Electricity & Magnetism
IGCSE Physics Topic 4 31:58 English narration · English + 中文 subtitles burned in
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Transcript
Flick a switch and a light comes on.
按下开关，灯就亮了。
Hold a magnet near iron and it pulls.
把磁铁靠近铁，它就会吸住。
These two forces — electricity and magnetism — look separate, but they are deeply linked.
电和磁这两种力看起来是分开的， 其实却紧密相连。
Together, they light our homes, spin our motors, and carry power across whole countries.
它们一起点亮我们的家、转动我们的马达，还把电力输送到整个国家。
This is electricity and magnetism — one of the biggest topics in the course, and one of the most useful.
这就是电与磁——课程中最大的专题之一，也是最有用的之一。
Let's build it up, piece by piece.
让我们一块一块地把它搭建起来。
Every magnet has two poles — north and south.
每块磁铁都有两个磁极——北极和南极。
Like poles push apart; opposite poles pull together.
同名磁极相互排斥，异名磁极相互吸引。
Around a magnet is a magnetic field, drawn as lines that run from north to south.
磁铁周围有一个磁场，用从北极到南极的磁感线来表示。
A magnet can even turn a nearby piece of iron into a magnet for a while — that is induced magnetism.
磁铁甚至能让附近的一块铁 暂时变成磁铁——这就是感应磁性。
Soft iron magnetises and loses it easily, perfect for electromagnets; hard steel keeps its magnetism, so it makes permanent magnets.
软铁容易被磁化、也容易失去磁性，非常适合做电磁铁； 硬钢能保持磁性，所以用来做永久磁铁。
A magnet attracts a magnetic material.
磁铁会吸引磁性材料。
There are only four you need: iron, steel, cobalt and nickel.
你只需要记住四种：铁、钢、钴和镍。
Everything else — copper, plastic and wood — is non-magnetic and feels no force at all.
其他的——铜、塑料和木头—— 都是非磁性的，完全不受力。
So a magnet lifts a steel paper clip, but it will not lift a copper coin, even though copper is an excellent conductor of electricity.
所以磁铁能吸起一枚钢制回形针，却吸不起一枚铜币， 尽管铜是极好的导电材料。
Hold a piece of iron near a magnet, or touching it, and the iron becomes a magnet itself.
把一块铁靠近磁铁，或者与它接触，这块铁本身就变成了磁铁。
That is induced magnetism.
这就是感应磁性。
The end of the iron closest to the magnet always gains the opposite pole, so the two then attract — never repel.
靠磁铁最近的那一端总是产生相反的磁极，所以两者随后互相吸引——绝不会排斥。
It is why one magnet can hold a chain of paper clips: each clip becomes a little magnet and passes the magnetism on to the next.
这就是一块磁铁能吊起一串回形针的原因：每个回形针都变成一块小磁铁， 再把磁性传给下一个。
Soft iron is easy to magnetise, but it loses its magnetism just as quickly, so it makes a temporary magnet.
软铁容易被磁化，但也同样很快失去磁性，所以它做成的是临时磁体。
Steel is harder to magnetise, but once it is magnetised it keeps it, so steel makes a permanent magnet.
钢比较难磁化，可是一旦磁化就能保持住，所以钢做成永久磁体。
That gives you the exam answer both ways round: unmagnetised soft iron is the right choice for the core of an electromagnet, and steel is the right choice for a bar magnet.
这就同时给出了考试的两个答案：未磁化的软铁适合做电磁铁的铁芯， 而钢适合做条形磁铁。
Now the exam definition.
现在来看考试的定义。
A magnetic field is a region where a magnetic pole feels a force.
磁场是磁极会受到力的区域。
We draw it with field lines, and three rules go with them.
我们用磁场线来画它， 还有三条规则要记住。
The lines always come out of the north pole and go into the south pole.
磁场线总是从北极出来、进入南极。
The direction of the field at a point is the direction of the force on a north pole placed there.
某一点的磁场方向， 就是放在那里的北极所受力的方向。
And where the lines are close together the field is strong; where they spread apart it is weak.
磁场线密集的地方磁场强，稀疏的地方磁场弱。
You can see the pattern for yourself in two ways.
有两种方法可以亲眼看到这个图样。
Sprinkle iron filings onto a sheet of paper resting over a magnet, tap the paper, and the filings line up along the field lines — exactly as in this photograph.
把铁屑撒在放在磁铁上方的纸上，轻敲纸面， 铁屑就会沿着磁场线排列——正如这张照片所示。
Or move a small plotting compass around the magnet: the needle always points along the field, so you can trace one line dot by dot.
或者把一个小的探测指南针 在磁铁周围移动：指针总是沿着磁场方向，于是你可以一点一点地把一条线描出来。
So where are magnets used?
那么磁铁用在哪里呢？
Permanent magnets sit in fridge door catches, in compass needles and in loudspeakers.
永久磁体用在冰箱门吸、指南针的指针和扬声器里。
An electromagnet is magnetic only while a current flows, and that is its advantage: it can be switched on and off, and made stronger by turning the current up.
电磁铁只有在有电流通过时才有磁性，而这正是它的优点：它可以被打开和关闭， 还能通过加大电流变得更强。
That is why cranes that lift scrap iron use electromagnets, and so do electric bells and relays.
所以吊起废铁的起重机用电磁铁，电铃和继电器也一样。
Rub two materials together and electrons jump from one to the other.
把两种材料摩擦，电子就从一个跳到另一个上。
The one that gains electrons becomes negative; the one that loses them becomes positive.
得到电子的一方带负电， 失去电子的一方带正电。
This is charging by friction.
这就是摩擦起电。
Like charges repel, unlike charges attract — the very same rule as magnets.
同种电荷相斥，异种电荷相吸—— 和磁铁完全一样的规则。
And a charged object sets up an electric field around it, which pushes or pulls on other charges.
