Electric Current
A-Level Physics Topic 9 17:50 English narration · English + 中文 subtitles burned in
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Flip a switch, and the light comes on instantly.
按下开关，灯瞬间就亮了。
So the electrons must be racing through the wire at the speed of light — right?
那么电子一定是以光速在导线里飞奔——对吧？
Wrong.
错。
Inside a copper wire, the electrons drift slower than a snail, less than a millimetre each second.
在铜导线内部，电子漂移得比蜗牛还慢，每秒还不到一毫米。
So how is the light instant?
那灯为什么能瞬间亮？
Because the moment you close the switch, an electric field pushes on every electron at once, all along the wire.
因为在你合上开关的那一刻，一个电场同时推动导线里每一个电子，沿着整根导线。
They all begin to crawl together, immediately.
它们立刻一起开始缓缓爬行。
The signal is fast, even though the electrons are slow.
信号很快，尽管电子很慢。
Electricity is charge on the move.
电就是运动中的电荷。
Today: what current really is, how we push it with voltage, how resistance holds it back, and the equations that tie them all together.
今天：电流究竟是什么、我们如何用电压去推动它、 电阻如何阻挡它，以及把它们全部联系起来的那些方程。
Let's begin.
让我们开始吧。
An electric current is simply a flow of charge.
电流就是电荷的流动。
Count how much charge passes a point each second, and you have the current, measured in amperes.
数一数每秒有多少电荷经过某一点，你就得到了电流，用安培量度。
So charge equals current, times time.
所以电荷等于电流乘以时间。
And that charge is not smooth — it comes in tiny, fixed lumps.
而这些电荷并不是连续平滑的——它以微小而固定的小块出现。
Every electron carries the same tiny charge: one point six times ten to the minus nineteen coulombs.
每个电子都带有相同的微小电荷：一点六乘以十的负十九次方库仑。
Charge is quantised — it only ever comes in whole numbers of these.
电荷是量子化的—— 它只能是这些小块的整数倍。
What actually carries the charge?
真正运载电荷的是什么？
It depends on the material.
取决于材料。
In a metal the carriers are negative conduction electrons.
在金属里，载流子是带负电的自由电子。
In an electrolyte they are positive and negative ions.
在电解质里，是正离子和负离子。
In a semiconductor they may be electrons or holes — empty places that act like positive charge.
在半导体里，可能是电子，也可能是空穴—— 像正电荷一样行为的空位。
The conventional current direction is the way positive charge would flow.
常规电流方向是正电荷会流动的方向。
So in a wire the conventional arrow points opposite to the real drift of electrons.
所以在导线里，常规箭头与电子的真实漂移方向相反。
Look at the diagram: panel a shows positive carriers drifting with the conventional current; panel b shows electrons drifting against it.
看图：甲图正载流子顺着常规电流漂移； 乙图电子逆着它漂移。
Same current equation — different carriers.
同一个电流方程——不同的载流子。
Current is the rate of flow of charge: I equals Q over t, and Q equals I times t.
电流是电荷的流动速率：电流等于电荷除以时间，电荷等于电流乘时间。
The ampere is one coulomb per second.
安培是每秒一库仑。
For a changing current, charge flowed is the area under an I against t graph.
电流在变时，流过的电荷是电流对时间图线下的面积。
Worked example: zero point five zero amperes for two point zero minutes.
例题：零点五零安培流了两点零分钟。
Convert time first — two minutes is one hundred and twenty seconds.
先换算时间——两分钟是一百二十秒。
Charge equals zero point five zero times one hundred and twenty, sixty coulombs.
电荷等于零点五零乘一百二十，六十库仑。
Divide by the elementary charge: about three point eight times ten to the twenty electrons.
除以基本电荷：约三点八乘以十的二十次方个电子。
Everyday currents move huge numbers of carriers.
日常电流推动海量载流子。
How big is the current?
电流有多大？
That depends on four things, tied together in one equation.
这取决于四样东西，被一个方程联系在一起。
The current equals the cross-section area of the wire, times the number density of electrons — how many are packed into each cubic metre — times their drift velocity, times the charge on each one.
