Alternating Current
A-Level Physics Topic 21 11:18 English narration · English + 中文 subtitles burned in
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The electricity in your wall is restless.
你墙上插座里的电，是不安分的。
Fifty times every second — sometimes sixty — it reverses direction, surging one way, then the other.
每秒钟五十次——有时是六十次——它就反转一次方向， 先朝一边涌，再朝另一边涌。
This is alternating current.
这就是交流电。
Yet your phone, your laptop, every chip inside them, needs the opposite: a steady, one-way flow.
可是你的手机、你的笔记本电脑， 里面的每一块芯片，需要的却正相反：一种平稳的、单向的电流。
So how do we get there?
那我们怎么做到呢？
Inside that little charger, alternating current is tamed — flattened, and smoothed, into steady direct current.
在那个小小的充电器里面，交流电被驯服了——被削平，被平滑，变成平稳的直流电。
That journey is today's lesson.
这段旅程，就是今天的课。
Out in the grid, substations do the heavy lifting.
在电网里，变电站干着重活。
Their transformers step the alternating voltage up for long-distance travel, then down again for homes and factories.
变压器把交变电压升高以便远距离输送， 再降下来供给家庭和工厂。
Alternating current is not a nuisance of wall sockets alone — it is how the whole supply network moves energy around the country.
交流电不只是墙上插座的麻烦—— 整个供电网络都靠它在全国范围内输送能量。
Alternating current powers the world — but taming it takes some clever physics.
交流电为整个世界供电——但驯服它需要一些巧妙的物理。
Today: the shape of alternating current, its power and root-mean-square value, rectification, and smoothing.
今天：交流电的形状、 它的功率和均方根值、整流，以及平滑。
Let's begin.
让我们开始吧。
Side by side, the contrast is clear.
并排放在一起，对比一目了然。
Direct current is a steady horizontal line — one direction, one size, all the time.
直流电是一条平稳的水平线——方向不变、大小不变、始终如此。
Alternating current is a sine wave: it climbs to a peak, falls through zero, dips to a trough of equal size the other way, and repeats.
交流电是一条正弦波：它升到峰值，穿过零点，跌到另一侧同样大小的谷底，再重复。
The peak is written I-nought.
峰值记作电流零。
The time for one full wave is the period T.
走完一整波的时间是周期。
Mains electricity is this sine shape, usually at fifty hertz — or sixty, depending where you live.
市电就是这种正弦形状， 通常是五十赫兹——或六十赫兹，取决于你住在哪里。
Alternating current follows a sine wave.
交流电遵循一条正弦波。
It rises to a peak, falls back through zero, dips to a trough, and returns — over and over.
它升到一个峰值，落回穿过零，跌到一个谷底，再回来——如此往复。
The time for one full cycle is the period.
走完一个完整循环所用的时间，叫周期。
The number of cycles each second is the frequency — the two are reciprocals.
每秒钟循环的次数，叫频率——两者互为倒数。
The height of the wave, from the middle to the top, is the peak value.
波的高度，从中间到顶部，叫峰值。
And from the very top to the very bottom is the peak-to-peak value, twice the peak.
而从最顶到最底，叫峰峰值，是峰值的两倍。
Lock in the vocabulary.
把术语记牢。
Period is the time for one full cycle, in seconds.
周期是走完一个完整循环的时间，单位是秒。
Frequency is cycles per second; frequency equals one over the period.
频率是每秒循环的次数； 频率等于一除以周期。
Angular frequency omega equals two pi times frequency, or two pi over the period — that is the ω you see inside the sine.
角频率欧米伽等于二圆周率乘以频率，或二圆周率除以周期—— 那就是正弦里的那个角频率。
The peak value is the largest in a cycle, also called the amplitude.
峰值是一个循环里的最大值，也叫振幅。
Peak-to-peak is twice that, from the top tip to the bottom tip — handy when you read an oscilloscope.
峰峰值是它的两倍，从最顶到最底——读示波器时很有用。
And for a purely resistive load in this syllabus, voltage and current stay in phase: they rise and fall together.