带电的物体会在周围建立一个电场，对别的电荷又推又拉。
Detecting a charge, and the one test that is conclusive.
怎么检测电荷，以及唯一具有决定性的那个检验。
A charged rod picks up small pieces of paper and bends a thin stream of water from a tap — but an uncharged object can be attracted too, because the charge induces the opposite charge in it.
带电的棒能吸起小纸片，也能让水龙头流下的细水流弯曲—— 但不带电的物体同样会被吸引，因为电荷会在它上面感应出相反的电荷。
So attraction proves nothing on its own.
所以「吸引」本身什么都证明不了。
Hang one charged rod from a thread and bring another near: if the hanging rod swings away, the two carry the same kind of charge.
把一根带电的棒用线吊起来，再把另一根带电的棒靠近： 如果吊着的那根荡开，说明两根带同种电荷。
Repulsion is the only sure test.
排斥才是唯一可靠的检验。
Here is static charge you can see.
这是你能看见的静电。
This girl is touching the metal dome of a Van de Graaff generator, and every single hair on her head picks up the same kind of charge from it.
这个女孩正摸着范德格拉夫起电机的金属球， 她头上每一根头发都从球上得到了同一种电荷。
Like charges repel, so each hair pushes away from all the others and her hair stands out in every direction.
同种电荷相斥， 所以每根头发都推开其他头发，头发就朝四面八方竖起来。
Same rule as the magnets: same pushes apart.
和磁铁是同一条规则：相同的互相推开。
Let's do the standard example: a plastic rod rubbed with a cloth.
我们来做这个标准例子：用布摩擦一根塑料棒。
Electrons are pulled off the cloth onto the rod, so the rod ends up negative and the cloth ends up positive.
电子从布上被拉到棒上， 于是棒最后带负电，布带正电。
Now notice the wording the exam wants.
现在注意考试要求的说法。
Only the electrons move.
只有电子会移动。
The positive charge cannot move — it stays where it is, inside the atoms.
正电荷不能移动——它留在原处，待在原子里面。
So never write that positive charge jumped across.
所以千万不要写成正电荷跳了过去。
Charge moves through some materials and not others.
电荷能通过某些材料，却不能通过另一些。
A conductor, like copper and the other metals, lets charge flow easily, because it has free electrons that can move.
导体，比如铜和其他金属， 让电荷很容易流过，因为它有可以移动的自由电子。
An insulator, like plastic, rubber or glass, does not, because its electrons are held tightly in place.
绝缘体，比如塑料、橡胶或玻璃， 则不行，因为它的电子被紧紧束缚住。
To test an unknown material, put it in a circuit with a lamp and a battery: the lamp lights only if the material is a conductor.
要检验一种不知名的材料， 把它接进一个有灯泡和电池的电路里：只有当这种材料是导体时，灯才会亮。
Charge itself is measured in coulombs.
电荷本身用库仑来计量。
One more piece of language: a normal atom has as many electrons as protons, so it is neutral.
再学一个说法：正常的原子里电子和质子数目相同， 所以是中性的。
If it loses one or more electrons it is left with extra positive charge, and we call it a positive ion.
如果它失去一个或多个电子，就剩下多余的正电荷， 我们把它叫做正离子。
If it gains electrons it becomes a negative ion.
如果它得到电子，就变成负离子。
So charging by friction simply makes ions on the two surfaces.
所以摩擦起电其实就是在两个表面上产生了离子。
A magnet has a magnetic field; a charge has an electric field, and an electric field is a region where a charge feels a force.
磁铁有磁场；电荷有电场，而电场就是电荷会受到力的区域。
Its direction is the direction of the force on a positive charge.
它的方向就是正电荷所受力的方向。
Learn three patterns.
要记住三种图样。
Around a point charge the lines are straight, pointing away from a positive charge and towards a negative one.
在点电荷周围， 电场线是直的，从正电荷指向外、指向负电荷。
Around a charged ball they spread out evenly all around.
在带电小球周围，电场线均匀地向四周散开。
And between two parallel plates with opposite charges the lines are straight and evenly spaced, running from the positive plate to the negative plate.
而在两块带相反电荷的平行板之间，电场线是直的、间距均匀，从正极板指向负极板。
An electric current is a flow of electric charge.
电流是电荷的流动。
It is measured in amperes, usually just called amps.
它用安培来计量，通常就简称安。
An ammeter measures it, and an ammeter must be joined in series — in the same loop as the component — because the current has to pass through it.
电流表用来测量它， 而电流表必须串联接入——和元件在同一个回路里——因为电流必须流过它。
In symbols, the current is the charge that passes a point divided by the time taken.
用符号来写，电流就是通过某一点的电荷除以所用的时间。
A worked example.
来看一道例题。
A current of three amps flows through a lamp for twenty seconds.
三安培的电流通过一个灯泡二十秒。
How much charge passes through it?
有多少电荷通过了它？
Start from the definition and rearrange it, so charge equals current times time.
从定义出发把它变形，于是电荷等于电流乘以时间。
Now put the numbers in: three times twenty.
现在把数字代进去：三乘二十。
That gives sixty coulombs.
结果是六十库仑。
Always write the unit — a bare number will not earn the mark.
一定要写单位——只写一个数字是拿不到分的。
Inside a metal wire the current is a flow of free electrons.
在金属导线里，电流是自由电子的流动。
But there are two directions to keep straight.
但有两个方向要分清楚。
Conventional current is taken to flow from the positive terminal, round the outside of the circuit, to the negative terminal.
常规电流规定为从正极出发，绕电路外部一圈，流到负极。
The electrons really drift the other way, from negative to positive, because they are negative and are pushed the opposite way.
电子其实是朝另一个方向漂移的，从负极到正极，因为它们带负电，受到的推力方向相反。
Circuit diagrams always use the conventional direction.
电路图上永远用常规电流的方向。
Current also comes in two types.
