从a流向a的，对吧？是从b流向a的。

so b has high potential.

所以b的电位较高。

and a has the low potential in this case.

而在这种情况下，a的电位较低。

so finally we have to find out the voltage. it's the minus difference between the two points. minus six.

最后，我们需要求出电压。就是两点之间的电位差。是负六。

okay, that is great.

好的，非常棒。

Now, let's get one more back.

现在，让我们再退后一步。

And we also have to show the whole circuit.

我们还需要展示整个电路。

So this is the circuit.

这就是电路。

And this is the circuit at the bottom. We also get to draw the circuit.

这是底部的电路。我们还可以绘制电路。

We use superposition again. But here there's something different. Here we have one independent source.

我们再次使用了叠加原理。但是这里有一些不同之处。这里我们有一个独立电源。

So here, remember, for

所以，请记住，对于

independent source, we should not remove it. in superposition.

独立电源，我们不应该将其移除。在叠加原理中。

Okay, maybe five minutes. So this is the solving example. So this is one independent source.

好的，大概还有五分钟。这就是解题示例。所以，这是一个独立电源。

And this is the independent current source.

这是一个独立电流源。

Okay, for the first circuit, here is a current source, this is a dependent current source. Here is a zero volt, right? It's connected with the ground.

好的，对于第一个电路，这里有一个电流源，这是一个受控电流源。这里是一个零伏，对吧？它接地了。

So zero volt.

所以是零伏。

And then, there is also the x1.

然后，这里还有x1。

You can apply Kirchhoff's current law. For example, here's the x1. So the current flowing the both resistors is downwards. and it expressed by

你可以应用基尔霍夫电流定律。比如，这里是x1。所以，流过这两个电阻的电流是向下的。它可以用

vx1 minus zero. divided by four. So this is the current here. And here is also a dependent source, a dependent current. The current is 0.1. times vx.

Vx1减去零来表示。再除以四。所以，这就是这里的电流。这里还有一个受控源，是一个受控电流源。电流是0.1。乘以Vx。

And the direction is

方向是

this direction. So the current here is 0.1 vx1.

这个方向。所以这里的电流是0.1Vx1。

dependent on the voltage here. The voltage is vx1. So the current is 0.1 times vx1. And we have two current here.

它取决于这里的电压。这个电压就是Vx1。所以电流就是0.1乘以Vx1。这里还有两个电流。

Then we can get the current, for example, let's assume this direction.

那么，我们可以得到这个电流，比如，我们假设它的方向是这个样子。

So the current here should be

所以这里的电流应该是

0.1 vx1.

0.1Vx1。

minus the voltage here. Here is the current entering the node, right? And here is leaving, here is also leaving. So minus the current here, we can get the current here.

减去这里的电压。这是流入节点的电流，对吧？这里是流出的，这里也是流出的。所以，用这个电流减去这里的电流，就能得到这里的电流。

And then for this,

然后，对于这个，

you have to apply the Kirchhoff's current law again. So what you need is upwards. of the current, upwards.

你必须再次应用基尔霍夫电流定律。所以，你需要的是向上的电流。也就是电流向上。

And here you can get the current here. for this 220 resistor, it's Vx1.

这样你就能得到这里的电流了。对于这220欧姆的电阻，它是Vx1。

So the current here is Vx1 minus 0. divided by 20.

所以这里的电流就是Vx1减去0。再除以20。

Okay. You know this is the current entering the load. And 2 ampere is also entering.

好的。你知道，这是流入负载的电流。还有2安培也是流入的。

And only one, this current is leaving. So these are the current entering the load. The leaving current is Vx1. minus 0, this Vx1 is 0. 0 divided by 20.

而只有一路电流是流出的。所以，这些都是流入负载的电流。流出的电流是Vx1。减去0，所以Vx1等于0。0除以20。

So this is the first equation. You can solve the Vx1.

这就是第一个方程。你可以解出Vx1。

Is this equation clear?

这个方程清楚吗？

Okay, if the law happens,

好的，如果发生这种情况，

I'll continue.

我就继续讲。

And a second case.

还有第二种情况。

He wants to obtain Vx2. Vx2 is 0.1. It's dependent on the voltage here.

他想求出Vx2。Vx2等于0.1。这取决于这里的电压。

It's 20.

是20。

Okay. Here's Vx2, so the current flowing from both resistors is Vx2 minus 0. divided by 4. And here is from right to left, 0.1 Vx2.

好的。这是Vx2，所以流过这两个电阻的电流是Vx2减去0。除以4。这里是从右到左，0.1乘以Vx2。

That's assume the current is flowing

这里假设电流是

for these branches from right to left.

从右向左流过这些支路的。

So this is the entering. 0.1 Vx2. here is leaving.

所以，这就是流入的电流。也就是0.1Vx2。这里是流出的。

minus, make it bigger.

减去，把它变大一点。

0.1 Vx2. This is entering the current. and here is out. So minus.

0.1Vx2。这是流入的电流。这里是流出的。所以是减号。

minus this current, we will get the current. for this branch.

减去这个电流，就能得到这个电流。对于这条支路来说。

And the current for this branch can also be expressed. here is zero. If there's a node here, here should be 10.

这条支路的电流也可以这样表示。这里是零。如果这里有一个节点，这里应该是10。

Right? The current is flowing from right to left. so it's also equals to Vx2. as the voltage is 10 volt. minus 10.

对吧？电流是从右向左流动的。所以它也等于Vx2。因为电压是10伏特。减去10。

It's the voltage difference. divided by 20 is the current.

这是电压差。除以20就是电流。

is the second equation clear?

第二个方程清楚了吗？

any problems, any questions?

有什么问题或疑问吗？

okay, let's solve the two equations. the first one. we multiply 20. both for the left side and the right side. 20 should be 2 Vx1.

好的，我们来解这两个方程。第一个方程。我们乘以20。左边和右边都乘以20。20应该等于2Vx1。

minus 5 Vx1.

减去5Vx1。

plus 40.

加上40。

equals to Vx1.

等于Vx1。

so we are get 40 equals to 4 Vx1.

所以我们得到，40等于4Vx1。

Vx1 is

所以Vx1是

10.

10。

So the final Vx

别忘了是正数。所以，最终的Vx

is the x1 plus the x2. because they're positive. So that makes 10 plus 2.5. You will get 12.5.

等于x1加上x2。因为它们是正数。所以，就是10加2.5。结果是12.5。

Let's check the solutions. The first one, what we thought. we ignored the current source. The current source is said to open circuit. And for the second case, we kept the current source. and we removed the voltage source. It's said it's a short circuit.

我们来检查一下答案。首先，我们之前的想法是，我们忽略了电流源。电流源被视为开路。而对于第二种情况，我们保留了电流源。并移除了电压源。这被视为短路。

And you get 12.5, okay, that's correct.

结果也是12.5，没错。

Any questions?

还有问题吗？

If there's no questions,

如果没有问题的话，

let's end the meeting.

我们就结束会议吧。

there's also one independent source here.

这里还有一个独立的来源。

you understand it correctly?

你理解对了吗？

so take at least one source. the problem is, if we go to one source, it means we say it's open source. so just remove this one.

所以，至少要引用一个来源。但问题是，如果我们只引用一个来源，那就意味着我们说它是开源的。所以，把这个去掉吧。

and you want to talk about Kendall Lee, ACR. this is the next one.

如果你想讨论Kendall Lee，ACR。这是下一个。

and there is an important note. so for this branch, because there's a dependent. the current source is here. the current direction is always this direction. it is upwards, right?

这里有一个重要的注意事项。对于这个分支来说，因为它有一个依赖项。当前的来源在这里。当前的方向总是这个方向。是向上的，对吧？

so the current direction is here for this branch is from right to left. but here you can assume both upward or downward. it doesn't matter. so for example, if you assume the current flowing this branch is upwards, let the current be zero.

所以对于这个分支来说，当前的方向是从右向左的。但是在这里，你可以假设是向上或向下。这没关系。比如，如果你假设流经这个分支的电流是向上的，那么电流就是零。

should be zero minus vx1. divided by the resistance is four.

应该是零减去Vx1。再除以电阻4。

if you assume the current flowing upwards, because the current flowing from high potential, right? so here is high potential. you should use high potential minus low potential. you will get the current here.

如果你假设电流是向上的，因为电流是从高电位流向低电位的，对吧？所以这里就是高电位。你应该用高电位减去低电位。这样你就能得到这里的电流了。

and both current are entering.

而且这两个电流都是流入的。

and here you can assume current is leaving. here is both entering, so it should be leaving.

而在这里，你可以假设电流是流出的。这里两个都是流入的，所以这里应该是流出的。

and here is zero and here is 25. 25 to both. there's no here. okay, the current is leaving. yes, from right to left.