电流等于导线的横截面积， 乘以电子的数密度——每立方米里挤了多少个——再乘以它们的漂移速度，再乘以每个电子的电荷。
A fatter wire, more electrons, or a faster drift: all of them mean more current.
更粗的导线、更多的电子，或更快的漂移：每一样都意味着更大的电流。
Here is the picture behind I equals A n v q.
这是电流等于面积乘数密度乘漂移速度乘电荷背后的图景。
A wire of cross-section area A carries n charge carriers in each cubic metre, each of charge q, drifting at average speed v.
横截面积为 A 的导线， 每立方米有 n 个载流子，每个电荷为 q，以平均速率 v 漂移。
In a short time the carriers that cross a face form a short cylinder of charge.
在短时间内， 穿过一个截面的载流子构成一小段电荷柱。
Multiply volume by number density by charge per carrier, divide by time, and the drift speed appears: current grows if the wire is wider, denser with carriers, or they crawl faster.
体积乘数密度乘每个载流子的电荷，再除以时间， 漂移速度就出现了：导线更宽、载流子更密，或爬得更快，电流就更大。
That is the whole equation in one diagram.
整个方程都在这张图里。
Worked numbers.
用数字算。
A copper wire has cross-sectional area one point zero times ten to the minus six square metres and carries five point zero amperes.
一根铜导线横截面积一点零乘以十的负六次方平方米，电流五点零安培。 铜每立方米约有八点五乘以十的二十八次方个自由电子。
Copper has about eight point five times ten to the twenty-eight free electrons per cubic metre.
变形：漂移速度 v 等于 I 除以 A n q。
Rearrange: drift velocity v equals I over A n q. Plug in q as one point six zero times ten to the minus nineteen coulombs. You get about three point seven times ten to the minus four metres per second — less than a millimetre each second.
把 q 取为一点六零乘以十的负十九次方库仑，得到约三点七乘以十的负四次方米每秒—— 每秒不到一毫米。
The snail comparison was not a joke.
蜗牛的比喻并不是玩笑。
Use the same equation to compare situations.
用同一个方程比较不同情况。
A thinner wire — smaller A — at the same current needs a faster drift velocity.
更细的导线——更小的 A——在相同电流下需要更快的漂移速度。
A semiconductor has far fewer free carriers than a metal, so smaller n: for the same current the drift velocity is much larger.
半导体的自由载流子远少于金属，所以 n 更小：相同电流下漂移速度大得多。
In series components the current is the same everywhere.
串联元件里电流处处相同。
If the cross-section stays the same but the material changes, then n times v must change the other way so that I stays fixed.
若横截面不变但材料变了，则 n 乘 v 必须反方向变化以保持 I 不变。
Same I, different carrier soup.
同样的电流，不同的载流子汤。
A wire that narrows is the standard test of whether you believe the equation.
变细的导线是检验你是否真的理解那个公式的标准题。
A wedge, a tapered rod, a cable of thick and thin strands: the same current passes every cross-section, so the drift speed must rise exactly where the area falls — v is proportional to one over A, and so to one over r squared.
楔形、锥形棒、由粗细不同的股组成的电缆： 同样的电流通过每一个横截面，所以漂移速度必须恰好在面积变小的地方变大—— v 与 A 成反比，也就是与 r 的平方成反比。
And for strands in parallel the current divides between them, so each strand carries less and the drift speed in one strand is lower than in a single wire of the same total area.
而对于并联的多股导线，电流在它们之间分配， 所以每一股承载的电流更小，一股里的漂移速度比同样总面积的单根导线里要低。
To make charge flow, you need a push — and that push is the potential difference, or voltage.
要让电荷流动，你需要一个推力——这个推力就是电势差，也就是电压。
It is the energy given to each unit of charge as it passes through a component.
它是每单位电荷经过某个元件时获得的能量。
So voltage equals the energy transferred, divided by the charge.
所以电压等于转移的能量除以电荷。
One volt means one joule of energy delivered for every coulomb of charge that flows.
一伏特意味着每流过一库仑电荷，就有一焦耳的能量被传递。
Electromotive force and potential difference share the same formula — energy per unit charge — but they point different ways.
电动势和电势差共用同一个公式——单位电荷的能量——但方向不同。
The e.m.f. of a source is the energy given to each coulomb by the source.