电流还分两种类型。
A direct current, or d.c., always flows the same way — that is what a battery gives you, so its graph is a steady flat line.
直流电，也就是 d.c.，总是朝同一个方向流动—— 电池给的就是这种，所以它的图像是一条平稳的水平线。
An alternating current, or a.c., keeps swapping direction many times each second, so its graph is a wave that crosses zero again and again.
交流电，也就是 a.c.， 每秒钟要改变方向很多次，所以它的图像是一条不断穿过零点的波。
The mains supply in your home is alternating current.
你家里的市电供应就是交流电。
When charges flow, we have an electric current — the amount of charge passing each second.
当电荷流动时，就有了电流——每秒通过的电荷量。
A battery gives the charges energy; the energy it gives to each unit of charge is the electromotive force, or e.m.f.
电池给电荷能量； 它给每单位电荷的能量就是电动势。
As the charges pass through a component, they give that energy up — and the energy lost per unit charge is the potential difference, or voltage.
当电荷通过某个元件时，它们把能量释放出来—— 每单位电荷损失的能量就是电势差，也就是电压。
Both are measured in volts — joules per coulomb — and the exam wants these definitions word for word.
两者都用伏特来计量——也就是每库仑多少焦耳——而考试要求这两个定义一字不差。
The electromotive force of a source is the electrical work done to drive one unit of charge all the way round a complete circuit.
电源的电动势，是把一单位电荷驱动着绕完整电路走一圈所做的电功。
The potential difference across a component is the work done by one unit of charge as it passes through that component.
元件两端的电势差，是一单位电荷通过这个元件时所做的功。
A voltmeter measures either one, and it is joined in parallel — across the component, not in the loop.
电压表可以测量其中任何一个，而它要并联接入——接在元件两端，而不是接在回路里。
Both are energy per unit charge, so both use the same equation: volts equals joules divided by coulombs.
两者都是每单位电荷的能量，所以用同一个式子：伏特等于焦耳除以库仑。
Here is the example.
来看例题。
A cell does one hundred and twenty joules of work moving sixty coulombs of charge round a circuit.
一个电池做了一百二十焦的功，把六十库仑的电荷送着绕电路一圈。
What is its e.m.f.?
它的电动势是多少？
Divide the energy by the charge: one hundred and twenty over sixty.
用能量除以电荷：一百二十除以六十。
The e.m.f. is two volts — two joules for every coulomb.
电动势是二伏——每一库仑得到两焦。
Every component resists the flow of current.
每个元件都会阻碍电流的流动。
The resistance is the voltage across it divided by the current through it.
电阻等于它两端的电压除以通过它的电流。
For many metal conductors at a steady temperature, doubling the voltage doubles the current — they obey Ohm's law, and their voltage–current graph is a straight line through the origin.
对许多金属导体来说，在温度稳定时，电压翻倍、电流也翻倍——它们遵守欧姆定律， 电压–电流图是一条过原点的直线。
A wire has more resistance when it is longer, thinner, or hotter.
导线越长、越细、越热，电阻就越大。
Resistance measures how hard it is for current to flow.
电阻衡量电流流动的困难程度。
A bigger resistance gives a smaller current for the same voltage.
在电压相同时，电阻越大，电流就越小。
It is measured in ohms, and it equals the voltage across a component divided by the current through it.
它的单位是欧姆，数值等于元件两端的电压除以通过它的电流。
To find it in the lab you need both readings: an ammeter in series to give the current, and a voltmeter across the component to give the voltage.
要在实验室里测出它，你需要两个读数：串联一个电流表读出电流， 在元件两端并联一个电压表读出电压。
Then divide.
然后相除。
Try one.
来试一题。
A twelve volt battery drives a current of zero point five amps through a lamp.
一个十二伏的电池驱动零点五安培的电流通过一个灯泡。
Find the lamp's resistance.
求灯泡的电阻。
Resistance is voltage divided by current, so that is twelve divided by zero point five.
电阻等于电压除以电流，所以就是十二除以零点五。
Dividing by a half doubles the number, so the answer is twenty-four ohms.
除以二分之一相当于翻倍， 所以答案是二十四欧姆。
And here is a check you can always use: for the same voltage, a smaller current means a bigger resistance.
还有一个你随时可以用的检查方法： 在电压相同时，电流越小，说明电阻越大。
For a metal wire at a steady temperature, two things about its shape matter.
对温度稳定的金属导线来说，它形状上的两件事很重要。
First, a longer wire has a bigger resistance — resistance is directly proportional to length.
第一，导线越长，电阻越大——电阻与长度成正比。
Second, a thicker wire has a smaller resistance — resistance is inversely proportional to the cross-sectional area.
第二，导线越粗，电阻越小——电阻与横截面积成反比。
So doubling the length doubles the resistance, while doubling the area halves it.
所以长度加倍，电阻就加倍；而面积加倍，电阻就减半。
Three current–voltage graphs come up again and again.
有三条电流–电压图像会反复出现。
A fixed resistor gives a straight line through the origin: the resistance stays constant, so current is proportional to voltage.
定值电阻给出一条过原点的直线： 电阻保持不变，所以电流与电压成正比。
A filament lamp gives a curve that flattens out as the voltage rises, because the wire gets hot and its resistance goes up.
灯丝灯泡给出一条随电压升高而逐渐变平的曲线， 因为灯丝变热、电阻变大。
A diode lets current through one way only, so its graph is flat on one side and rises sharply on the other.
二极管只让电流从一个方向通过， 所以它的图像一侧是平的，另一侧则急剧上升。
Now the components you must recognise.
现在来看你必须认识的元件。
A cell drives the current round the circuit, and two or more cells joined together make a battery.
电池驱动电流绕电路流动，两个或更多电池连起来就成了电池组。
A power supply does the same job, giving either d.c. or a.c.