这里是零，这里是25。两边都是25。这里没有电流。好的，电流是流出的。是的，从右向左。

so it should be v x 1. current flowing from right to left, so here is high potential. minus 25.

所以应该是Vx1。电流从右向左流，所以这里是高电位。减去25。

divided by 20.

除以20。

okay.

好的。

but if you assume the current there is flowing from downwards, so it should be v x 1 minus 0, divided by 5 ohms.

但是，如果你假设那里的电流是从向下流的，那么应该是Vx1减去0，再除以5欧姆。

if this one is downwards and here is to the left, and for this direction, you can also assume the right or the left, both are okay.

如果这个是向下的，而这个是向左的，对于这个方向，你可以假设是向右或向左，都可以。

but if you assume the direction, change the equation correspondingly. the current always flowing from high potential to low potential.

但是，如果你假设了方向，就要相应地改变方程。电流总是从高电位流向低电位。

so here are two cases. the first one, we get a voltage source. and remove the current source, say it will open circuit. and for the second case, we keep the current. and remove the voltage. so there's no voltage drop here.

所以这里有两种情况。第一种情况是，我们有一个电压源。然后把电流源去掉，相当于开路。第二种情况是，我们保留电流源。然后把电压源去掉。所以这里没有电压降。

and for both case, we apply KCL, it's a current source. and we add v1 and v2 together. both are positive.

对于这两种情况，我们都应用基尔霍夫电流定律，也就是电流源。然后把V1和V2加起来。它们都是正的。

so we get them together. that's it for lecture eight. we have introduced the maximum power transfer, right? we know the conclusion. when the load resistance equals the Thevenin resistance, or load resistance equals the Thevenin voltage,

所以我们把它们加在一起。第八讲的内容就到这里。我们介绍了最大功率传输定理，对吧？我们知道结论。当负载电阻等于戴维南电阻时，或者负载电阻等于戴维南电压时，

load resistance. and previously we have introduced this conclusion. but this lecture, we also give the process. why we obtain this equation.

就是负载电阻。之前我们已经介绍过这个结论。但这一讲，我们也给出了推导过程。也就是为什么我们会得到这个公式。

and the resistance, going to the resistivity, the resistance depends on the length of the material and also the cross-sectional area. and we have introduced the temperature dependence. this is rho zero, alpha zero is the temperature coefficient.

关于电阻，也就是电阻率，电阻取决于材料的长度和横截面积。我们还介绍了电阻的温度依赖性。这是ρ0，α0是温度系数。

and theta zero is the reference temperature. Sometimes people use zero degree as reference temperature. And sometimes people are using the 20 degree. If 20 degree is used as reference, the R0 should be changed to R20.

而θ0是参考温度。有时候，人们会用0度作为参考温度。有时候也会用20度。如果以20度为参考，那么R0就应该改为R20。

And we have introduced the breakdown voltage.

我们还介绍了击穿电压。

that happens when the voltage is too high. And then electrical strength. This is the dielectric strength.

当电压过高时，就会发生这种情况。接下来是电气强度。这就是介电强度。

And finally, we have introduced the light-dependent resistors. LDR. The resistance can be changed depending on the light intensity.

