So

那么，

if the wire is very fine, which means it means the cross section

如果这根线非常细，那就意味着它的横截面积

area

很小。

is quite low. If A is quite low, this means the resistance is quite high.

非常小。如果A很小，那就意味着电阻非常高。

So, fine wire, you will get low power. low current and high resistance.

所以，使用细线的话，得到的功率会很低。电流小，电阻大。

And this moving coil meter is only suitable for DC. direct current. direct current circuit, sorry.

而且，这种动圈式仪表只适用于直流电。也就是直流电。抱歉，是直流电路。

And here is how it works.

下面是它的工作原理。

So if you want to measure the current, you put the meter with the circuit in series. If you want to measure the voltage, we connect the meter. This is our meter, right? moving coil meter. We connect our moving coil meter in parallel. This is the circuit.

那么，如果你想测量电流，就需要把仪表与电路串联起来。如果你想测量电压，就把仪表并联上去。这就是我们的仪表，对吧？是动圈式仪表。我们把动圈式仪表并联连接。这就是这个电路。

and actually the moving coil meter has an internal resistance. and this can introduce some errors. this can introduce some very small errors in the measurement. They are not ideal.

实际上，动圈式仪表有一个内阻。这会导致产生一些误差。在测量中会产生非常微小的误差。它们并不理想。

They have a resistance associated with them.

它们都带有内阻。

They have very small resistance. so they are not ideal.

不过这个内阻非常小。所以它们并不完美。

But an ideal voltmeter, actually, should have infinite resistance. which means the resistance is quite large. The resistance is very, very, very large. so it draws no current.

但实际上，理想的电压表，应该具有无限大的内阻。这意味着它的电阻非常大，可以说是极其巨大。因此，它不会消耗电流。

And for an ideal ammeter,

而对于理想的电流表，

it should have zero resistance. so it has no voltage drop.

它的电阻应该为零。这样就不会产生电压降。

For ammeter, ideally, it should have zero resistance. For voltmeter, ideally, it should have very large, very large. so it has no current.

对于电流表来说，理想情况下，它的电阻应该为零。而对于电压表，理想情况下，它的电阻应该非常大，非常大。这样就不会有电流流过。

Here is an ammeter. So this is the ammeter has three components. So this circuit is just one ammeter. If you want to use ammeter to measure current, we have to connect this part with the circuit in series. to measure the current. So inside of the ammeter, actually there is a resistor. connected in parallel.

这里是一个电流表。这个电流表有三个组成部分。所以，这个电路就是一个电流表。如果你想用电流表来测量电流，就必须把它串联在电路中。也就是把这部分和电路串联起来。这样才能测量电流。那么，在电流表的内部，其实有一个电阻。它是并联连接的。

with another resistor. So inside of the ammeter is actually parallel.

和另一个电阻并联。所以，电流表的内部实际上是并联结构。

The elements are connected in parallel. But when we want to measure current, we use the ammeter. We use the ammeter to connect with the element in series.

这些元件是并联连接的。但是，当我们想要测量电流时，我们会使用电流表。我们使用电流表时，需要将其与元件串联连接。

And if you want to measure a current I, where I is much larger than the current inside of the ammeter. So in this case,

如果你想测量一个电流I，而这个电流I远大于电流表内部的电流，那么在这种情况下，

the current is outside of the range. outside of the measuring range. That's the reason we have to use a shunt resistor. to make sure we can also measure this large current. to expand the measuring range.

电流超出了量程。超出了测量范围。这就是为什么我们必须使用一个分流电阻。以确保我们也能测量这个大电流。从而扩大测量范围。

So once we know the current here and the voltage, we can compute how big is the shunt resistor inside of the ammeter.

所以，一旦我们知道了这里的电流和电压，就可以计算出电流表内部的分流电阻的阻值。

Is it clear?

清楚了吗？

So this part is a complete part. This part is an integral. These three elements are inside. of one ammeter. And there is a shunt resistor inside of the ammeter.

所以，这一部分是一个完整的部分。它是一个整体。这三个元件都在内部。在一个电流表里。而且，电流表内部还有一个分流电阻。

And this resistor usually have very small value.

而且这个电阻的阻值通常非常小。

to make sure there is no voltage drop.

这是为了确保没有电压降。

Because for an ideal ammeter, it should have zero resistance. So ideally, it should have no voltage drop. That's the reason it must have very small. shunt resistor inside of the ammeter to make sure the total resistance of the ammeter is very small. So it is close to an ideal.

因为对于一个理想的电流表来说，它的电压降应该为零。也就是电阻为零。所以，理想情况下它不应该有电压降。这就是为什么它的阻值必须非常小的原因。电流表内部的这个分流电阻，就是为了确保总电阻非常小。这样它就接近于理想状态了。

And this is the voltmeter. voltmeter also has three elements. And there's also one shunt resistor.

接下来是电压表。电压表也有三个组成部分。还有一个分流电阻。

Okay, it's not called a shunt resistor, it's called a multiplier. multiplier resistor.

其实，它不叫分流电阻，而是叫倍率器。倍率电阻。

If we don't have the multiplier resistor, we cannot measure very large voltage. because the internal voltage is very small. So there should be a multiplier resistor connected with these two elements. And these three elements together. So these three elements together is a voltmeter.

如果没有倍率电阻，我们就无法测量很高的电压。因为电压表的内阻非常小。所以，必须有一个倍率电阻与这两个元件串联。这三个元件组合在一起。这样，这三个元件就构成了一个电压表。

And this multiplier resistor actually have very large. so it has very large resistance. make sure there's no current drop. because as I say here, ideal voltmeter should have very large resistance. to make sure there's no current drop. so based on the almost no, right? if the resistance is quite large, is infinite, you will get I is close to zero. that's the reason the multiplier resistor should be large.