对本大纲里的纯电阻负载，电压与电流同相：它们一起升、一起降。
An oscilloscope — a cathode-ray oscilloscope, or C.R.O. — shows how a voltage changes with time.
示波器——阴极射线示波器——显示电压如何随时间变化。
Reading the trace is the same skill as for any wave.
读波形与读任何波一样。
Horizontal divisions times the time-base give the period T, so frequency is one over T.
水平格数乘以时基得到周期，所以频率是一除以周期。
Vertical divisions times the y-gain give the peak voltage: measure from the centre line to a peak, or take peak-to-peak and halve it.
竖直格数乘以竖直增益得到峰值电压：从中线量到峰值，或先量峰峰值再除以二。
Practice that routine — exam questions love a C.R.O. screen full of numbers.
练熟这套步骤——考试题很爱在示波器屏幕上写满数字。
Now, power.
现在来看功率。
In a resistor, the power is the current squared, times the resistance.
在电阻里，功率等于电流的平方乘以电阻。
Because the current is squared, it is always positive — even when the current runs backwards, power is still delivered.
因为电流被平方了，它总是正的—— 哪怕电流反着流，功率照样在输送。
So the power pulses, twice as fast as the current, from zero up to a peak and back.
所以功率是脉动的，比电流快一倍，从零升到峰值再回落。
And its average, over a whole cycle, sits exactly halfway: the average power is half the peak power.
而它在一整个循环里的平均值，恰好落在正中间：平均功率是峰值功率的一半。
Write it out.
把它写出来。
Instantaneous power is I-nought squared times R times sine-squared of omega t.
瞬时功率是电流零的平方乘以电阻，再乘以角频率时间正弦的平方。
The peak of that curve is I-nought squared R.
那条曲线的峰值是电流零的平方乘以电阻。
Over a full cycle the mean of sine-squared is exactly one half, so the average power is one half I-nought squared R — half the peak power.
在一个完整循环里，正弦平方的均值恰好是二分之一， 所以平均功率是二分之一乘以电流零的平方乘以电阻——也就是峰值功率的一半。
That factor of one half is the whole point of the next idea: root-mean-square.
这个二分之一的因子，正是下一个概念的全部用意：均方根。
Here is a clever idea.
这里有一个巧妙的想法。
What steady direct current would heat a resistor at that same average rate?
什么样的平稳直流电，能以同样的平均速率加热一个电阻？
We call it the root-mean-square current — and for a sine wave, it is the peak, divided by the square root of two.
我们把它叫做均方根电流——对正弦波来说，它等于峰值除以根号二。
The same holds for voltage.
电压也是一样。
This is why quoted a.c. values are always root-mean-square.
这就是为什么标称的交流电数值，总是均方根值。
Two hundred and thirty volt mains has a peak of about three hundred and twenty-five volts — and power uses the root-mean-square values, just like direct current.
两百三十伏的市电， 峰值大约是三百二十五伏——而功率就用均方根值来算，跟直流电一模一样。
An alternating supply has a peak voltage of twelve volts.
一个交流电源的峰值电压是十二伏。
Find its root-mean-square voltage.
求它的均方根电压。
The r.m.s. voltage is the peak divided by the square root of two.
均方根电压等于峰值除以根号二。
So write twelve over the square root of two.
所以写出十二除以根号二。
That is about eight point five volts.
大约是八点五伏。
Why the square root of two?
为什么是根号二？
The name root-mean-square tells you: square the sine, take the mean — which is one half — then take the square root.
均方根这个名字已经告诉你了： 把正弦平方，取平均——那是二分之一——再开方。
Square root of one half is one over root two.
二分之一的平方根就是一除以根号二。
Only the sinusoidal case is needed for this syllabus.
本大纲只需要正弦这一种情况。
Once you have r.m.s. values, average power takes the same form as direct current: I-r.m.s. squared times R, or V-r.m.s. squared over R, or V-r.m.s. times I-r.m.s.