电源的电动势是电源给予每一库仑的能量。
The p.d. across a component is the energy each coulomb gives up as it passes through.
元件两端的电势差是每一库仑经过时交出的能量。
In this circuit the cell supplies energy per coulomb; the resistor takes it.
在这个电路里，电池给每库仑供能；电阻把它取走。
If one joule of electrical energy becomes heat, light or kinetic energy when one coulomb passes, the p.d. is one volt.
若一流过一库仑，一焦耳电能变成热、光或动能， 电势差就是一伏特。
Same units, opposite energy bookkeeping.
同样的单位，相反的能量记账。
Charge flowing through a voltage delivers energy every second — that is electrical power.
电荷流过一个电压，每秒都在传递能量——这就是电功率。
The power equals the voltage, times the current.
功率等于电压乘以电流。
Using the resistance, you can write it two more ways: the current squared, times the resistance, or the voltage squared, divided by the resistance.
借助电阻，你还能把它写成另外两种形式：电流的平方乘以电阻，或者电压的平方除以电阻。
Three forms of the same idea — pick whichever fits the quantities you know.
同一个意思的三种形式——用哪一个，看你已知哪些量。
High-voltage power lines carry energy across the country — power is energy per unit time.
高压线把能量送到全国——功率是单位时间的能量。
Pick the form that matches what you know.
选与已知量匹配的形式。
Two heaters of equal resistance: the larger current gives more power, because P equals I squared R.
两个等电阻加热器：电流更大的功率更大，因为功率等于电流平方乘电阻。
Two resistors in parallel across the same voltage: the smaller R gives more power, because P equals V squared over R.
两个并联在同一电压上的电阻：电阻更小的功率更大，因为功率等于电压平方除以电阻。
A kettle marked two point four kilowatts at two hundred and forty volts draws ten amperes and has resistance twenty-four ohms.
标着两点四千瓦、二百四十伏的电热水壶，电流十安培，电阻二十四欧。
Energy transferred in time t is simply E equals P t.
时间 t 内转移的能量就是能量等于功率乘时间。
And the efficiency version: cables with resistance dissipate I squared R.
还有效率的版本：有电阻的导线会耗散 I 平方 R 的功率。
A kettle drawing ten amps through cables of zero point two ohms loses a hundred times zero point two, that is twenty watts, in the cables, so of two thousand four hundred watts the kettle receives two thousand three hundred and eighty.
一个通过零点二欧姆导线取用十安培电流的电热水壶， 在导线上损失一百乘以零点二，也就是二十瓦， 所以两千四百瓦里，水壶实际得到两千三百八十瓦。
The efficiency of the circuit is the useful power out over the total power in.
电路的效率，就是有用输出功率除以总输入功率。
Every component fights the flow of charge to some degree — that is its resistance.
每个元件都在某种程度上阻挡电荷的流动——这就是它的电阻。
Resistance is the voltage across it, divided by the current through it.
电阻是它两端的电压，除以流过它的电流。
A big resistance means a big push is needed for only a small current.
大电阻意味着需要很大的推力才能得到很小的电流。
For some components, at constant temperature, the current is simply proportional to the voltage — double the voltage, and you double the current.
对某些元件，在温度恒定时，电流与电压恰好成正比——电压加倍，电流也加倍。
That neat rule is Ohm's law.
这条简洁的规律就是欧姆定律。
These are real fixed resistors — small barrels with wire leads and coloured bands that code the resistance in ohms.
这些是真实的定值电阻——带引线的小圆筒，彩色色环编码欧姆值。
The unit of resistance is the ohm: one volt per ampere.
电阻的单位是欧姆：每安培一伏特。
Remember that resistance depends on the conditions when you measure it, especially temperature.
记住电阻取决于测量时的条件，尤其是温度。
The colour code is a lab convenience; the physics definition is always R equals V over I for any component at the moment you measure it.
色环是实验室的便利； 物理定义始终是：在你测量的那一刻，对任何元件，R 等于 V 除以 I。
A careful distinction.
要仔细区分。
The definition R equals V over I works for every component, ohmic or not.
定义 R 等于 V 除以 I 对每一个元件都成立，不论是否欧姆元件。
Ohm's law is an experimental claim: the current through a conductor is proportional to the p.d. across it, provided conditions — especially temperature — stay constant.