最后，我们介绍了光敏电阻。简称LDR。电阻值会根据光线的强度而变化。

你要不要试用一下？

你要不要试用一下？

我点两份过来

我点两份过来。

我能吃吗哥

我能吃吗，哥？

两份菜啊

可以可以，两份菜啊。

你别给我记辣了我求你了

你别给我记辣了，我求你了。

你就给我送一份啊

你就给我送一份啊。

米饭都不够两份的量 你他妈扯犊子吧

这米饭都不够两份的量。你他妈扯淡吧。

你让他配一份配个一份上过来

你让他配一份，配一份上来。

能信的也是

能信的也是。

就这么着吧

那就这么着吧。

偷着给我

偷偷给我。

你说两个人吃

你说两个人吃，

说过了说过了

说过了，说过了。

我饿了，再算一份不够吃

我饿了，再算一份不够吃。

你说他妈两个人吃，你说这送他一份，他也不吃

你说他妈两个人吃，你说送他一份，他也不吃。

这不一人吃一份也差不多

这不一个人吃一份也差不多。

我操，他妈竟然不给我送两份，我操，生气了

我操，他妈竟然不给我送两份，我操，生气了。

今天晚上那个下课直接就开始上班了

今天晚上那个下课直接就开始上班了。

要不然不理我了

要不然不理我了。

你要不再点一份算了 都吃嘛

你要不再点一份算了。都吃嘛。

那个网络安全中心

喂，那个网络安全中心，

网络信息员

网络信息员。

网络信息，网络与信息中心

网络信息，网络与信息中心。

我看那啥，我看歌单

我看那啥，我看歌单。

看老爽了

看着老爽了。

哦，我知道了

哦，我知道了。

我喝一口

我喝一口。

你不是点俩汉堡吗

你不是点了俩汉堡吗？

咋没看见啊

咋没看见啊？

吃不饱

吃不饱。

我他妈看这饭吧，就他妈不吃了。

我他妈看这饭，就不吃了。

吃不饱 你还硬吃吗

吃不饱。你还硬吃吗？

怪不得感觉很酸呢 上面就不能吃

怪不得感觉很酸呢。上面就不能吃。

不见的话你别吃

不见的话你别吃。

见见好吃

见了才好吃。

来吃吧 别别别 这太凉了 来来肉

来，吃吧。别别别。这太凉了。来来，肉。

你妈

你妈

不见好就别吃

不见好就别吃。

还有勺子

还有勺子。

来肉片来肉片，肉片挺好的，高蛋白

来肉片，肉片挺好的，高蛋白。

我先吃

我先吃。

这烤肉串

这烤肉串，

这给我送了一 块

这给我送了一块。

我点上两个

我点了两个。

这肉串不一般

这肉串不一般。

那个老孙现在有多少点点小小游戏吗

那个老孙，现在有多少点点小小游戏吗？

不要看电视

不要看电视。

吃的时间要看电视

吃饭的时候要看电视。

哦明天还要去啊

哦，明天还要去啊？

我操老弟买了一包酸奶 高蛋白水果酸奶饮

我操，老弟，买了一包酸奶。高蛋白水果酸奶饮。

老板

老板，

我喝我喝 不好意思

我喝，我喝。不好意思。

你比我的好

你的比我的好。

我他妈在东北 在济南就有啊

我他妈在东北，在济南就有啊。

那芒果也好

那个芒果也很好。

然后我喝我的

然后我喝我的。

这个好喝

这个好喝。

老好喝了

特别好喝。

我上次给我妈点了个，妈的，我点错了

我上次给我妈点了个，妈的，我点错了。

我妈喝死了

我妈喝死了。

那你姥姥姥爷去哪 你姥姥去哪了

那你姥姥姥爷去哪了？你姥姥去哪了？

你肯定去过

你肯定去过。

那可不不考初中也

那可不，不考初中也。

要考 考出来应该还是找大哈密

要考。考出来应该还是找大哈密。

你俩还去啊

你们俩还去啊？

那过些年去啊

那过些年去啊。

花个一百块钱没必要

花一百块钱没必要。

我买的麦片饭都没开封啊 你买的意义是啥呗

我买的麦片饭都没开封呢。那你买的意义是啥呗？

我明天吃

我明天吃。

我他妈七点起来他妈之后就开始

我他妈七点起来，之后就开始

你俩还想要了不

你们俩还要了不？

那到时候我就我自己去吧

那到时候我就我自己去吧。

我妈真生气了

我妈真生气了。

去了还给我一打视频

去了还给我一打视频。

秋冬给我弟去

秋冬给我弟去。

那要干啥去呢

那要干啥去呢？

打篮球 我

打篮球。我。

就这个不打，其他都可以打

行，就这个不打，其他都可以打。

你先想，我再考虑考虑 去不去

你先想，我再考虑考虑。去不去。

要不然我们跑山吧

要不然我们跑山吧。

就那种一小块一块的

就那种一小块一小块的。

你给他带一个 多少钱 我不知道

你给他带一个。多少钱？我不知道。

我再说吧

回头再说吧。

这么有名了都 不是

都这么有名了。不是，

哎我这我这好像我生日是那个 是不是

哎，我这好像，我生日是那个。是不是？

我剪到

我剪到。

我去

我去，

这样

这样。

明天打

明天打。

明天不上明天打

明天不上，明天打。

明天十一点

明天十一点。

真的吗

真的吗？

后天后天不打 明天打

后天不打。明天打。

不打不打

不打不打。

这周都不打

这周都不打。

我那我我那过两天去那，我那个后天去威海

我那我那过两天去那，我那个后天去威海。

明天不去打

明天不去打。

那你们俩都去呢

那你们俩都去呢？

不是，那你俩你要去的话，你俩那来回都 你俩都不能 让我那

不是，那你俩你要去的话，那你俩来回都你们俩都不能让我那。

我不太，我不带你去了

我不太，我不带你去了。

操你妈

操你妈。

这人真死疯了

这人真疯了。

你他妈个屌，你他妈要去去哪啊

你他妈个屌，你他妈要去去哪啊？

他他不去，

啊？他他不去，

你咋他妈天天睡觉呢

你咋他妈天天睡觉呢？

改到啥时候了

改到啥时候了？

你晓得不知道

你知道不知道？

不一定

不一定。

哦哦这个

哦，哦，这个。

你他妈这么埋汰我

你他妈这么埋汰我。

笑死他了

笑死他了。

这什么鬼啊

这什么鬼啊？

做光头的

做光头的。

我骗你干屌啊

我骗你干嘛？

我骗你干屌啊

又不是我。

这咋

这咋了？

这不是你的

这不是你的。

你们那老房子那群

你们那个老房子那个群，

比那个群老大了 你们啥时候发的

那个群可大了。你们啥时候发的？

不是咋就咋了

不是，咋就咋了？

我就这么打算说的

我就是这么打算说的。

因为我也做处理

因为我也做处理。

你呢

你呢？

我去有什么好处啊

我去有什么好处啊？

我他妈一秒都待不了

我他妈一秒都待不了。

你们这个活动单飞人不要我

你们这个活动单飞人不要我，我他妈不用参加了。

那朝阳不应该要这个单飞啊 不是朝阳不应该要这个单飞啊

那朝阳不应该要这个单飞啊。不是，朝阳不应该要这个单飞啊。

我操你妈

我操你妈。

那为什么咱们这个活动可以参加

不是，那为什么咱们这个活动可以参加？

这有啥好说的

这有啥好说的？

给我退钱我操 我找老 他们干好多事呢

给我退钱，我操。我找老他们干好多事呢。

你能吃个宫保鸡丝，我那二婚能吃的啥呢

你能吃个宫保鸡丝，我那二婚能吃的啥呢？

我看你有那个二十十八块那个辣酱

我看你有那个十八块那个辣酱。

我这个能吃个那啥

我这个能吃个那啥。

我那个能吃个包子

我那个能吃个包子。

我就是 我那时候也没人找我

我就是那时候也没人找我。

我不是这么打算换的

不是，我不是这么打算换的。

那咋调嘛

那怎么调啊？

现在谁给你

现在谁给你

我操

弄啊？我操。

王牌飞行员

王牌飞行员。

我他妈是王牌飞行员

我他妈就是王牌飞行员。

有我来守护

有我来守护。

不要不要不要不要不要玩手机了

我操，不要不要

这电话给我打的

这电话给我打的，

还没给我发消息

怎么还没给我发消息呢？

都给我打了

都给我打了。

这网卡

这网太卡了。

总有一天你会超越我

总有一天你会超越我。

哎呦疲惫啊

哎哟，好疲惫啊。

我操

我操，这一拳。

不是我操

不是，我操，

就是滑不动

就是滑不动。

就是我操我真是 就是滑不动

不是，我他妈真是滑不动。

我靠

我靠，

这把会

这把会。

不行不行

不行，不行。

我不会

我不会。

我操 这他妈滑都滑不动

我操，这他妈根本滑都滑不动。

我这关注从买手机到现在就一直没修 然后给我充了钱你看了吗 我说我也就四年

我从买手机到现在就一直没修过。然后给我充了钱，你看了吗？我说我也就四年。

那我不是经常送

那我不是经常送。

我可是从那个贴膜店办了卡

我可是从那个贴膜店办了卡。

不是这样的

不是，是这样的。

我也没学

我也没学。

牛逼啊

哇，太厉害了。牛逼啊。

点另外一个

再点另一个。

那个他妈的啥蚊子啊

那他妈的是什么蚊子啊？

扣死了今天

太恶心了，今天。

这是啥玩意儿

这是什么东西啊？

我练了一套

我练了一套。

我再打回去

我再打回去。

我周二走

我周二走。

我找出来了

我找出来了。

你这筷子这是哪

你这筷子是哪的？

他想打我 怎么跳这么远啊

哎，他想打我，他想打我。怎么跳这么远啊？

这能吃啊

这能吃啊？

喝完了

喝完了。

我今天不也喝完了 你前面还喝不喝

我今天不也喝完了。你前面还喝不喝？

我可以去打一会儿

我可以去打一会儿。

再来一个牛肉饭

再来一个牛肉饭。

我s都穿了

我连S码都穿了。

这玩意能跟我玩小游戏

这东西还能玩小游戏。

我怎么算的四千多

我怎么算的是四千多？

这是乘十的负三 那个乘十的负十六

这个是乘以10的负3。那个是乘以10的负16。

这地方好堵

这个地方好堵啊。

这个截止日期是有点晚的感觉

这个截止日期感觉有点晚了。

我想把这个节日提前 现在四月二十六号嘛

我想把这个节日提前。现在是4月26号嘛。

这个我们早就讲完了

这个我们早就讲完了。

不要

不要。

你都发你了

你都发给他了。

转他号

转给他吧。

不知道 他妈考试跟他妈中专考一个试

不知道。这考试跟中专的考试一样。

They are designed for small changes in temperature. If the temperature change is a small value, the change in resistance is proportional to the change in temperature. When the temperature changes, the resistance also changes, and they have a linear relation. The coefficient of temperature dependence, alpha, is defined as the ratio of the change in resistance per degree of temperature to the resistance at a defined temperature.

它们适用于温度的微小变化。若温度变化量较小，则电阻的变化与温度的变化成正比。当温度改变时，电阻也随之改变，二者呈线性关系。温度系数 alpha 定义为每度温度下电阻的变化量与某一参考温度下电阻值的比值。

And here is the definition expressed by equation. The change in resistance per degree of temperature divided by the reference resistance gives us the temperature coefficient of resistance.

以下是用方程表示的定义。电阻随温度的变化量除以参考电阻，即为电阻的温度系数。

The initial resistance is R0 and the current resistance is R1. So R1 minus R0 is the change in resistance. And theta1 is the current temperature. If we use zero degree as the reference, the change in temperature should be theta1 minus zero, because zero is defined as the reference temperature.

初始电阻为R0，当前电阻为R1，因此R1减去R0即为电阻的变化量。θ1为当前温度。若以零度作为参考，则温度的变化量应为θ1减去零，因为零被定义为参考温度。

The reference basis sets, R0, allow us to obtain an equation expressing the electron configuration. By changing the formal density, we arrive at this expression. However, note that this expression only holds under specific conditions.

参考基组 R0 使我们能够得到一个表达电子构型的方程。通过改变形式密度，我们可以得到这个表达式。但请注意，该表达式仅在特定条件下成立。

Entropy can be zero. This equation has only one difference: you can choose a different temperature as reference. If you use a different temperature as reference, you get the following equation. Here, S₀ is the entropy at the reference temperature. If S at T₀ is zero, you get the equation above.

熵可以为零。这个方程只有一个区别：你可以选择不同的温度作为参考。如果你使用不同的温度作为参考，就会得到下面的方程。这里，S₀ 是参考温度下的熵。如果 T₀ 处的熵为零，就得到上面的方程。

Based on this equation, you can compute an unknown resistance at a given temperature. Once the temperature T₁ is given, you can compute the unknown resistance at that temperature. Here, the reference temperature is T₀ and the reference resistance is R₀. Alternatively, if you know the resistance at a certain temperature, you can use this equation to compute the corresponding temperature T₁. If R₁ is given, you can use this equation to find T₁. So what is the corresponding temperature for this resistance?

根据这个方程，你可以计算某一给定温度下的未知电阻。一旦温度 T₁ 已知，你就可以求出该温度下的未知电阻。其中，参考温度为 T₀，参考电阻为 R₀。反过来，如果你已知某一温度下的电阻值，也可以利用这个方程求出对应的温度 T₁。若 R₁ 已知，就可以用这个方程求得 T₁。那么，对于这个电阻值，对应的温度是多少？

At higher temperature, you have higher resistance. The temperature coefficient is not solely dependent on the material. Given the material and the temperature, you obtain the coefficient. You do not need to conduct experiments; the values are provided.

温度越高，电阻越大。温度系数并非仅取决于材料本身。给定材料和温度，即可得到该系数。无需进行实验，相关数值已直接给出。

Sometimes people use zero degree as reference; sometimes people use twenty degree as reference. If we use twenty degree as reference, we should change the equation accordingly. Set T zero here as twenty. Alpha twenty is the temperature coefficient at twenty degree, and R twenty is the resistance at temperature twenty. So we should change Equation 3.1.