电源做同样的事，可以提供直流或交流。
A switch breaks or completes the circuit.
开关断开或接通电路。
A fixed resistor gives one fixed resistance.
定值电阻提供一个固定的电阻。
A variable resistor is one you can change, to control the current — turn it up and the lamp dims.
可变电阻是一个你可以改变的电阻，用来控制电流——把它调大，灯就变暗。
Five more.
再看五个。
A fuse melts and breaks the circuit if the current gets too big.
保险丝在电流过大时熔断，切断电路。
A lamp turns electrical energy into light, and a heater turns it into heat.
灯把电能变成光，加热器把电能变成热。
A thermistor is a resistor whose resistance falls as it gets hotter.
热敏电阻是一种电阻，温度升高时它的阻值下降。
And a light-dependent resistor, or L.D.R., has a resistance that falls as the light gets brighter.
而光敏电阻，也就是 LDR， 它的阻值会随着光线变亮而下降。
Those last two are the sensors in automatic circuits.
最后这两个就是自动电路里的传感器。
And the last group.
最后一组。
A diode lets current pass one way only; a light-emitting diode, an L.E.D., does the same and gives out light as well.
二极管只让电流从一个方向通过；发光二极管，也就是 LED， 作用相同，而且还会发光。
A relay is a switch worked by an electromagnet, so a small current can turn a big one on and off.
继电器是一个由电磁铁带动的开关， 所以小电流可以控制大电流的通断。
A motor turns electrical energy into movement, a bell makes a sound, and a transformer changes the size of an alternating voltage.
电动机把电能变成运动，电铃发出声音， 而变压器改变交流电压的大小。
Every one of those components has a standard symbol, and you are expected to read them and draw them.
上面每一个元件都有一个标准符号，而你需要会读、也会画它们。
Spend a few minutes with this chart.
花几分钟看看这张图。
The pairs students mix up most are the ammeter and the voltmeter — an A in a circle goes in the loop, a V in a circle goes across a component — and the fixed resistor, a plain rectangle, against the variable resistor, a rectangle with an arrow through it.
学生最容易混淆的两对是：电流表和电压表—— 圆圈里的 A 接在回路中，圆圈里的 V 接在元件两端—— 以及定值电阻（一个普通的矩形）和可变电阻（矩形上多一个箭头）。
Components can be joined two ways.
元件有两种连接方式。
In a series circuit, there is one single loop: the same current flows through everything, and the voltages across the parts add up.
在串联电路中，只有一个回路：相同的电流流过每个元件， 各部分两端的电压相加。
In a parallel circuit, there are separate branches: each branch gets the full voltage, and the branch currents add up.
在并联电路中，有各自分开的支路：每条支路都得到全部电压， 各支路的电流相加。
That is why the lights in your home are wired in parallel — switch one off, and the rest stay on.
这就是为什么家里的灯是并联的——关掉一盏，其余的照样亮。
In a series circuit the parts form one single loop, and four rules follow.
在串联电路里，各元件组成一个单一的回路，由此得出四条规则。
The current is the same at every point — there is nowhere else for it to go.
电流处处相同——它没有别的地方可去。
The supply voltage is shared between the components.
电源电压由各元件分担。
Cells joined in series add their e.m.f.s together, as long as they point the same way.
串联的电池把它们的电动势相加，只要方向一致。
And resistors in series simply add up: two plus three gives five ohms.
而串联的电阻直接相加：二加三得五欧姆。
In a parallel circuit the parts sit on separate branches, and the rules change.
在并联电路里，各元件分在不同的支路上，规则也就变了。
Each branch gets the full supply voltage.
每条支路都得到全部的电源电压。
Then the current splits between the branches, so the current leaving the source is bigger than the current in any one branch.
接着电流在各支路之间分开， 所以从电源流出的电流比任何一条支路的电流都大。
And here is the surprising one: the total resistance is always less than the smallest single resistance in the combination, because another branch gives the current another route.
还有一条令人意外：总电阻总是小于组合里最小的那个电阻， 因为多一条支路就给电流多一条通路。
That is why home lamps are wired in parallel: if one fails, the rest stay on.
所以家里的灯是并联的：一盏坏了，其余的照样亮。
That splitting obeys a simple rule.
这种分流遵守一条简单的规则。
At a junction, the current flowing in equals the total current flowing out — charge cannot pile up or vanish.
在节点处，流入的电流等于流出的总电流—— 电荷不会堆积，也不会消失。
So if three amps arrives at a junction and two amps goes one way, the other branch must carry one amp.
所以如果三安培到达一个节点， 其中两安培走一条路，另一条支路就必须带一安培。
Exam questions love this: they give you all but one of the currents and ask for the missing one.
考题很爱考这个：给你除一个之外的所有电流，问你缺的那个是多少。
Let's use the parallel formula.
我们来用并联公式。
A six ohm resistor and a three ohm resistor are joined in parallel.
一个六欧的电阻和一个三欧的电阻并联在一起。
One over the total equals one over each resistance added together: one sixth plus one third.
总电阻的倒数等于各电阻倒数之和：六分之一加三分之一。
Write them over the same bottom number — one sixth plus two sixths is three sixths, which is a half.
把它们化成同一个分母——六分之一加六分之二等于六分之三，也就是二分之一。
So one over the total is a half, and the total is two ohms.
所以总电阻的倒数是二分之一，总电阻就是两欧姆。
Two ohms is less than three ohms, as the parallel rule promised.
两欧姆小于三欧姆，正是并联规则所保证的。
Two resistors in series share the supply voltage, and that arrangement is called a potential divider.
两个串联的电阻分担电源电压，这样的接法叫做分压器。
The same current goes through both, so the bigger resistance takes the bigger share of the voltage — in fact the ratio of the resistances equals the ratio of the voltages.
