电子电气工程导论10月22日第一至二节

Aries, Aries.

白羊座，白羊座。

Find the I and U C.

找到“I”和“U C”。

And you should find the energy stored in the capacitor and the inductor.

你应该找到电容器和电感器中储存的能量。

So you don't have to consider the changing process. of the voltage or current, both of the capacitor or inductor.

所以你不需要考虑变化的过程。无论是电容器还是电感器的电压或电流。

otherwise it's too complex. but the potential theory means the final steady state.

否则，会变得太复杂。但势理论指的是最终的稳态。

there's no voltage drop. so Vc

没有电压降。所以Vc

is exactly the voltage of this 5 ohms resistor.

正好等于这个5欧姆电阻上的电压。

so by applying the current, you can get the voltage. and for the energy, just use the equation of capacitor. the equation is half of the capacitance. times its voltage squared. you know the capacitance. Capacitance is 1 farad. And the voltage is 10 volt. so you can get the energy. and for the inductor, also, similar equation. half of the inductance times the current squared. the inductance is 2 henry. and the current is 1 ampere. you can get the energy.

所以通过应用电流，你可以得到电压。至于能量，只需使用电容器的公式。公式是电容的一半。乘以电压的平方。你知道电容是多少。电容是1法拉。电压是10伏特。所以你可以算出能量。对于电感器，也有类似的公式。一半的电感乘以电流的平方。电感是2亨利。电流是1安培。你可以算出能量。

great. here is another example. the inductance

很好。这里还有一个例子。电感

very similar to resistor, right? if you have so many resistors connected you can do the equivalent resistance. and here we just replace the resistance with inductance. how can you calculate the inductance?

和电阻非常相似，对吧？如果你有好多电阻连接，就可以计算出等效电阻。而在这里，我们只是用电感代替了电阻。那么，如何计算等效电感呢？

至少是输入全靠

至少输入全靠

大声出

大声说出来。

so inductance the equation is identical to resistor. and here three inductor are connected in series. 10 henry, 10 henry and 10 henry. So we just add them together. and this is combined three. this combined three are connected in parallel. this is 7 henry inductor. so the first equation might be you add them together, you will get 40. 2 henries.

所以，电感的公式和电阻是一样的。这里有三个电感串联在一起。分别是10亨利、10亨利和10亨利。所以我们直接把它们加起来。这就是三个的组合。这三个组合是并联的。这是一个7亨利的电感。那么，第一个方程可能是把它们加起来，得到40。2亨利。

and this three combined in parallel is 7. so you can get 50 against 6 henry. and this combined four, finally connect in series in the both really and 20 henry. so just add them together. you have the total.

而这三个并联起来是7。所以你可以得到50比6亨利。而这四个组合起来，最后串联起来，总共是20亨利。所以只要把它们加起来。你就得到了总数。

here's a brief summary of

好的，这里是对

what is covered. so the main points is the Faraday's law.

所学内容的简要总结。所以，主要知识点是法拉第定律。

so the change of a magnetic flux is equal to the emf.

也就是磁通量的变化。等于电动势。

So the change of magnetic flux can produce a voltage. A change magnetic flux linking with a circuit induces an electric voltage.

所以，磁通量的变化可以产生电压。与电路相连的磁通量变化会感应出电动势。

And

而且，

the magnitude of that electric voltage is proportional to the rate of change.

该电动势的大小与变化率成正比。

And the produced electric voltage was always opposed the change of the magnetic flux. So we have a minus. And the voltage can also be expressed by the inductance. inductance is the property of the inductor. to oppose the change of the current.

而且，产生的电动势总是阻碍磁通量的变化。所以这里有一个负号。电压也可以用电感来表示。电感是电感器的一种特性。它的作用是阻碍电流的变化。

And we know how to compute the inductance when they connect in series and connect in parallel. The energy stored in the inductor is half of the inductance times current square.

我们知道如何计算电感器串联和并联时的总电感。电感器中储存的能量等于电感乘以电流平方的一半。

That's all for this lecture. I'll have our last lecture. So now we have finished all lectures. So let's go to the problem. So let's do the problem for this one for the last lecture. Okay, this question is the end of things.

本次讲座就到这里。我们还有最后一场讲座。现在，所有的讲座都结束了。接下来我们来看习题。我们来做一下上一节课的这个习题。好的，这个问题就是本次课程的最后一题了。

Come on, I will check the answer. Please use your pen.

大家来吧，我来检查一下答案。请拿出你们的笔。

Don't use your hand.

不要用手。

Any questions for this one?

对这个有什么问题吗？

Okay, the second exercise. What is what is 100 plus 100?

好的，第二个练习。是100加100等于多少？

What is 100 plus 100? It's 200.

100加100。是200。

The company is very famous in our city. What is the value of the electric one-kilowatt-hour in your area?

这家公司在我们这座城市非常有名。你们那边一千瓦时的电价是多少？

It's very famous.

非常有名。

in 0.2 seconds.

在0.2秒内。

The current is reversed. You are getting -5.5. So the change of the flux is 500 in 5. And this happens in 0.2 seconds.

电流反向了。你得到的是负5.5。所以磁通量的变化是500除以5。而这发生在0.2秒内。

So finally we get the

所以最后我们得到

an emf of this one.

这个电动势。

So what this question asking me to keep on is that if he reverse the current,

这个问题要求我们继续思考的是，如果他反转电流，

the direction of the magnetic flux will also be changed. if he reverse the current. This is the big one.