有时人们使用零度作为参考温度，有时使用二十度作为参考温度。如果我们使用二十度作为参考温度，就应当相应地修改方程。这里令 T 零等于二十。阿尔法二十是二十度时的温度系数，R 二十是温度为二十度时的电阻值。因此我们需要修改公式 3.1。

There are three ways to obtain a different result. First, you can change the reference temperature. Second, you can change the temperature coefficient α. Third, you can change the initial resistance. There is another table showing the temperature coefficients at 30 degrees.

获得不同结果有三种方法。第一，可以改变参考温度。第二，可以改变温度系数 α。第三，可以改变初始电阻。还有一张表列出了 30 度时的温度系数。

By looking up this table, we can also get the temperature coefficient: alpha T zero, alpha T one, alpha T two. We also have another concept introduced here: conductance. Conductance is the reciprocal of resistance. So G equals one divided by R.

通过查阅这张表，我们还可以得到温度系数：α_T0、α_T1、α_T2。这里还引入了另一个概念：电导。电导是电阻的倒数。所以 G 等于 1 除以 R。

The resistance of a given object depends on two factors. One is the material, because the material decides the resistivity. The other is the shape, which decides the length and also the cross-sectional area. So based on these three quantities, you can get the resistance.

给定物体的电阻取决于两个因素。一是材料，因为材料决定了电阻率。二是形状，它决定了长度和横截面积。因此，根据这三个量，你就可以得到电阻。

The resistance is inversely proportional to the cross-sectional area. A thick copper wire has lower resistance than an otherwise identical thin copper wire because a thick copper wire has a larger cross-sectional area, so the resistance is lower. Resistance is also proportional to length, so longer...

电阻与横截面积成反比。一根粗铜线的电阻比一根其他条件相同的细铜线低，因为粗铜线的横截面积更大，所以电阻更低。电阻还与长度成正比，所以更长的……

Conductance is the inverse resistance; it equals one divided by R. And here we use another…

电导是电阻的倒数，等于一除以R。这里我们使用另一个……

Lambda Q is also the inverse of resistivity. Lambda Q is the inverse of resistivity: one divided by rho. This is how it must be used. Based on the definition, you can get these two equations.

Λ_Q 也是电阻率的倒数。Λ_Q 是电阻率的倒数，即 1 除以 ρ。使用时必须如此。根据定义，你可以得到这两个方程。

This is the inverse of resistance. Sigma is the inverse of resistance. Sigma is defined as conductivity. Here are some concepts: electrical breakdown and chemical breakdown.

这是电阻的倒数。Sigma 是电阻的倒数。Sigma 被定义为电导率。以下是几个概念：电击穿和化学击穿。

It is not biodegradation; it is bioelectric breakdown. Bioelectric is a kind of electric breakdown. In biodegradation, it is not only breakdown but also bioelectric breakdown. So for high electric breakdown, it is a post-synthetic—

这不是生物降解，而是生物电击穿。生物电是一种电击穿。在生物降解中，不仅是降解，还涉及生物电击穿。因此对于高电击穿而言，它是一种后合成——

When an electric field is applied to the material, something happens — the voltage suddenly becomes an electric field conductor, and electricity current flows through it. Initially, the material is not conductive. But if you apply a very high voltage to the material, the material suddenly becomes conductive. This is known as electrical breakdown.

当电场施加于材料时，会发生某种变化——电压突然使材料成为电导体，电流随之通过。起初，材料并不导电。但如果你对材料施加非常高的电压，材料会突然变为导体。这被称为电击穿。

What happens when you apply voltage? You apply voltage to x, the material, and the electric field E equals V over d. So what is voltage? For x, the material, E equals V over d — the electric field. Now, when you apply voltage to a material, the material will produce an electric field. So if the electric field is too large, and x is the material, E equals V over d.

当我们施加电压时会发生什么？将电压施加于材料 x 上，电场 E 等于 V 除以 d。那么电压是什么？对于材料 x，E 等于 V 除以 d，即电场。现在，当你对材料施加电压时，材料会产生电场。因此，如果电场过大，而 x 是材料，则 E 等于 V 除以 d。

At a certain voltage level, when the insulation of a device breaks down, the voltage is called breakdown voltage. The voltage at which electrical breakdown occurs is defined as breakdown voltage. Breakdown voltage depends on...

当器件的绝缘在某一电压水平下发生击穿时，该电压称为击穿电压。发生电击穿时的电压被定义为击穿电压。击穿电压取决于……

The size and shape of the material. So different material requires different breakdown voltage. Some material you must apply a very high voltage in order to get breakdown, and some material you don't have to apply very much voltage. You can just apply very small voltage and still get its breakdown. And breakdown can happen easily using different materials. You can have either a solid material or liquid material or gas material or vacuum material. Different kinds of material go at breakdown.

材料的尺寸和形状。不同材料需要不同的击穿电压。有些材料必须施加非常高的电压才能实现击穿，而有些材料则不需要施加很高的电压，只需施加很小的电压就能实现击穿。使用不同材料时，击穿很容易发生。可以是固体材料、液体材料、气体材料或真空材料。不同种类的材料都会发生击穿。

There is a yield strength, or a breaking point. Even though glass is not conductive, if you apply a very large voltage, the glass can become conductive.

存在一个屈服强度，或者说击穿点。尽管玻璃本身不导电，但如果施加非常大的电压，玻璃可以变为导体。

When you apply a voltage across two plates separated by a certain distance, you obtain an electric field intensity. This phenomenon is also referred to as electrical breakdown. The breakdown strength, or dielectric strength, is the maximum electric field that the material can withstand.

当你在两块相距一定距离的极板之间施加电压时，会产生电场强度。这一现象也被称为电击穿。击穿强度，即介电强度，是材料所能承受的最大电场。

Dielectric strength is the electric field strength a material can withstand under ideal conditions without undergoing electrical breakdown. The electric field is 10^7. When the electric field E produced by voltage is high, the material will undergo breakdown.

介电强度是材料在理想条件下能够承受而不发生电击穿的电场强度。该电场值为10^7。当由电压产生的电场E足够高时，材料将发生击穿。

And also we have line independence. At the beginning, you introduce different signals for the system. The system consists of objects, but some systems have line independence to existence.

此外，我们还有线性无关性。一开始，你为系统引入不同的信号。系统由对象组成，但某些系统具有存在上的线性无关性。

Here is a photoresistor, also known as a light-dependent resistor, or LDR. It is a variable resistor whose resistance changes according to the intensity of light. When the intensity of light increases, the resistance decreases. When the light intensity decreases, the resistance becomes higher.

这里是一个光敏电阻，也称为光依赖电阻，即LDR。它是一种可变电阻，其阻值随光照强度而变化。当光照强度增大时，电阻减小；当光照强度减小时，电阻增大。

It is a very special resistor. It shows photoconductivity, and it is made using low-dimensional materials, specifically semiconductors. So a photoresistor uses semiconductor materials.

这是一种非常特殊的电阻器。它表现出光电导性，并且使用低维材料制成，具体来说是半导体。因此，光敏电阻使用的是半导体材料。

This kind of transistors also have a spectral response similar to that of human eyes.

这类晶体管的光谱响应也与人眼相似。

When the light intensity is higher, you get lower resistance. When the light intensity is lower, you get higher resistance. Let's look at the figure. This is an LDR — a light-dependent resistor. The x-axis is the light intensity; the y-axis is the resistance. When the light intensity is increased, you get lower resistance. When the light intensity is lower, you get higher resistance. You get a curve like this.

当光强较高时，电阻较低；当光强较低时，电阻较高。我们来看这张图。这是一个LDR——光敏电阻。横轴是光强，纵轴是电阻。当光强增大时，电阻降低；当光强降低时，电阻升高。你会得到这样一条曲线。

This image shows the rear ADR. The vehicle looks like this — this is the vehicle product, rear ADR. We also use these two symbols to represent ADR. You can see two arrows; arrows represent the lines.

这张图展示的是后部ADR。车辆看起来是这样的——这是车辆产品，后部ADR。我们还使用这两个符号来表示ADR。你可以看到两个箭头，箭头代表线。

When light is applied, you get different resistance depending on the light intensity. There are two different symbols to represent LDR. The LDR has different applications. It can be used to detect whether there is light.

当施加光照时，电阻会随光强不同而变化。LDR有两种不同的符号表示。LDR有不同的应用，它可以用来检测是否有光。

If there is no light, the resistance will be high. If there is light, the resistance will be low. So you can use this function to detect whether the light is present or absent. And you can measure the light intensity by how much the resistance has changed.