通过两者的电流相同，所以较大的电阻分到较大的一份电压—— 实际上电阻之比就等于电压之比。
A variable potential divider lets you slide the output smoothly, from zero volts up to the full supply.
可变分压器让你平滑地调节输出， 从零伏一直到电源的全部电压。
Now swap one resistor for a thermistor, and the output voltage changes with temperature: as the thermistor gets hotter its resistance falls, so its share of the voltage falls and the other resistor's share rises.
现在把其中一个电阻换成热敏电阻，输出电压就会随温度变化： 热敏电阻变热时阻值下降，所以它分到的电压下降，另一个电阻分到的电压上升。
Use a light-dependent resistor instead and the output changes with brightness.
改用光敏电阻，输出就随亮度变化。
Feed that voltage into a switching circuit and a heater or a street lamp can switch on automatically — the heater when the room gets cold, the lamp when the sky gets dark.
把这个电压送进一个开关电路， 加热器或路灯就能自动开启——房间变冷时开加热器，天色变暗时开路灯。
Electrical power is the energy delivered each second — the current times the voltage.
电功率是每秒送出的能量——电流乘以电压。
Your electricity bill measures energy in kilowatt-hours: a one-kilowatt heater running for one hour uses one kilowatt-hour.
你的电费单用千瓦时来计量能量： 一台一千瓦的电暖器工作一小时，用掉一千瓦时。
So a two-kilowatt kettle, running for half an hour, also uses one kilowatt-hour of energy.
所以一台两千瓦的电水壶， 工作半小时，同样用掉一千瓦时的能量。
Power in watts is current times voltage, and the energy in joules is that power multiplied by the time.
功率的单位是瓦特，等于电流乘以电压；能量的单位是焦耳，等于功率乘以时间。
Here is the example.
来看例题。
A twelve volt motor draws a current of two amps.
一台十二伏的电动机通过两安培的电流。
First the power: two times twelve is twenty-four watts.
先算功率：二乘十二得二十四瓦。
Now the energy it transfers in thirty seconds: twenty-four times thirty is seven hundred and twenty joules.
再算它在三十秒内转移的能量：二十四乘三十得七百二十焦。
Always in that order — find the power first, then multiply by the time.
顺序永远是这样——先求功率，再乘以时间。
Bills use a bigger unit, because a joule is tiny.
电费单用的是更大的单位，因为一焦耳太小了。
Energy in kilowatt-hours is the power in kilowatts times the time in hours, and the cost is that energy times the price of one unit.
以千瓦时为单位的能量， 等于以千瓦为单位的功率乘以以小时为单位的时间，而费用等于这个能量乘以每度电的价格。
So a two kilowatt heater left on for three hours uses six kilowatt-hours.
所以一台两千瓦的电暖器开三小时，用掉六千瓦时。
If one kilowatt-hour costs twenty cents, that comes to six times twenty — one hundred and twenty cents.
如果一千瓦时二十分钱， 那就是六乘二十——一百二十分钱。
The two things you multiply are always kilowatts and hours, never watts and seconds.
相乘的两个量永远是千瓦和小时， 不是瓦特和秒。
This is where that number is counted.
这个数字就是在这里被记录下来的。
Every home has an electricity meter, and it adds up the energy the whole house uses, in kilowatt-hours.
每户人家都有一个电能表， 它把整栋房子用掉的能量以千瓦时累加起来。
The reading on the display is exactly what you pay for.
显示屏上的读数正是你要付钱的部分。
Notice the unit printed on it: not joules, but kilowatt-hours, because one kilowatt-hour is a far bigger amount of energy than one joule.
注意上面印的单位：不是焦耳，而是千瓦时，因为一千瓦时比一焦耳的能量大得多。
An analogue ammeter has a needle that moves over a scale; a digital one shows the reading as a number.
模拟式电流表有一根在刻度上移动的指针；数字式的直接显示一个数字。
Both come with different ranges, and choosing matters: pick the range just above the biggest current you expect, so the reading uses most of the scale and is as accurate as the instrument allows.
两种都有不同的量程，而选量程是有讲究的： 选一个刚好高于你预期的最大电流的量程， 这样读数占据刻度的大部分，精度也就达到仪器所能给的最好水平。
Four mains hazards, and each one has a reason attached — the reason is where the mark is.
市电有四种危险，每一种都要配一个原因——分数就在原因上。
Damaged insulation leaves bare wire exposed, which can give a shock or start a fire.
绝缘层破损让导线裸露在外，可能造成电击或引起火灾。
Overheating cables: too much current makes a cable hot enough to set fire to what is around it.
电缆过热：电流太大会让电缆热到足以点燃周围的东西。
Damp conditions let current pass into a person, so the risk of a shock goes up.
潮湿的环境让电流通到人身上，因此电击的风险上升。
And overloading a socket with too many appliances draws too much current through one cable.
而在一个插座上接太多电器造成过载，会让一根电缆里流过太大的电流。
Mains electricity is dangerous, so a plug has three wires.
市电很危险，所以插头有三根线。
The live wire carries the high voltage in.
火线把高电压送进来。
The neutral completes the circuit.
零线让电路闭合。
And the earth wire is a safety line: if a fault makes the metal casing live, the earth carries the current safely away.
而地线是一条安全线：如果故障让金属外壳带电，地线就把电流安全地导走。
A fuse — or a circuit breaker — holds a thin wire that melts and breaks the circuit the moment the current climbs too high.
保险丝——或断路器——里面有一根细线，一旦电流升得太高，它就熔断、切断电路。
One detail is worth a mark on its own: the switch and the fuse must both go in the live wire.
有一个细节本身就值一分：开关和保险丝都必须装在火线上。
Then, when the switch is off, the appliance is completely cut off from the high voltage and is safe to touch.
这样一来，开关断开时，电器就与高电压完全隔断，摸起来是安全的。
Fit them in the neutral wire instead and the appliance stays joined to the live side even when switched off — so it could still give you a shock.