欧姆定律是一个实验结论：在条件——尤其是温度——保持不变时，导体中的电流与两端电势差成正比。
Only then is R constant and the I–V characteristics a straight line through the origin.
只有这时 R 才恒定，伏安图才是过原点的直线。
A filament lamp has a resistance you can always compute as V over I, but that resistance is not constant, so the lamp is non-ohmic.
灯丝灯泡的电阻始终可以算成 V 除以 I， 但那个电阻不恒定，所以灯泡是非欧姆的。
Plot current against voltage, and each component tells its own story.
画出电流对电压的图，每个元件都讲出自己的故事。
A metal wire at constant temperature gives a straight line through the origin — it obeys Ohm's law.
金属导线在温度恒定时， 给出一条过原点的直线——它遵守欧姆定律。
A diode lets current through one way only — a sharp curve.
二极管只让电流朝一个方向通过——一条急转的曲线。
And a filament lamp curves over: as more current flows, the filament heats up, its atoms vibrate harder, and its resistance rises.
而灯丝灯泡的线会弯过来：随着电流增大，灯丝变热，它的原子振动得更剧烈，电阻升高。
So the line bends away from straight.
所以这条线就偏离了直线。
Zoom in on the ohmic conductor — a metal wire at constant temperature, or a constantan sample in the lab.
细看欧姆导体——温度恒定的金属导线，或实验室里的康铜样品。
The I–V graph is a straight line through the origin in both directions.
伏安图是过原点的直线，两个方向都是。
Reverse the p.d. and the current reverses, still on the same straight line.
把电势差反向，电流也反向，仍在同一条直线上。
Gradient is one over R, so constant slope means constant resistance.
斜率是一除以 R，所以恒定斜率意味着恒定电阻。
That is the sketch the examiner expects for "ohmic conductor".
这就是考官对「欧姆导体」期望的草图。
The filament lamp goes through the origin, steep at first, then flatter as voltage and current grow.
灯丝灯泡过原点，起初陡峭，随着电压和电流增大而变平。
Reason: more current heats the filament, lattice vibration rises, electrons scatter more, and resistance rises.
原因：更大的电流加热灯丝， 晶格振动加剧，电子散射增多，电阻升高。
The gradient of the I–V curve is one over R, so as R grows the curve flattens.
伏安曲线的斜率是一除以 R，所以 R 增大时曲线变平。
Sketch an S-shaped curve, not a straight line — and be ready to say why it bends.
画成 S 形曲线，不要画直线——并准备好说明它为什么弯曲。
Say why the line bends, because that is the question: as the current rises the filament gets hotter, the lattice ions vibrate more, the free electrons collide with them more often, so the resistance rises and the graph curves towards the voltage axis.
要说清楚这条线为什么会弯，因为题目问的就是这个： 电流增大时灯丝变得更热，晶格离子振动更剧烈， 自由电子和它们碰撞得更频繁，于是电阻变大，图线朝电压轴弯过去。
It is not a failure of Ohm's law being disobeyed by magic — the law holds only at constant temperature, and here the temperature is not constant.
这不是欧姆定律莫名其妙失效了—— 那条定律只在温度恒定时成立，而这里温度并不恒定。
A semiconductor diode almost blocks current for negative voltage or for small positive voltage.
半导体二极管在负电压或很小的正电压下几乎不通电流。
Above a switch-on voltage — about zero point seven volts for silicon — the current rises sharply.
超过开启电压——硅大约零点七伏特—— 电流急剧上升。
Reverse bias stays near zero on the sketch.
反向偏置在草图上接近零。
One-way traffic: that is why diodes rectify alternating current in other topics, and why the exam wants a flat reverse branch and a steep forward rise.
单向通行：这就是二极管在其他专题里整流交流电的原因， 也是考试要你画平的反向支路和陡峭正向上升的原因。
Resistance depends on the wire itself — how long it is, how thick, and what it is made of.
电阻取决于导线本身——它有多长、多粗，以及由什么材料制成。
Longer wire, more resistance.
导线越长，电阻越大。
Thicker wire, less resistance.
导线越粗，电阻越小。
The material's own contribution is called its resistivity.