如果没有光，电阻会很高；如果有光，电阻会很低。因此你可以利用这一特性来检测光是否存在，并且可以通过电阻变化的大小来测量光的强度。

For example, you can use this LDR resistor as a fire detector. Fire produces light. If there is fire, the resistance of the resistor changes. Then you should call the firefighter. You can use this function to design a warning system. If fire happens, the resistance will change, so you can activate the warning system and call the firefighter.

例如，你可以使用这个光敏电阻（LDR）作为火灾探测器。火会产生光。如果有火，电阻的阻值会发生变化，这时你就应该呼叫消防员。你可以利用这一功能设计一个报警系统。一旦发生火灾，电阻值会改变，从而触发报警系统并呼叫消防员。

Here is an example application of AGR. Depending on the resistance properties, it can have different applications. You don't have to remember these examples. These examples are just used to explain the possible applications of AGR.

这里有一个AGR的应用实例。根据其电阻特性，它可以有不同的应用。你们不需要记住这些例子。这些例子仅用于说明AGR的可能应用。

This is Lecture 8. This is repeated knowledge we introduced at the beginning. We introduced the resistance equation depending on the length and the cross-sectional area. We also know that resistance depends on temperature. Based on the reference temperature, you can get the…

这是第八讲。这些是我们在开头已经介绍过的重复知识。我们介绍了电阻方程，它取决于长度和横截面积。我们还知道电阻取决于温度。基于参考温度，你可以得到……

A new resistance appears at a certain temperature. And finally, we have introduced electrical stress breakdown: when the voltage is too high, even low-conductivity materials exhibit conductivity. Those are the three aspects covered in this lecture. Now, for the exercise—this exercise is drawn from Lectures Six and Seven. It uses superposition.

在一定温度下会出现新的电阻。最后，我们介绍了电应力击穿：当电压过高时，即使是低电导率材料也会表现出导电性。以上就是本次讲座涵盖的三个方面。接下来看练习——这道练习出自第六讲和第七讲，用到了叠加原理。

Seven parameters. For the multi-source, it is sent into...

七个参数。对于多源情况，它被送入……

For a short circuit, there is no voltage drop across it. For a current source that is turned off, it becomes an open circuit, so no current flows through it.

对于短路，其两端没有电压降。对于被关断的电流源，它等效为开路，因此没有电流流过。

When there is a short circuit, current flows through it. When it is open, there is no current—current cannot flow through this branch. Now we can compute the series resistance. Starting from terminal A, these two resistors are connected in series, then go back to terminal B. We simply add them: R + R = 2R. This is the series resistance. The fourth step is to put the source back and obtain the original circuit. Then we compute the open-circuit voltage.

当存在短路时，电流流过该支路。当支路断开时，没有电流——电流无法通过该支路。现在我们可以计算串联电阻。从端子A出发，这两个电阻串联连接，然后回到端子B。我们只需将它们相加：R + R = 2R。这就是串联电阻。第四步是将电源放回，得到原始电路。然后我们计算开路电压。

Terminals, open circuit, V_AB. Open circuit voltage. Now we should use superposition. Based on the question, we should use superposition. Superposition is used to compute voltage or current for several resistors. You just follow the normal process. You use only superposition to compute the voltage or current. Right. Now you want to compute the open circuit voltage based on superposition.

端子，开路，V_AB。开路电压。现在我们应该使用叠加定理。根据题目要求，我们应使用叠加定理。叠加定理用于计算多个电阻上的电压或电流。你只需按照正常流程进行，仅使用叠加定理来计算电压或电流。好。现在你要基于叠加定理来计算开路电压。

We just keep one resource. If we keep the voting resource and we remove the current resource, how do we remove it? We set it for consensus so that there is no current resource. So what is voting here? Voting is BFT.

我们只保留一个资源。如果我们保留投票资源并移除当前资源，该如何移除？我们将其设置为共识状态，这样就不存在当前资源了。那么这里的投票是什么？投票就是BFT（拜占庭容错）。

Because it is an open circuit, it is not a closed loop. Therefore, the voltage over AB is directly the source voltage. This is the first case. Since it is an open loop, there is no voltage drop and no current in the circuit. So V_AB equals the voltage of the source. For the second case, we remove the voltage source. How do we remove the voltage source? We replace the voltage source with a wire.

因为这是一个开路，不是闭合回路，所以AB两端的电压直接等于电源电压。这是第一种情况。由于是开路，电路中没有电压降，也没有电流。因此V_AB等于电源电压。第二种情况，我们移除电压源。如何移除电压源？我们用一根导线替代电压源。

Starting from this point, look at this. At this time, you get the current sources A and B. For this case, the open circuit gives the open circuit voltage here, A and B. This loop is open; it is an open circuit. So there is no voltage drop on this resistor. Therefore, VAB is directly the voltage of this resistor, because the branch is not closed, so there is no current flowing here. So VAB is directly the voltage across this resistor.

从这一点开始，看这里。此时，你得到电流源A和B。对于这种情况，开路给出此处的开路电压，即A和B。这个回路是断开的，是一个开路。因此，该电阻上没有电压降。所以VAB直接等于该电阻上的电压，因为该支路没有闭合，所以这里没有电流流过。因此，VAB直接等于该电阻两端的电压。

Now let us determine the voltage across this resistor. In this case, the current is 1 ampere and the resistance is 6 ohms, so we get 6 volts. Pay attention to the direction of the potential. In the first case, point A is at high potential and point B is at low potential.

现在我们来确定这个电阻两端的电压。在这种情况下，电流为1安培，电阻为6欧姆，因此我们得到6伏特。请注意电位的方向。在第一种情况下，A点处于高电位，B点处于低电位。

In the second case, the current is flowing from A to B. In the other case, the current is flowing from B to A. Here, B has higher potential and A has lower potential. Finally, we have to find out the voltage, which is minus six, because A is more negative than B.

在第二种情况下，电流从A流向B。在另一种情况下，电流从B流向A。此时，B的电势较高，A的电势较低。最后，我们需要求出电压，其值为负六，因为A比B更负。

The circuit involves x plus y over x. We can also analyze the series circuit and the parallel circuit. This is the series circuit, and this is the parallel circuit with resistance and voltage. Don't forget to draw the circuit.

该电路涉及 x 加 y 除以 x。我们还可以分析串联电路和并联电路。这是串联电路，这是包含电阻和电压的并联电路。别忘了画出电路图。

Whereas we previously used superposition of the amplitude, here there is something different. Here we have one incident source.

此前我们使用的是振幅叠加，但这里有所不同。这里我们只有一个入射源。

[No speech content in this segment; the instructor is writing on the board in silence.]

【该时段无语音内容；教师正在黑板上书写，全程沉默。】

For the first circuit, here is an independent current source. Here is zero volts, connected to ground. And this node is also Vx1.

对于第一个电路，这里是一个独立电流源。这里是零伏，连接到地。而这个节点也是Vx1。

We can apply Kirchhoff's Current Law. For example, here is Vx1. The current flowing through the resistor is downwards, expressed as Vx1 minus 0 divided by 4. This is the current here. And then here is also a dependent current source. The current is 0.1 times...

我们可以应用基尔霍夫电流定律。例如，这里是Vx1。流过电阻的电流方向向下，表示为Vx1减去0除以4。这就是这里的电流。然后这里还有一个受控电流源，其电流为0.1乘以……

We can apply Kirchhoff's Current Law. For example, here is Vx1. The current flowing through the resistor is downwards, expressed as Vx1 minus 0 divided by 4. This is the current here. And then here is also a dependent current source. The current is 0.1 times...

我们可以应用基尔霍夫电流定律。例如，这里是Vx1。流过电阻的电流方向向下，表示为Vx1减去0除以4。这就是这里的电流。然后这里还有一个受控电流源，其电流为0.1乘以……

The direction is as shown. The current here is 0.1 times dx1. It depends on the voltage. If the voltage is dx1, then the current is 0.1 times dx1. We have two currents here. Let us assume this direction.

方向如图所示。此处的电流为0.1乘以dx1。它取决于电压。如果电压为dx1，则电流为0.1乘以dx1。这里有两个电流。我们假设这个方向。

This should be 0.1 V times 1, minus the voltage here. Here is the current entering the load, and here it is leaving—also leaving. So by subtracting the voltage here, you can obtain the current here. Then from this result, you need to apply the drift current formula.