如果把它们装在零线上，即使开关断开，电器仍然连着火线那一侧—— 所以它还是可能让你被电击。
A fuse is a thin wire that melts if the current gets too big, breaking the circuit before the cable overheats.
保险丝是一根细导线，电流过大时它会熔断，在电缆过热之前切断电路。
Choose a rating just above the normal working current: an appliance that normally draws about ten amps takes a thirteen amp fuse.
选择的额定值要略高于正常工作电流：一个正常用大约十安培的电器，配十三安培的保险丝。
Too big a fuse never blows and the cable cooks; too small a fuse blows every time you switch on.
保险丝选得太大就永远不会熔断，电缆会被烤坏；选得太小则每次开机都会熔断。
A trip switch, or circuit breaker, does the same job faster and can be reset instead of replaced.
跳闸开关，也就是断路器，做同样的事，但动作更快，而且可以复位而不必更换。
The metal case of an appliance must be made safe in one of two ways.
电器的金属外壳必须用两种方法之一做到安全。
With an earthed metal case, the case is joined to the earth wire; if a live wire touches it, a very large current flows straight to earth and blows the fuse, so the appliance is cut off.
如果是接地的金属外壳，外壳就与地线相连；一旦火线碰到外壳， 一个很大的电流会直接流入大地，把保险丝熔断，于是电器被切断电源。
Or the appliance is double insulated: the outside is plastic, so the case can never become live, and no earth wire is needed at all.
或者电器采用双重绝缘：外壳是塑料的，所以外壳永远不会带电，也就完全不需要地线。
This is a real home consumer unit — the box where the mains comes in.
这是一个真实的家用配电箱——市电进入房子的那个箱子。
Each of those small switches is a circuit breaker protecting one circuit: the lights, the sockets, the cooker.
里面每一个小开关都是一个断路器，保护一条电路：照明、插座、炉具。
If the current in that circuit gets too big, its breaker trips and you simply push it back up.
如果那条电路里的电流变得太大，它的断路器就会跳闸，你只要把它推回去就行。
The two larger units cut off even faster if current starts leaking to earth.
那两个较大的装置在有电流开始漏向大地时，切断得更快。
Here is the deep link.
关键的联系在这里。
An electric current makes a magnetic field of its own, in circles around the wire.
电流会产生自己的磁场，绕着导线成一圈圈。
Wind that wire into a coil around iron and you get an electromagnet — a magnet you can switch on and off.
把导线绕成线圈、套在铁芯上，你就得到一个电磁铁——一块可以开关的磁铁。
Now put a current-carrying wire inside another magnetic field: the two fields push on each other, so the wire feels a force.
再把一根通电的导线放进另一个磁场里：两个磁场互相推挤，导线就受到一个力。
Let that force spin a coil, and you have built an electric motor.
让这个力去转动一个线圈，你就造出了一台电动机。
Look closely at the field a current makes.
仔细看电流产生的磁场。
Around a straight wire the field lines are circles going round the wire, and the field is strongest close to the wire, where the circles are packed together.
在直导线周围，磁场线是绕着导线的一圈圈圆， 而且在靠近导线处磁场最强，那里的圆最密。
Reverse the current and the whole field reverses direction.
把电流反向，整个磁场的方向也跟着反过来。
No magnet is needed anywhere — moving charge is enough.
这里根本不需要磁铁——运动的电荷就够了。
Two rules, and mixing them up is the classic lost mark.
两条定则，把它们弄混是最经典的失分。
Fleming's left-hand rule is for the motor effect — a current in a field feels a force.
左手定则用于电动机效应——处在磁场中的电流受到力。
Fleming's right-hand rule is for the generator effect — a conductor moved in a field induces an e.m.f.
右手定则用于发电机效应——导体在磁场中运动，感应出电动势。
Left for motor, right for generator; in both, the first finger is the field, the second finger the current, and the thumb the motion or force.
左手对应电动机，右手对应发电机； 两条定则里，食指都表示磁场，中指表示电流，拇指表示运动或者力。
Wind that wire into a long coil and you have a solenoid.
把导线绕成一个长长的线圈，你就得到一个螺线管。
Its field looks just like a bar magnet's: a north pole at one end, a south pole at the other, and a strong, even field down the middle.
它的磁场看起来就像条形磁铁的磁场： 一端是北极，另一端是南极，中间是很强而且均匀的磁场。
Three things make the field stronger — turn the current up, add more turns of wire, or slide a soft-iron core inside.
有三件事能让磁场更强——加大电流、增加线圈匝数，或者在里面插入一个软铁芯。
You can show the pattern with iron filings or a plotting compass.
你可以用铁屑或探测指南针把这个图样显示出来。
Two uses of that effect.
这个效应有两个用途。
In a relay, a small current through an electromagnet pulls a switch closed, and that switch controls a much bigger current — so a low-power circuit can start a motor safely.
在继电器里，通过电磁铁的一个小电流把开关拉合， 而这个开关控制着一个大得多的电流——于是一个小功率电路可以安全地启动电动机。
In a loudspeaker, a changing current in a coil sitting in a magnetic field pushes and pulls a paper cone.
在扬声器里，处于磁场中的线圈里的变化电流推拉一个纸盆。
The cone moves the air, and moving air is sound.
纸盆推动空气，而运动的空气就是声音。
Now run it backwards.
现在把它反过来。
Move a magnet near a coil — or a wire through a magnetic field — and you induce a voltage that drives a current.
让磁铁在线圈附近移动——或让导线穿过磁场——你就感应出一个电压， 驱动电流。
This is electromagnetic induction.
这就是电磁感应。
Spin a coil between magnets and it makes electricity without stopping: that is a generator, the heart of every power station.
让线圈在磁铁之间旋转，它就不停地产生电—— 这就是发电机，每座发电站的心脏。
The faster you move, and the stronger the magnet, the bigger the induced voltage.