材料自身的贡献叫做电阻率。
Put it together: resistance equals the resistivity, times the length, divided by the cross-section area.
把它们放在一起： 电阻等于电阻率，乘以长度，再除以横截面积。
Resistivity is a property of the material; resistance also depends on the shape.
电阻率是材料的性质；电阻还取决于形状。
Two pictures fix the geometry.
两张图钉死几何关系。
Double the length of a uniform conductor and you double the resistance — carriers must travel twice as far through the lattice.
均匀导体长度加倍，电阻加倍——载流子要在晶格里多走一倍路。
Double the cross-section area and you half the resistance — there are two paths in parallel, in effect.
横截面积加倍，电阻减半——相当于两条并联路径。
Halve the diameter and the area falls by a factor of four, so resistance becomes four times bigger.
直径减半，面积变成四分之一， 电阻就变成四倍。
The formula R equals rho L over A packages all of that.
公式电阻等于电阻率乘长度除以面积，把这一切都装进去了。
Worked example.
例题。
A copper wire of length two point zero metres and cross-sectional area one point seven times ten to the minus seven square metres has resistivity one point seven times ten to the minus eight ohm metres.
一根铜导线长两点零米，横截面积一点七乘以十的负七次方平方米， 电阻率一点七乘以十的负八次方欧米。
Resistance equals rho L over A: that is one point seven times ten to the minus eight, times two point zero, divided by one point seven times ten to the minus seven, which is zero point two zero ohms.
电阻等于电阻率乘长度除以面积： 一点七乘以十的负八，乘以两点零，再除以一点七乘以十的负七，等于零点二零欧。
Typical copper is around that order; insulators have resistivities of ten to the fifteen ohm metres or more.
典型铜线大约是这个数量级；绝缘体的电阻率是十的十五次方欧米或更高。
Most resistivity questions are ratios, and stretching is the standard one.
大多数电阻率的题目都是比例题，而拉伸是最标准的一道。
Stretching a wire keeps its volume — area times length — constant, so if the length becomes k times longer the area becomes k times smaller, and the resistance, which is rho L over A, goes up by k squared.
把金属丝拉长，它的体积——面积乘长度——保持不变， 所以长度变成 k 倍时，面积变成原来的 k 分之一， 而电阻等于 ρL 除以 A，就变成原来的 k 平方倍。
The resistivity of a metal rises with temperature.
金属的电阻率随温度升高而增大。
Hotter lattice atoms vibrate harder and scatter electrons more, so resistance climbs.
更热的晶格原子振动更剧烈，更多地散射电子，所以电阻上升。
That is exactly why the filament lamp's I–V line curves: as current grows the filament heats, resistivity rises, and the gradient falls.
这正是灯丝灯泡伏安线弯曲的原因：电流增大时灯丝变热，电阻率升高，斜率下降。
Metals get more resistive when hot; keep that contrast for the thermistor later.
金属变热时电阻更大；把这个对比留给后面的热敏电阻。
Two special components change their resistance with the world around them.
有两种特殊元件，会随着周围环境改变自己的电阻。
A light-dependent resistor: in the dark, its resistance is high; shine light on it, and its resistance drops.
光敏电阻：在黑暗中，它的电阻很高； 用光照它，电阻就下降。
A thermistor: as it gets hotter, its resistance falls.
热敏电阻：随着它变热，电阻就下降。
These let electronics sense the world — a street lamp that switches on at dusk, or a thermostat that feels the heat.
这些让电子设备能够感知世界——一盏在黄昏自动点亮的路灯，或一个能感受热度的恒温器。
On this graph, resistance of an LDR falls as light intensity rises — often plotted on logarithmic scales.
在这张图上，光敏电阻的电阻随光强升高而下降——常画在对数坐标上。
In bright light the resistance may be only a few hundred ohms; in the dark it can climb into the megaohms.
强光下电阻可能只有几百欧；黑暗中可升到兆欧。
Light frees more charge carriers in the semiconductor, so resistance drops.
光在半导体里释放更多载流子，所以电阻下降。
That is how street lamps, camera light meters, and automatic night circuits sense the day.
路灯、相机测光表和自动夜间电路，就是这样感知白天的。
For the syllabus thermistor, resistance falls as temperature rises — a negative temperature coefficient.