这一项应为 0.1 V 乘以 1，再减去此处的电压。这里是电流流入负载的方向，而这里是流出的方向——同样是流出。因此，用此处电压相减即可得到该处的电流。然后，根据这一结果，需要应用漂移电流公式。

The voltage is upwards relative to the current. At the end, we can determine the current through this 270-ohm resistor. It is Vx1, so the current here is Vx1 minus 0 — here it is 0 — divided by 270. We know that this is the current flowing through the load, and 2 ampere is also entering. The only one…

电压相对于电流方向是向上的。最后，我们可以求出流过这个270欧姆电阻的电流。它是Vx1，所以这里的电流就是Vx1减去0——这里是0——再除以270。我们知道这是流过负载的电流，同时2安培也在流入。唯一的一个……

The current is leaving the node. The current leaving is Vx1 minus zero, divided by twenty. This gives us our first equation, from which we can solve for Vx1. Is this equation clear?

电流从节点流出。流出的电流为 Vx1 减去零，再除以二十。这就是我们的第一个方程，由此可以求解 Vx1。这个方程清楚吗？

For the second case, we want to obtain Vx2 expressed as a function of... There is another kind of bound where Vx2 is dependent on the velocity here.

对于第二种情况，我们希望将Vx2表示为……的函数。还有另一种约束，其中Vx2依赖于这里的速度。

There is one current flowing from B to A through a four-ohm resistor. It equals V_x2 minus zero divided by four ohms, which gives us 0.1 times V_x2, directed from right to left. We assume the current for this branch flows from right to left. This is entering the node.

有一条电流从B点经四欧姆电阻流向A点。它等于V_x2减去零再除以四欧姆，即0.1乘以V_x2，方向从右向左。我们假设该支路的电流从右向左流动。这是流入节点的。

Zero times one, e to the x—this is entering the current, entering this node. The minus sign has meaning. So minus this current here gives the current for this branch.

零乘以一，e的x次方——这是流入电流，流入这个节点。负号是有意义的。所以减去这里的这个电流，就得到这条支路的电流。

The current in this branch can also be expressed as V₀. If that value is known here, it should be 10. The current is flowing from right to left, so it is also equal to V_X2, which is 10 volts, minus 10. The voltage difference divided by 20 gives the current.

该支路的电流也可以表示为 V₀。如果该值已知，则应为 10。电流从右向左流动，因此它也等于 V_X2，即 10 伏特减去 10。电压差除以 20 即为电流。

We have e equals e_x1. Adding to both sides, we get 4g equals 4e_x1 cos φ. This is the second equation.

我们有 e 等于 e_x1。两边同时加上，得到 4g 等于 4e_x1 cos φ。这是第二个方程。

Are the equations clear? Any problems? Any questions? Let's solve the two equations. For the first one, we multiply 20 on both the left side and the right side. 20 should give us 4x₁ minus 5x₁ plus 40.

方程清楚了吗？有没有问题？有没有疑问？我们来解这两个方程。对于第一个方程，我们在左右两边同时乘以20。20应该得到4x₁减去5x₁加上40。

Here is e to the x minus 1, minus 1, equals e to the x minus lambda. So here is minus 2. Here is e to the x minus lambda. But e to the x times 1 is equal to 1.

这里是 e 的 x 减 1 次方，减 1，等于 e 的 x 减 λ 次方。所以这里是负 2。这里是 e 的 x 减 λ 次方。但 e 的 x 乘 1 次方等于 1。

Both are positive, so the integral is zero. For the final dx, the final dx is dx plus dx. Both are positive, so that gives us plus 25.

两项均为正，因此积分为零。对于最终的 dx，最终 dx 等于 dx 加 dx。两项均为正，所以结果为加 25。

Two situations. In the first one, we kept the working source W and removed the current source; the current source is set to 130k. In the second case, we kept the current source and removed the working source; we set it to 30k. Any questions?

两种情况。第一种，我们保留工作源W，移除电流源，将电流源设定为130k。第二种情况，我们保留电流源，移除工作源，将其设定为30k。有没有问题？

If there are no questions, let's end here. We will continue next time. Next class is on Monday.

如果没有问题，我们就到此结束。下次继续。下节课在周一。

Do you understand correctly how to solve independent equations? What is the solution?

你们是否正确地理解了如何求解独立方程？解是什么？

No intelligible lecture content is present in this segment. The audio consists of ambient noise, paper rustling, a cough, and indistinct background murmuring with no discernible instructional speech.

该时间段内无可辨识的课堂讲授内容。音频仅包含环境噪音、翻动纸张声、一声咳嗽以及无法听清的背景低语，没有可提取的教学语句。

Take one source. The first thing is, we have both partial sources. Take both partial sources, which means we say the open circuit is open. So just remove this one and make it open.

取一个电源。首先，我们有两个部分电源。取两个部分电源，也就是说开路是断开的。所以只需移除这一个，使其断开。

You can take Vx1 for both KCL equations. For this branch, because there is a dependent current source here, the current direction is always upward. So the current direction for this branch is from right to left. But here, you can assume the current flowing in this branch is either upward or downward; it does not matter. For example, if you assume the current flowing in this branch is upward, then the current should be 0 minus Vx1.

你可以对两个KCL方程都取Vx1。对于这条支路，因为这里有一个受控电流源，电流方向始终向上。所以这条支路的电流方向是从右到左。但在这里，你可以假设流过这条支路的电流向上或向下，都无所谓。例如，如果你假设流过这条支路的电流向上，那么电流应该等于0减去Vx1。

Divided by the resistance equals four. If you assume the current flows upwards, because current flows from high potential to low potential—here is high potential—so you use high potential minus low potential, and you will get the current here. Both currents are entering. Here you can assume the current is leaving; since both are entering here, it should be leaving. Here is zero and here is twenty-five volts; here is low. The current is leaving, from right to left, so it should be...

除以电阻等于四。如果你假设电流向上流动，因为电流从高电位流向低电位——这里是高电位——所以用高电位减去低电位，就能得到这里的电流。两个电流都是流入的。这里你可以假设电流是流出的；既然这里两个都是流入，那它应该是流出的。这里是零，这里是二十五伏特；这里是低电位。电流是流出的，从右到左，所以它应该是……

For Vx1, the current is flowing from right to left, so the time potential is minus 25 divided by 20. But here, assume the current is flowing downwards.

对于 Vx1，电流从右向左流动，因此时间电位为负25除以20。但在这里，假设电流向下流动。

This should be Vx1 minus V0 divided by h. If this one is downwards and here is to the left, for this direction you can assume either way; both are okay. But if you assume a direction, it will change the equation correspondingly. Current always flows from higher potential to lower potential.

这里应该是 Vx1 减去 V0 再除以 h。如果这个方向是向下的，而这里是向左的，对于这个方向你可以假设任意一种，两种都可以。但如果你假设了一个方向，方程会相应地改变。电流总是从高电势流向低电势。

We consider two cases. In the first case, we obtain both the body source and remove the parent source, so there is no parent. In the second case, we obtain the parent and remove the body, so there is no body problem. For both cases, we apply TCM, get the parent source, and obtain V₁ and V₂ together. Both are positive, so we get them together.

我们考虑两种情况。第一种情况下，我们同时获得体源并移除父源，因此不存在父源。第二种情况下，我们获得父源并移除体源，因此不存在体源问题。对于这两种情况，我们都应用TCM，得到父源，并将V₁和V₂一起求出。两者均为正，因此我们将它们一起得到。

In Lecture A, we introduced the maximum power transfer formula. The conclusion was that maximum power is delivered when the load resistance equals the source resistance. Previously in this lecture, we introduced this conclusion and also provided the derivation process showing how we obtain this equation. So how can you get this conclusion? And the resistance going into the resistance—

在A讲中，我们引入了最大功率传输公式。结论是：当负载电阻等于源电阻时，传输功率最大。在本讲前面，我们已经介绍了这一结论，并给出了推导过程，说明如何得到这个方程。那么，如何得出这个结论呢？而电阻进入电阻——

The resistance depends on the length of the material and the cross-sectional area of the material. We have introduced the temperature dependence: resistivity ρ equals ρ₀(1 + α ΔT). α₀ is the temperature coefficient. ΔT is the reference temperature difference. Sometimes people use zero degrees as reference, and sometimes people use twenty degrees as reference.

电阻取决于材料的长度和横截面积。我们已经引入了温度依赖性：电阻率 ρ 等于 ρ₀(1 + α ΔT)。α₀ 是温度系数，ΔT 是参考温差。有时人们以零度作为参考，有时以二十度作为参考。

R0 should be changed into R20. We have introduced a breakdown that happens when the voltage is too high and the electrical strength exceeds the dielectric strength. And finally, we have introduced a dependency matrix.

R0应改为R20。我们已经介绍了击穿现象，它发生在电压过高且电场强度超过介质强度时。最后，我们引入了依赖矩阵。

In AFM, the change in intensity depends on the light intensity. Next, we move on to CRND.