你动得越快、磁铁越强，感应出的电压就越大。
Watch the idea run backwards.
来看这个想法反过来运行。
Move a wire across a magnetic field, or change the field passing through a coil, and an e.m.f. is induced in the wire.
让导线穿过磁场移动，或者改变穿过线圈的磁场， 导线里就会感应出一个电动势。
If the wire is part of a complete circuit, that e.m.f. drives a current.
如果导线是完整电路的一部分， 这个电动势就会驱动电流。
To show it, push a magnet in and out of a coil joined to a sensitive meter, and watch the needle flick one way, then the other.
要演示它，把一块磁铁在接了灵敏电流计的线圈里推进拉出， 看指针先往一边偏，再往另一边偏。
Two exam points about induction.
关于感应有两个考点。
The induced voltage is bigger if you move faster, use a stronger magnet, or put more turns on the coil — and it is zero if nothing is moving or changing.
如果你动得更快、用更强的磁铁，或者在线圈上绕更多匝， 感应出的电压就更大——而如果什么都不动、什么都不变，感应电压就是零。
Second, the induced e.m.f. always opposes the change that caused it.
第二，感应电动势总是阻碍产生它的那个变化。
So when you push a magnet into a coil, the coil pushes back, and you have to do work to keep pushing.
所以当你把磁铁推进线圈时， 线圈会往回推，你必须做功才能继续推。
That work is where the electrical energy comes from.
这些功就是电能的来源。
An a.c. generator turns movement into electricity.
交流发电机把运动变成电。
A coil is spun between the poles of a magnet, so the field through it keeps changing and an alternating e.m.f. is induced.
一个线圈在磁铁的两极之间旋转， 所以穿过它的磁场不断变化，就感应出一个交变的电动势。
Slip rings and carbon brushes carry the current out while the coil keeps turning.
滑环和碳刷在线圈继续转动的同时把电流引出去。
The e.m.f. is biggest when the coil is flat, because it is then cutting across the field fastest, and zero when the coil is upright.
当线圈处于水平位置时电动势最大，因为那时它切割磁场最快； 当线圈竖直时电动势为零。
So each turn gives one full wave.
所以每转一圈就产生一个完整的波。
Put a current-carrying wire in a magnetic field and the two fields push on each other, so the wire feels a force.
把一根通电的导线放进磁场里，两个磁场互相推挤，于是导线受到一个力。
This is the motor effect.
这就是电动机效应。
Reverse the current and the force reverses; reverse the field and it reverses too — but reverse both and the force stays as it was.
把电流反向，力就反向；把磁场反向，力也反向—— 但两个都反向，力就和原来一样。
Make the current bigger or the field stronger and the force grows.
加大电流或加强磁场，力就变大。
And the force, the field and the current are all at right angles to one another — fix that picture in your head before you reach for a rule.
而且力、磁场和电流三者互相垂直——在用任何定律之前，先把这幅图记在脑子里。
To get the direction, use the left-hand rule.
要判断方向，就用左手定律。
Hold the thumb and first two fingers of your left hand at right angles.
把左手的拇指和前两根手指互相垂直地伸开。
The thumb is the force, or the motion.
拇指代表力，也就是运动的方向。
The first finger is the field, pointing from north to south.
食指代表磁场，从北极指向南极。
And the second finger is the current, in the conventional direction.
中指代表电流，取常规电流的方向。
Point the first two correctly and your thumb shows which way the wire moves.
把前两个方向摆对，拇指就指出导线运动的方向。
A moving stream of charge is a current, even with no wire around it.
运动的电荷流就是电流，即使周围没有导线也一样。
So if a beam of charged particles crosses a magnetic field, that same sideways force acts: the field deflects the beam.
所以如果一束带电粒子穿过磁场，同样的侧向力就会起作用，粒子束被偏转。
One trap here: electrons flow in the opposite direction to the conventional current, so work out the conventional direction first, then use the left-hand rule.
这里有一个陷阱：电子的流动方向与常规电流相反， 所以要先确定常规电流的方向，然后再用左手定律。
Put a whole coil in the field and the forces on its two sides act in opposite directions — one side pushed up, the other pushed down — so the coil gets a turning effect and spins.
把一整个线圈放进磁场里，它两边所受的力方向相反——一边被往上推，另一边被往下推—— 于是线圈获得一个转动效应，转起来。
That is a d.c. motor.
这就是直流电动机。
The turning effect is bigger with more turns on the coil, a bigger current, or a stronger field.
线圈匝数越多、电流越大或磁场越强，转动效应就越大。
And a split-ring commutator swaps the current direction every half turn, which keeps it spinning the same way instead of stopping.
而换向器每转半圈就把电流方向调换一次，让它一直朝同一个方向转，而不是停下来。
Here is what that looks like in a real machine.
这就是它在真实机器里的样子。
Those copper bars are the commutator, and the two blocks pressed against them on springs are the carbon brushes.
那些铜条就是换向器， 被弹簧压在它们上面的两块黑色的东西就是碳刷。
The brushes feed current into the spinning coil without any wires twisting, and as the coil turns, the bars slide past the brushes so the current in the coil is reversed automatically.
碳刷把电流送进旋转的线圈，而不会把导线缠住； 线圈转动时，铜条从碳刷下滑过，于是线圈里的电流就自动反向了。
Finally, the transformer — two coils sharing an iron core.
最后是变压器——两个线圈共用一个铁芯。
It changes voltage: more turns on the second coil steps the voltage up; fewer turns steps it down.
它改变电压：第二个线圈的匝数越多， 电压就升高；匝数越少，电压就降低。
This is how power reaches you.
电就是这样送到你身边的。
Power stations step the voltage far up to send it across the country, because high voltage means low current — and low current wastes far less energy as heat in the cables.