对本考纲的热敏电阻，电阻随温度升高而下降——负温度系数。
The curve is steep at low temperature and gentler when warm.
曲线在低温处陡峭，变暖后较缓。
Put the thermistor in a potential divider and the output voltage tracks temperature.
把热敏电阻放进分压器，输出电压就跟踪温度。
Uses: thermostats, overheat protection, and any circuit that must feel the heat without a mercury thermometer.
用途：恒温器、过热保护，以及任何无需水银温度计就要感知热度的电路。
A thermistor behaves the opposite of a metal.
热敏电阻的行为与金属相反。
In a metal, heat mainly increases scattering, so resistance rises.
在金属里，热主要增加散射，所以电阻升高。
In a semiconductor thermistor, more thermal energy frees more charge carriers, and that surge in n matters more than the extra scattering — so resistance falls.
在半导体热敏电阻里，更多热能释放更多载流子，数密度的激增比额外散射更重要——所以电阻下降。
Remember both stories: metal filament curves flatten as R rises with heat; thermistor R falls as temperature rises.
记住两个故事：金属灯丝因电阻随热升高而曲线变平；热敏电阻的电阻随温度升高而下降。
Same heat, opposite resistance change.
同样的热，相反的电阻变化。
Three marks to secure.
三个要拿稳的分。
First, current is charge per second — charge equals current times time.
第一，电流是每秒的电荷——电荷等于电流乘以时间。
Second, power has three forms: voltage times current, current squared times resistance, or voltage squared over resistance.
第二，功率有三种形式：电压乘电流、电流平方乘电阻，或电压平方除以电阻。
Third, a filament lamp's resistance rises with current because it heats up.
第三，灯丝灯泡的电阻会随电流升高，因为它变热了。
Master these, and current is yours.
掌握这些，电流就是你的了。
The fixed-wording definitions, one answer only.
固定措辞的定义，只给一个答案。
Electric current: a flow of charge carriers.
电流：电荷载流子的流动。
The coulomb: the charge passing a point in one second when the current is one ampere.
库仑：电流为一安培时，一秒内通过某点的电荷量。
Potential difference: the energy transferred from electrical to other forms per unit charge passing through a component.
电势差：单位电荷通过某元件时，从电能转化为其他形式的能量。
Electromotive force: the energy transferred from other forms to electrical per unit charge, by a source driving charge round a complete circuit.
电动势：电源驱动电荷绕完整电路一周时，单位电荷从其他形式转化为电能的能量。
The volt: one joule per coulomb.
伏特：一焦耳每库仑。
Resistance: the ratio of the potential difference across a component to the current in it.
电阻：元件两端的电势差与其中电流之比。
The ohm: the resistance in which one volt produces one ampere.
欧姆：一伏特电压产生一安培电流时的电阻。
Ohm's law: the current in a metallic conductor is directly proportional to the potential difference across it, provided its temperature remains constant.
欧姆定律：在温度保持不变的前提下，金属导体中的电流与其两端的电势差成正比。
And the traps.
再说陷阱。
Resistance is V over I at a point, so never take it from the gradient of a curved I-V graph — only a straight line through the origin makes it the reciprocal of the gradient.
电阻是某一点上的 V 比 I，所以绝不能从弯曲的 I—V 图线的斜率去取—— 只有过原点的直线，电阻才是斜率的倒数。
Convert time to seconds in Q equals I t.
Q 等于 I t 里时间要换算成秒。
The filament's resistance rises through a chain — current, temperature, ion vibration, more collisions, more resistance — not "because of the voltage".
灯丝电阻升高是通过一条链条——电流、温度、离子振动、碰撞增多、电阻变大—— 不是「因为电压」。
A stretched wire changes in two ways at once, so R goes as L squared.
被拉长的金属丝同时有两处变化，所以 R 随 L 的平方变化。
Halve the diameter before pi r squared, and convert square millimetres.
用 πr² 之前先把直径减半，并换算平方毫米。
And compare powers with the right form: series components share the current, so use I squared R; parallel components share the p.d., so use V squared over R.
另外比较功率要用对形式：串联元件共用电流，用 I²R；并联元件共用电压，用 V²/R。