一旦有了均方根值，平均功率就用和直流相同的形式：均方根电流的平方乘以电阻， 或均方根电压的平方除以电阻，或均方根电压乘以均方根电流。
Quoted a.c. numbers are always r.m.s.
标称的交流数值总是均方根。
So two hundred and thirty volt mains means V-r.m.s. is two hundred and thirty volts, and the peak is two hundred and thirty times root two — about three hundred and twenty-five volts.
所以两百三十伏市电的意思是均方根电压为两百三十伏，峰值是两百三十乘以根号二—— 大约三百二十五伏。
Components must be rated for the peak, not the quoted r.m.s., or they fail at the tip of each cycle.
元件必须按峰值额定，而不是按标称均方根，否则会在每个循环的尖端损坏。
A heater of resistance fifty ohms is connected to the two hundred and thirty volt r.m.s. mains.
一个五十欧姆的加热器接到两百三十伏均方根市电上。
Find the r.m.s. current and the average power.
求均方根电流和平均功率。
First, I-r.m.s. equals V-r.m.s. over R: two hundred and thirty over fifty is four point six amps.
首先，均方根电流等于均方根电压除以电阻：两百三十除以五十是四点六安。
Average power is voltage times current using those r.m.s. values: two hundred and thirty times four point six is about one point one times ten to the three watts — about one point one kilowatts.
平均功率是用这些均方根值算的电压乘以电流：两百三十乘以四点六， 大约是一点一乘以十的三次方瓦——约一点一千瓦。
Notice: same formulas as direct current, once the values are r.m.s.
注意：一旦用的是均方根值， 公式就和直流相同。
To make direct current, we use diodes — components that let current pass only one way.
为了得到直流电，我们用二极管——一种只让电流朝一个方向通过的元件。
A single diode passes just the positive halves and blocks the rest: half-wave rectification.
一个二极管只让正的半波通过， 把其余的挡住：这就是半波整流。
Half the power is thrown away.
一半的功率被扔掉了。
Better is a bridge of four diodes: whichever way the input points, they steer the current through the load the same way — full-wave rectification.
更好的是用四个二极管组成的桥—— 不管输入朝哪个方向，它们都把流过负载的电流引向同一个方向——这就是全波整流。
Now every half-cycle is used, giving a run of positive humps with no gaps.
现在每一个半周期都用上了，得到一连串没有缝隙的正向凸包。
Look at half-wave carefully.
仔细看半波。
One diode sits in series with the load.
一只二极管与负载串联。
On the positive half of the cycle the diode is forward-biased and conducts.
在正半周，二极管正向偏置并导通。
On the negative half it is reverse-biased and no current flows — the output sits flat at zero.
在负半周它反向偏置，没有电流流过——输出平躺在零。
So you get positive half-waves with gaps between them.
于是你得到带缝隙的正半波。
The mean output is V-nought over pi — about nought point three two times the peak.
平均输出是峰值电压除以圆周率——大约是峰值的零点三二倍。
The drawback is clear: half the input is wasted, and the output is very uneven.
缺点很清楚：一半输入被浪费了，而且输出非常不均。
The bridge rectifier uses four diodes as the arms of a diamond.
桥式整流器把四只二极管当作菱形的四条边。
The alternating input joins one pair of opposite corners; the load sits across the other pair.
交流输入接到一对对角；负载接在另一对对角上。
On each half-cycle a different pair of diodes conducts, but the load always sees the same polarity.
每个半周有不同的一对二极管导通，但负载总是看到相同的极性。
Draw the diamond, mark the diode directions carefully, and the load terminals keep the same sign whichever a.c. terminal is positive.
画好菱形，仔细标好二极管方向，无论哪个交流端为正，负载两端的符号都保持不变。
The full-wave output is a continuous run of positive humps with no gaps, at twice the input frequency.
全波输出是一连串没有缝隙的正向凸包，频率是输入的两倍。
Its mean is two V-nought over pi — about nought point six four times the peak — double the half-wave value.