在原子力显微镜（AFM）中，强度的变化取决于光强。接下来，我们进入CRND部分。

[No instructional content detected in this segment. The audio consists entirely of informal student chatter and social banter with no pedagogical material.]

[该片段未检测到教学内容。音频内容完全为学生间的非正式闲聊与社交对话，不包含任何教学信息。]

This segment contains only casual, non-instructional conversation among students regarding food portions. No lecture content is present.

本片段仅包含学生之间关于食物份数的随意闲聊，无课堂教学内容。

No substantive English lecture content is discernible in this segment. The audio consists primarily of background classroom noise, indistinct murmuring, and non-speech sounds with no recoverable pedagogical material.

该片段中无可辨识的实质性英文授课内容。音频主要由教室背景噪音、模糊的低语和非语音声音组成，没有可提取的教学材料。

As I have already mentioned, the question is how one would know. This relates to the point we discussed earlier.

正如我之前已经提到的，问题在于如何得知。这与我们之前讨论的观点相关。

I'm hungry. Two skewers aren't enough for us. One person can't finish one skewer alone.

我饿了。两串不够我们吃。一个人连一串都吃不完。

Assume I₂. Because I₁ is given, we can derive the result from this assumption.

假设 I₂。因为 I₁ 已知，我们可以从该假设推导出结果。

The relevant department is the Network and Information Center.

相关部门是网络与信息中心。

I see. You haven't eaten yet? Let's go. I'll ask you what you want to eat.

我知道了。你还没吃饭吧？走吧。我问你想吃什么。

Zhao Minting can't eat that. Brother, it's unhealthy—don't eat it. No, no. Come, have some meat. Actually, this is very healthy. Here, some meat. No, I won't give you any. Brother… Come, have some meat skewers. Good brother, you can eat the crab roe. Here, meat skewers—they're about six yuan. High protein. I'll eat it myself.

赵敏婷不能吃那个。哥哥，不健康你别吃。不行不行。来，吃肉。这其实很健康。来，肉。不给。哥哥……来，吃肉串。好哥哥，蟹黄你能吃。来，肉串，六块钱好像。高蛋白。我自己吃。

The work score is not 100. It is 98. There is also a small game involved.

工作评分不是一百分，是九十八分。另外还涉及一个小游戏。

[No discernible lecture content in this segment. The audio consists primarily of background noise, indistinct chatter, and non-speech sounds with no intelligible instructional material.]

[该片段无可辨识的课堂讲授内容。音频主要由背景噪音、模糊人声及非语音声音组成，不含可理解的教学信息。]

The discussion centers on yogurt and nut products. One speaker notes having bought a pack of high-calcium yogurt with nuts, mentioning it was purchased multiple times. Another speaker comments that the product tastes good and is popular in Northeast China.

讨论围绕酸奶和坚果产品展开。一位发言人提到自己买了一包高钙坚果酸奶，并表示已购买多次。另一位发言人评论说该产品口感好，在东北地区很受欢迎。

This segment contains only fragmented, informal conversational speech with no discernible academic or instructional content. The speakers appear to be discussing casual topics such as dining, with repeated references to hot pot and family members, but no coherent lecture material can be extracted.

该片段仅包含碎片化的非正式对话语音，无可辨识的学术或教学内容。说话者似乎在讨论用餐等日常话题，反复提及火锅和家人，但无法提取出连贯的课堂讲授材料。

No instructional content detected in this segment. The audio consists entirely of casual student conversation (discussing graduate entrance exams, meal plans, and errands) with no lecture material.

该片段未检测到任何教学内容。音频内容全部为学生之间的闲聊（讨论考研、用餐计划和日常事务），不包含任何课堂讲授材料。

Are you going? If you're not going, I'll take a taxi by myself. I'll go on my own. Who's going? I am.

你去不去？你要是不去，我自己打车去。我自己去。谁去？我去。

You think about it first; I'll consider whether to go or not. How about we go hiking?

你先想想，我再考虑去不去。要不然我们去爬山吧？

Those come in small boxes. How much are they? Is this brand really that well-known? One box of chocolate—that's all I need.

那种是一小盒一小盒装的。多少钱？这个牌子真的那么有名吗？一盒巧克力——我只要这些就够了。

我去过。明天打球？明天不下雨吗？明天不打，后天打。不打不打，这周都不打了。我过两天去。

我去过。明天打球？明天不下雨吗？明天不打，后天打。不打不打，这周都不打了。我过两天去。

[No substantive instructional content in this segment; only background noise, coughing, and fragmented off-topic remarks.]

[本段无实质性教学内容；仅有背景噪音、咳嗽声及零散的无关对话。]

Are you sure? Let me take a look. Why would I lie to you? I can't stand it.

你确定吗？让我看一下。我骗你干什么？我受不了了。

This is about surveillance. Monitoring.

这是关于监控的。监测。

No coherent lecture content is discernible in this segment. The audio consists primarily of indistinct background chatter and fragmented, unintelligible speech with no identifiable academic material.

该片段中无法辨识出连贯的课堂讲授内容。音频主要由模糊的背景闲聊和碎片化、不可理解的语音组成，没有可识别的教学材料。

When was it sent? Look at the question. What are you afraid of? Speak up loudly. How would I know?

什么时候发的？看题。怕啥？大声说。我咋知道？

The audio in this segment consists of fragmented, informal speech with no coherent instructional content. No formal lecture material can be extracted.

该时间段音频为碎片化的非正式口语，无可提取的连贯教学内容。

[No instructional content detected in this segment. The audio consists of informal, non-academic conversation with no lecture material.]

[该片段未检测到教学内容。音频为非正式的随意对话，不含任何课堂讲授信息。]

我们一起去吧。到时候我送你。我们买那个卡，买完卡之后再去。业绩什么的，买了卡再说。

我们一起去吧。到时候我送你。我们买那个卡，买完卡之后再去。业绩什么的，买了卡再说。

The audio in this segment consists of fragmented, informal speech with no discernible continuous lecture content. The speakers exchange brief, incomplete remarks about a previously shared item, ask "What is this?", and mention that basketball is not played in their area. No coherent academic material can be extracted.

该片段音频由零散的非正式对话组成，无法辨识出连续的课堂讲授内容。说话者简短地提及之前分享过的某样东西，询问"这是什么"，并提到他们那边不打篮球。无法提取出连贯的学术教学内容。

What a waste. So what?

什么废物啊。那咋了。

[No coherent lecture content detected in this segment. The audio consists primarily of background noise, shuffling sounds, and unintelligible speech fragments.]

[该片段未检测到连贯的课堂讲授内容。音频主要由背景噪音、翻动物品声及无法辨识的语音碎片组成。]

[Audio quality is too degraded and fragmented to produce a coherent lecture transcript. The recording contains overlapping, unintelligible speech in Chinese with heavy background noise. No continuous instructional content can be reliably extracted.]

[音频质量极差，内容严重碎片化，无法整理出连贯的课堂讲稿。录音中包含大量重叠的、难以辨认的中文语音，背景噪音严重，无法可靠提取任何连续的教学内容。]

[No discernible lecture content in this segment. The audio consists of background noise and unintelligible fragments with no coherent instructional material.]

【该片段无可辨识的课堂教学内容。音频仅包含背景噪音和无法听清的碎片化语句，无连贯的教学信息。】

Someday you will surpass me.

总有一天你会超越我。

My screen protector cost 499. I never wanted to spend that much. I've been using the same one for a long time. Someone topped up money for me. My screen protector is only around 400. His might cost three to four hundred. He probably got it from that screen protector shop. That's hilarious. How much was yours? Who gave it to me? My left hand. This is really hard. Let me lift it up. Gloves. Damn.

我的贴膜花了四百九十九。我一直没舍得花那么多钱。我一直用着同一张。有人给我充了钱。我的贴膜也就四百左右。他的可能贴三四百。他大概是从那家贴膜店弄的。笑死了。你那张多少钱？谁给我的？我左手。真难弄。我抬一下。手套。我操。

There are three levels. One, two, three. That is correct.

共有三个层级。一、二、三。没错。

[No discernible instructional content. The segment consists primarily of background noise, coughing, and indistinct overlapping speech with no recoverable lecture material.]

[无可辨识的教学内容。该片段主要由背景噪音、咳嗽声及含糊的重叠对话组成，无法提取出可用的课堂讲授内容。]

The audio segment consists primarily of overlapping informal conversation among multiple speakers, with no clearly discernible structured lecture content. Fragments of casual dialogue are audible but largely unintelligible due to simultaneous speech and poor signal separation.