而这个倍率电阻，实际上阻值非常大。所以它的电阻非常大。这样可以确保没有电流损耗。因为正如我在这里所说的，理想的电压表应该具有非常大的电阻。以确保没有电流通过。所以，基于几乎没有电流这一前提，对吧？如果电阻非常大，甚至是无穷大，那么电流I就会接近于零。这就是为什么分流电阻应该很大的原因。

in the voltmeter, the multiplier resistor should be large.

在电压表中，分流电阻应该很大。

great, that's all for today.

很好，今天就到这里。

If the wire is very fine, the cross-sectional area A is quite low. If A is low, the resistance is quite high. Therefore, with a fine wire, you get low current and high resistance. This moving coil ammeter is only suitable for DC circuits.

如果导线非常细，则横截面积 A 很小。A 小意味着电阻很高。因此，使用细导线时，电流低而电阻高。这种动圈式电流表仅适用于直流电路。

Here is how it works. To measure current, we connect the meter in series with the circuit. To measure voltage, we connect the meter—in this case, our moving coil meter—in parallel with the circuit.

以下是它的工作原理。要测量电流，我们将电表与电路串联。要测量电压，我们将电表——这里就是我们的动圈式电表——与电路并联。

The moving coil ammeter has an internal resistance. This can introduce systematic errors in the measurement because it is not ideal; it has a resistance.

动圈式电流表具有内阻。由于它并非理想器件——它存在电阻——这会在测量中引入系统误差。

Associated with them, they have lots more resistance. They are not ideal. An ideal voltmeter actually should have infinite resistance. This means the resistance is very, very large, so it draws no current.

与之相关联的是，它们具有很大的电阻。它们并非理想的。一个理想的电压表实际上应该具有无穷大的电阻。这意味着电阻非常大，因此它不汲取电流。

An ideal ammeter should have zero resistance, so it has no voltage drop. An ideal voltmeter should have very large resistance, so it has no current drawn. Here is an ammeter. The ammeter has three components. This circuit is just one ammeter. If you want to use an ammeter to measure current, we have to connect this part with…

理想电流表的内阻为零，因此不会产生压降。理想电压表的内阻极大，因此不会分流。这是一只电流表，它由三个部件组成。这个电路就是一台电流表。如果要使用电流表测量电流，我们需要将这一部分与……

The circuit is connected in series to measure current — this is what an ammeter does. Inside the ammeter, there is actually a resistor connected in parallel with another resistor. So the elements inside the ammeter are in parallel.

电路串联接入以测量电流——这就是电流表的作用。在电流表内部，实际上有一个电阻与另一个电阻并联连接。因此，电流表内部的元件是并联的。

To measure a current, we use an ammeter connected in series with the element. If we want to measure a current I where I is much larger than the current inside the ammeter, then in this case...

要测量电流，我们使用安培表，将其与元件串联。如果我们要测量的电流 I 远大于安培表内部的电流，那么在这种情况下……

The current is outside the measuring range of the ammeter. That is the reason we have to use a shunt resistor to make sure we can also measure this large current, to expand the measuring range. So once we know the current here and the voltage, we can compute how big the shunt resistor inside the ammeter should be.

电流超出了电流表的量程。这就是我们必须使用分流电阻的原因——通过它来扩展量程，从而能够测量这个大电流。一旦我们知道了这里的电流和电压，就可以计算出电流表内部的分流电阻应该多大。

Is it clear? This part is a complete unit. These three elements are inside one ammeter, and there is a shunt resistor inside the ammeter.

清楚了吗？这一部分是一个完整的单元。这三个元件都在一个电流表内部，电流表内部还有一个分流电阻。

This resistor should have a very small value to make sure there is no voltage drop, because for an ideal ammeter, it should have zero resistance. So ideally it should have no voltage drop. That is the reason you must have a very small shunt resistor inside the ammeter, to make sure the total resistance of the ammeter is quite small, so it is close to an ideal ammeter.

这个电阻的阻值必须非常小，以确保没有电压降，因为理想电流表的内阻应为零，理想情况下不应产生任何电压降。这就是为什么必须在电流表内部放置一个非常小的分流电阻，以确保电流表的总电阻足够小，使其接近理想电流表。

This is a voltmeter. A voltmeter also has three elements, and there is also one multiplier resistor.

这是一个电压表。电压表也有三个元件，此外还有一个倍率电阻。

A multiplier resistor is necessary because we cannot measure very large voltage directly—the internal voltage is quite small. So there should be a multiplier resistor connecting these three elements together to form a voltmeter. This multiplier resistor should actually have very large values, i.e., very large resistance, to make sure there is no current drop. As I say here, an ideal voltmeter should have very large resistance to make sure there is no current flow. Based on Ohm's law, if the resistance is quite large—infinity—

需要一个倍增电阻，因为我们无法直接测量非常大的电压——内部电压很小。因此需要一个倍增电阻将这三个元件连接在一起，构成一个电压表。这个倍增电阻实际上应该具有非常大的阻值，即非常大的电阻，以确保没有电流降。正如我这里所说的，理想电压表应该具有非常大的电阻，以确保没有电流流过。根据欧姆定律，如果电阻非常大——趋于无穷大——

It's infinite. The current I is close to zero. That's the reason the multiplier resistor should be large in the voltmeter. The multiplier resistor should be large in the voltmeter. Right, that's all for today.

它是无穷大的。电流 I 接近于零。这就是为什么电压表中的倍率电阻应该很大。倍率电阻在电压表中应该很大。好，今天就到这里。