磁通量的方向也会改变。如果他反转电流。这是关键的一点。

First, I will define how to find the energy stored in a capacitor and an inductor.

首先，我将定义如何求解电容和电感中储存的能量。

If you do not have a catalyst or a buffer, you cannot consider a cyclic process. A cyclic process requires one complete cycle. You must have a catalyst or a buffer. You cannot consider a cyclic process unless you can return from any state. But for a steady state, you only need the final steady state. What is the final steady state? It is the steady state.

如果没有催化剂或缓冲剂，就不能考虑循环过程。循环过程需要一个完整的循环。你必须拥有催化剂或缓冲剂。除非你能从任意状态返回，否则不能考虑循环过程。但对于稳态，你只需要最终的稳态。什么是最终的稳态？就是稳态本身。

Sister has no homogeneous property. So this E is exactly homogeneous.

姐妹体不具有均质性质。因此这个E是完全均质的。

This is another example: equivalent inductance. It is very similar to resistors. If you have so many resistors connected in parallel, you can compute the equivalent resistance. Here we simply replace resistance with inductance, and we can compute the equivalent inductance.

这是另一个例子：等效电感。它与电阻的情况非常相似。如果有许多电阻并联连接，你可以计算等效电阻。这里我们只需将电阻替换为电感，就可以计算等效电感。

Power equals voltage times current. For energy stored in a capacitor, we use the equation: half of the capacitance times the voltage squared. That is, one-half C times V squared. For an inductor, there is a similar equation: half of the inductance times the current squared. Here, the inductance is two henries and the current is one ampere. You can then calculate the energy.

功率等于电压乘以电流。对于电容器中储存的能量，我们使用以下公式：电容的一半乘以电压的平方，即二分之一C乘以V的平方。对于电感器，也有一个类似的公式：电感的一半乘以电流的平方。这里，电感为两亨利，电流为一安培。由此即可计算出能量。

The inductance equation is identical to the resistance equation. Here, three inductors are connected in series: 10 henry, 12 henry, and 10 henry.

电感方程与电阻方程相同。这里有三个电感器串联：10亨利、12亨利和10亨利。

L1 is 8 millihenry. L3 combined with L1 in parallel gives a 7-millihenry equivalent inductor. The first equation: L1 and L3 together yield 14 millihenry. L3 combined in parallel is 7. L4 is 4. Finally, L3 is in series. To combine, connect in series between L3 and L1—just add L1 together—and you obtain the total equivalent inductance.

L1 为 8 毫亨。L3 与 L1 并联，得到 7 毫亨的等效电感。第一个方程：L1 与 L3 串联得到 14 毫亨。L3 并联后为 7。L4 为 4。最后，L3 处于串联状态。要合并时，将 L3 与 L1 串联——直接将 L1 相加——即可得到总等效电感。

Here is a brief summary of what is covered in this lecture. The main point is Faraday's law. The time rate of change of magnetic flux produces voltage. A change in magnetic flux linking with a circuit induces an electric voltage in that circuit.

以下是本讲内容的简要总结。核心要点是法拉第定律。磁通量的时间变化率产生电压。与电路交链的磁通量发生变化时，会在该电路中感应出电动势。

A change in magnetic flux linking a circuit induces an electric voltage across the circuit. Faraday's law states that the magnitude of the induced voltage is proportional to the rate of change. Lenz's law tells us that the induced voltage always opposes the change of the magnetic flux, so we have a minus sign here. What we have can also be expressed by inductance. Inductance is a property of the conductor to oppose the change of current.

穿过回路的磁通量发生变化时，会在回路两端感应出电动势。法拉第定律指出，感应电动势的大小与磁通量的变化率成正比。楞次定律告诉我们，感应电动势总是阻碍磁通量的变化，因此这里有一个负号。我们还可以用电感来表达这一关系。电感是导体阻碍电流变化的一种属性。

We all know how to calculate the inductance when it is connected in series and connected in parallel. The energy stored in the inductor is half of the inductance times current squared. This is our last lecture. There will be a tutorial for this part next time.

我们都知道如何计算电感串联和并联时的电感值。电感器中储存的能量等于电感乘以电流平方的一半。这是我们的最后一节课，下次会针对这部分内容安排一次辅导课。

Right, families. I'll check now. You can have a pen. This is your turn. Go on, use your pen.

好，家庭部分。我现在来检查。你们可以用笔了。轮到你们了，继续，用你们的笔。

Go to the corner.

到角落去。

Any questions?

有什么问题吗？

The second exercise. For water, one thousand times the currents. For this one, one minus one minus. That will make the current of certain currents. If the current is reversed, one minus. What is the body of water? One knows if you are in water. If you reverse the currents.

第二个练习。对于水，一千倍的水流。对于这个，一减一减。这将产生某些水流的水流。如果水流反向，一减。水体是什么？如果你在水中，你是知道的。如果你反转水流。

In 0.05 seconds, what are the probabilities? In three words: you are going to get minus 0.55, minus 0.55. The probability is 0.55. That is what happens when this occurs in 0.05 seconds—you are going to get...

在0.05秒内，概率是多少？用三个词概括：你会得到负0.55，负0.55。概率为0.55。这就是当该事件在0.05秒内发生时的结果——你会得到……

An equation for this one—what is the equation? I think it is T1. If you reverse the current, then the direction of the magnetic flux will also be changed. This is T1.

这一条对应的方程是什么？我认为是T1。如果你反转电流，那么磁通量的方向也会随之改变。这就是T1。

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