它的平均值是二倍峰值电压除以圆周率——大约是峰值的零点六四倍—— 是半波的两倍。
It uses all of the input, is smoother already, and is easier to filter with a capacitor next.
它用上了全部输入，本身已经更平滑，接下来用电容滤波也更容易。
Summarise the means.
总结一下平均值。
The half-wave mean is V-nought over pi, about nought point three two V-nought, with flat zero gaps and half the input wasted.
半波均值是峰值电压除以圆周率，大约零点三二倍峰值， 带有平坦的零缝隙，一半输入被浪费。
The full-wave mean is two V-nought over pi, about nought point six four V-nought, continuous humps at twice the input frequency.
全波均值是二倍峰值电压除以圆周率， 大约零点六四倍峰值，是输入频率两倍的连续凸包。
How you draw them matters in the exam: half-wave is source, single diode, load in series; full-wave is a diamond of four diodes with a.c. on one pair of opposite corners and the load on the other.
考试里怎么画图很重要：半波是电源、单二极管、负载串联； 全波是四只二极管的菱形，交流在一对对角，负载在另一对。
The output is bumpy, still.
输出还是坑坑洼洼的。
To smooth it, place a capacitor in parallel with the load.
为了把它平滑掉，在负载两端并联一个电容器。
As each hump rises, the capacitor charges up to the peak.
当每一个凸包升起时， 电容器充电到峰值。
As the hump falls away, the capacitor discharges through the load, holding the voltage up until the next peak arrives.
当凸包落下去时，电容器通过负载放电，把电压撑住，直到下一个峰值到来。
The result is a nearly steady voltage, with just a small wobble — the ripple.
结果是一个几乎平稳的电压，只带着一点小小的起伏——纹波。
A bigger capacitor, or a bigger resistance, makes the ripple smaller still.
更大的电容，或更大的电阻， 能让纹波变得更小。
On the graph, the dashed line is the unsmoothed full-wave humps.
在图上，虚线是未平滑的全波凸包。
The solid line sits near the peaks and sags only a little between them — that sag is the ripple.
实线贴在峰值附近，只在峰与峰之间略微下沉—— 那一点下沉就是纹波。
While the diodes are reverse-biased on the falling part, the capacitor alone feeds the load.
在下落段二极管反向偏置时，只有电容在给负载供电。
The voltage falls with the time constant R C you met under capacitance.
电压按你在电容一章见过的时间常数电阻乘电容下降。
Then the next peak recharges the capacitor, and the cycle repeats.
然后下一个峰值给电容再充电，循环重复。
Three levers shrink the ripple.
三个杠杆能缩小纹波。
A larger capacitor stores more charge, so the dip between peaks is smaller.
更大的电容储存更多电荷，所以峰与峰之间的下沉更小。
A larger resistance means a smaller load current, so the capacitor discharges more slowly.
更大的电阻意味着更小的负载电流，电容放电更慢。
A higher rectified frequency — and full-wave is already twice the input — leaves less time to fall between peaks.
更高的整流频率——全波已经是输入的两倍——留给下落的时间更少。
All three ideas are the same fact: when the time constant R C is large compared with the time between peaks, the smoother the output.
三条思路其实是同一件事：当时间常数电阻乘电容相对峰间时间很大时，输出就越平滑。
That nearly steady d.c. is what sensitive electronics need.
敏感电子器件需要的，正是那种几乎平稳的直流。
Three marks to secure.
三个要拿稳的分。
First, the root-mean-square current is the peak over root two, and power uses root-mean-square values.
第一，均方根电流等于峰值除以根号二，而功率要用均方根值来算。
Second, average power in a resistor is half the peak power.
第二，电阻里的平均功率是峰值功率的一半。
Third, rectification turns alternating current into direct current with diodes, and a smoothing capacitor across the load cuts the ripple.
第三，整流用二极管把交流电变成直流电， 而负载两端的平滑电容能削掉纹波。
Master these, and alternating current is yours.
掌握这些，交流电就是你的了。