发电站把电压升得很高，才把电送到全国，因为高电压意味着小电流—— 而小电流在电缆里以热的形式浪费的能量少得多。
Near your home, another transformer steps it safely back down.
在你家附近，另一个变压器再把它安全地降回来。
Look inside.
来看看里面。
A transformer is two coils wound on a soft-iron core: the primary takes the voltage in, the secondary gives the changed voltage out.
变压器就是绕在软铁芯上的两个线圈：原线圈把电压输入， 副线圈把改变后的电压输出。
The alternating current in the primary makes a changing magnetic field in the core, the core carries that field to the secondary, and there the changing field induces an alternating e.m.f.
原线圈里的交流电在铁芯中产生一个变化的磁场， 铁芯把这个磁场传到副线圈，在那里变化的磁场感应出一个交变电动势。
Which explains an exam favourite: a transformer only works on alternating current, because steady d.c. would give a steady field and induce nothing.
这就解释了考试爱考的一点：变压器只对交流电有用， 因为稳定的直流会产生稳定的磁场，什么也感应不出来。
The numbers follow one rule: the ratio of the voltages equals the ratio of the turns.
数字只遵守一条规则：电压之比等于匝数之比。
A transformer has twelve hundred turns on the primary and one hundred on the secondary, and the primary is joined to a two hundred and forty volt supply.
一个变压器原线圈有一千二百匝，副线圈有一百匝，原线圈接在二百四十伏的电源上。
Find the secondary voltage.
求副线圈的电压。
Well, the turns ratio is twelve to one, so the voltage ratio is twelve to one too.
匝数比是十二比一，所以电压比也是十二比一。
Two hundred and forty divided by twelve is twenty volts — fewer turns, so this is a step-down transformer.
二百四十除以十二得二十伏——匝数更少，所以这是一个降压变压器。
So more turns on the secondary steps the voltage up, and fewer turns steps it down.
所以副线圈匝数多就升压，匝数少就降压。
But a transformer is not a source of free energy.
但变压器不是免费能量的来源。
If it is one hundred per cent efficient, the power in equals the power out: current times voltage on the primary equals current times voltage on the secondary.
如果它的效率是百分之百，输入功率就等于输出功率： 原线圈的电流乘电压，等于副线圈的电流乘电压。
That means a step-up transformer raises the voltage but lowers the current by the same factor: double the voltage and the current halves.
这意味着升压变压器提高了电压，却按同样的倍数降低了电流： 电压翻倍，电流就减半。
And that is the fact the national grid is built on.
而这正是全国电网建立的基础。
Some power is always wasted as heat in the cables, and the power wasted depends on the current squared times the resistance of the cables.
总有一部分功率以热的形式在电缆里被浪费掉， 而浪费的功率取决于电流的平方乘以电缆的电阻。
Halve the current and you waste only a quarter as much.
把电流减半，浪费的功率只剩四分之一。
So a step-up transformer at the power station raises the voltage and drops the current.
所以发电站的升压变压器提高电压、降低电流。
Then close to your town, a step-down transformer brings the voltage back to a safe value.
然后在靠近你所在城镇的地方，一个降压变压器再把电压降回到安全的数值。
These are the cables doing that job — held high in the air on steel pylons, well away from anything that could touch them, and carrying electricity at hundreds of thousands of volts.
这些就是在做这件事的电缆——高高地架在钢制铁塔上，远离任何可能碰到它们的东西， 以几十万伏的电压输送电力。
High voltage keeps the current small, and a small current keeps the wasted heat small.
高电压让电流保持很小，而小电流让浪费的热量保持很少。
Those insulators hanging under each arm stop the huge voltage reaching the metal tower.
每根横臂下面挂着的那些绝缘子，挡住了巨大的电压，使它到不了金属塔身。
Three marks to lock in.
锁住三个分。
First, like poles repel and like charges repel; only opposite ones attract.
第一，同名磁极相斥、同种电荷相斥；只有异性的才相吸。
Second, in a series circuit the current is the same everywhere, while in parallel the voltage is the same across each branch.
第二，在串联电路中电流处处相同，而在并联电路中每条支路两端的电压相同。
Third, high-voltage transmission saves energy because it means a smaller current, and it is the current that heats the cables.
第三，高压输电省能量，是因为它意味着更小的电流，而正是电流让电缆发热。
Master these, and this topic is yours.
把这些掌握好，这个专题就是你的了。
Three more marks that get thrown away.
还有三分常常被白白丢掉。
An ammeter goes in series, and it must have a very low resistance, so it hardly changes the current it is measuring.
电流表要串联接入，而且它的电阻必须非常小， 这样它几乎不会改变自己所测的电流。
In contrast, a voltmeter goes in parallel, across the component, and must have a very high resistance, so almost no current flows through it.
相反，电压表要并联接在元件两端， 而且电阻必须非常大，这样几乎没有电流流过它。
And remember that resistors in series add up, while a parallel pair always comes out below the smaller of the two.
还要记住：串联的电阻相加，而并联的一对电阻，其总值总是小于两者中较小的那个。
Always check a parallel answer against the smaller resistance.
并联的答案，永远要拿去和较小的那个电阻比一比。
And the last three.
最后三条。
In a transformer, the voltage ratio equals the turns ratio, so more turns on the secondary steps the voltage up.
在变压器里，电压之比等于匝数之比，所以副线圈匝数越多，电压就升得越高。
Next, transformers work on alternating current only — steady d.c. makes a steady field and induces nothing.
接着，变压器只对交流电起作用——稳定的直流会产生稳定的磁场，什么也感应不出来。
Finally, the switch and the fuse go in the live wire, and you pick a fuse rated just above the appliance's normal working current.
最后，开关和保险丝要装在火线上， 而且保险丝的额定值要略高于电器的正常工作电流。
Get those right and you will collect marks other students hand back.
把这些都做对，你就能拿到别的同学白白送掉的分数。