该音频片段主要由多名说话人重叠的非正式对话组成，没有清晰可辨的结构化讲课内容。可以听到一些零散的随意对话片段，但由于同时说话和信号分离效果差，大部分内容无法辨认。

[No coherent lecture content identified in this segment. The audio consists of overlapping informal conversation among multiple speakers with no discernible structured teaching material.]

【该时间段内未识别出连贯的课堂教学内容。音频为多人重叠的非正式交谈，无可辨识的结构化教学材料。】

This segment consists primarily of overlapping casual conversation among students with no discernible instructional content.

本段音频主要为多名学生之间的重叠闲聊，无可辨识的教学内容。

Wait a moment. Hold on.

等一下。稍等。

No English lecture content is present in this audio segment. The recording contains only indistinct background chatter and ambient noise with no identifiable instructional speech.

该音频片段中不存在英文授课内容。录音仅包含模糊的背景闲聊和环境噪音，无可辨识的教学语音。

No English university lecture content was identified in this audio segment. The recording consists of overlapping casual Mandarin Chinese conversation among multiple speakers, including greetings, laughter, and informal remarks, with no discernible pedagogical material, structured explanation, or instructional discourse.

该音频片段中未识别出英文大学课堂内容。录音为多名说话人重叠的中文日常对话，包含问候、笑声及非正式闲聊，无可辨识的教学材料、结构化讲解或课堂讲授话语。

[No discernible lecture content in this segment. The audio consists primarily of background noise, indistinct chatter, and handling sounds without any coherent instructional material.]

[该片段无可辨识的课堂教学内容。音频主要由背景噪音、模糊的交谈声和物品移动声组成，没有连贯的教学信息。]

This segment contains only informal, overlapping casual conversation among multiple speakers discussing wake-up times and meals. No structured lecture content, definitions, arguments, or teaching material is present.

该片段仅包含多位说话人之间非正式的、相互重叠的日常对话，内容涉及起床时间和吃饭等话题。其中不含任何结构化的讲授内容、定义、论证或教学材料。

讨论小蜜蜂能否回来。有人问小蜜蜂还能不能回来。对，他有个败者组，双败赛制。真能回来。能回来。我忘了，他要是不是双败的话他就回不来了，双败就能回来。能回来。他去败者组决赛，然后他们再出一个。那行。我觉得他要是再赢不了打这玩意儿的话，真神了。真有。

讨论小蜜蜂能否回来。有人问小蜜蜂还能不能回来。对，他有个败者组，双败赛制。真能回来。能回来。我忘了，他要是不是双败的话他就回不来了，双败就能回来。能回来。他去败者组决赛，然后他们再出一个。那行。我觉得他要是再赢不了打这玩意儿的话，真神了。真有。

[No coherent English lecture content identifiable in this segment. The audio consists of overlapping conversational speech in Chinese with no discernible structured teaching material.]

[该片段无可辨识的英文课堂讲授内容。音频为重叠的中文对话，无结构化教学材料。]

[No coherent instructional content detected in this segment. The audio consists primarily of overlapping background chatter and indistinct speech with no extractable lecture material.]

[本片段未检测到连贯的教学内容。音频主要由重叠的背景交谈声和模糊不清的语音组成，无可提取的讲课素材。]

No coherent lecture content is identifiable in this segment. The audio consists of overlapping, fragmented casual speech with no discernible teaching material, definitions, arguments, or structured academic content.

该片段中无法识别出连贯的课堂教学内容。音频由重叠、碎片化的随意对话组成，没有可辨识的教学材料、定义、论证或结构化的学术内容。

[No coherent instructional content detected in this segment. The audio consists primarily of overlapping casual conversation, coughing, and ambient noise among students, with no discernible lecture material.]

【该时间段未检测到可提取的课堂教学内容。音频主要由学生之间的重叠闲聊、咳嗽声和环境噪音组成，无可辨识的讲授材料。】

[No instructional content detected in this segment. The audio consists of background student chatter, laughter, and indistinct conversations with no discernible lecture material.]

【本片段未检测到教学内容。音频内容为学生背景闲聊、笑声及模糊对话，无可辨识的课堂讲授信息。】

[No instructional content detected in this segment. The audio consists entirely of casual student chatter regarding removing shoes and sleeping arrangements, with no pedagogical material present.]

【本片段未检测到任何教学内容。音频内容全部为学生之间的闲聊，涉及脱鞋和睡觉安排等话题，无任何教学信息。】

I can't stand it. Let's see if there's anything worth filming. This place is too stiff. We sat in the bathroom for a while. It's dark in there. The door was locked. We just paired up and left.

我受不了了。看看有没有什么值得拍的。这个地方太僵硬了。我们在厕所里坐了一会儿。里面很黑。门被锁上了。我们直接配对就离开了。

[No substantive instructional content detected in this segment. The audio consists entirely of informal student chatter, exclamations, and non-academic conversation with no lecture material, definitions, formulas, or teaching discourse.]

[该片段未检测到实质性教学内容。音频全部由学生间的非正式闲聊、感叹及与课程无关的对话组成，不包含任何讲授材料、定义、公式或教学论述。]

他想打我，跳这么远。这能吃子弹啊。你看这个，不对不对，这个不帅。他打我。这个护盾还能这样？不用不用，他们有线的，不充点。蓝色心。这怎么有侧键？这个扫花天是拿手切的？不切。扫花天你抹抹它没有任何效果。什么话？不对不对，没拿那个啥。哎我好卡。

He tried to hit me and jumped so far. You can eat bullets here? Look at this—no, no, this one isn't cool. He hit me. This shield can do that too? No need, no need—they have wired ones, no recharge needed. Blue heart. How come there are side keys? Is this 'Sweep Flower Sky' cut by hand? No cutting. If you swipe 'Sweep Flower Sky' on it, it has no effect at all. What are you talking about? No, no, didn't grab that thing. Ugh, I'm so laggy.

[No instructional content detected. This segment consists entirely of informal student chatter during a class transition period, including remarks about class ending, drinking water, and unrelated personal complaints. No lecture material, definitions, examples, or teaching facts are present.]

【未检测到教学内容。本片段完全由课间学生闲聊组成，包括下课通知、喝水、以及无关的个人抱怨。无讲义材料、定义、示例或教学事实。】

[This segment contains no coherent lecture content. It consists primarily of background noise, paper rustling, coughing, and fragmented, unintelligible student chatter during what appears to be a class transition or break period. No teaching material is present.]

【本段无可辨识的课堂教学内容。音频主要由背景噪音、翻纸声、咳嗽声以及学生在课间或换课时的零碎交谈组成，未包含任何教学信息。】

No discernible lecture content detected in this segment. The audio consists of ambient classroom noise including paper shuffling, chair movement, coughing, and unintelligible background murmur.

该片段未检测到可辨识的授课内容。音频仅包含教室环境噪音，如翻动纸张、移动椅子、咳嗽及无法辨认的背景低语。

[No discernible lecture content identified in this segment. The audio consists primarily of ambient noise, paper shuffling, chair movement, and unintelligible background murmuring.]

[该片段未识别出可辨别的课堂教学内容。音频主要由环境噪音、翻纸声、椅子移动声及无法听清的背景低语组成。]

[This segment contains predominantly ambient classroom noise—paper shuffling, chair movement, and indistinct murmuring—with no clearly intelligible instructional content.]

该片段主要为课堂环境噪音——翻纸声、椅子移动声及模糊的低语声，无可辨识的教学内容。

[No substantive lecture content identified in this segment. The audio consists primarily of background murmuring, indistinct chatter, and coughing with no discernible instructional speech.]

【该片段未识别出实质性讲课内容。音频主要由背景低语、模糊交谈声和咳嗽声组成，无可辨识的教学语音。】

This city has 36. This city has 16. I want to solve this problem, but it's getting a bit late. I'd like to finish solving this problem first.

这个城市有36。这个城市有16。我想把这道题解完，但时间有点晚了。我想先把这道题解完。

No clear English lecture content is discernible in this segment. The audio consists primarily of background noise, indistinct murmuring, and ambient classroom sounds with no substantive instructional speech.

该片段中无可辨识的英文讲课内容。音频主要由背景噪音、模糊的低语和教室环境声组成，没有实质性的教学内容。

If you give the number to get the expression, you can get the resistance. The expression for resistance is resistivity times the length divided by the cross-sectional area. So if the length is L, the resistance is... The area is just one circle.

如果你给出数值来得到表达式，你就可以求得电阻。电阻的表达式是电阻率乘以长度除以横截面积。所以如果长度为 L，电阻就是……面积就是一个圆。

So this is our progress. They are collected by using typical methods. Basically, we have to compute the final result.

这就是我们的进展。它们是通过典型方法收集的。基本上，我们需要计算最终结果。