Electric Circuits
AP Physics 2 Topic 11 7:45 English narration · English + 中文 subtitles burned in
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Transcript
You flip a switch, and the light comes on at once.
你按下开关，灯立刻亮了。
So the electrons must be racing down the wire.
那么电子一定在导线里飞奔吧。
They are not.
并不是。
Inside copper, electrons crawl — less than a millimetre every second.
在铜里，电子只是缓慢爬行——每秒不到一毫米。
They would need hours to reach the lamp.
它们要走好几个小时才能到达灯泡。
Yet the lamp lights instantly.
可是灯却在一瞬间就亮了。
This is Unit Eleven: electric circuits.
这是第十一单元：电路。
We will build the whole toolkit — current, resistance, power, the two ways of wiring, Kirchhoff's rules, and circuits that take time.
我们要把整套工具建立起来——电流、电阻、功率、 两种连接方式、基尔霍夫定律，以及需要时间的电路。
Let's begin.
让我们开始吧。
Here is the answer.
答案在这里。
Current is the rate at which charge passes a point: the charge that goes by, divided by the time.
电流是电荷通过某一点的快慢：通过的电荷量除以所用的时间。
The wire is already full of free electrons.
导线里本来就到处都是自由电子。
When you close the switch, the battery sets up an electric field along the whole wire almost at once.
当你合上开关，电池几乎瞬间就在整根导线上建立起电场， 于是所有电子一起开始漂移。
So every electron starts to drift together — slow drift, instant start.
漂移很慢，启动却是瞬间的。
And conventional current points the way positive charge would move, opposite to the electrons.
还要注意方向：约定的电流方向是正电荷会移动的方向，与电子相反。
A circuit is a closed loop that charge can travel around.
电路是一个电荷可以绕行一周的闭合回路。
Three words.
记住三个词。
A closed circuit has a complete path, so there is a current.
通路有完整的路径，所以有电流。
An open circuit is broken, so nothing flows.
断路被切断，所以没有电流。
A short circuit offers a path with almost no resistance, so a large current takes the shortcut.
短路提供一条几乎没有电阻的路径，于是很大的电流从这条捷径通过。
And a circuit diagram draws them with the same standard symbols every time — reading it correctly is the first step of any circuit problem.
我们用电路图来画电路，每次都使用同样的符号。
Now the most useful rule in the unit.
现在是本单元最有用的规律。
Ohm's law: the current through a component equals the potential difference across it, divided by its resistance.
欧姆定律：通过一个元件的电流， 等于它两端的电势差除以它的电阻。
Raise the voltage across a metal wire at a steady temperature, and the current climbs in proportion — a straight line through the origin.
在温度不变的金属导线两端把电压升高， 电流就成正比地上升——一条过原点的直线。
That is an ohmic component, and the gradient of that line gives one over the resistance.
有这种性质的元件叫做欧姆元件， 而这条直线的斜率就是电阻的倒数。
What decides the resistance?
是什么决定电阻？
The shape of the object, and the material.
物体的形状，以及它的材料。
Resistance grows with length and falls with cross-sectional area.
电阻随长度增大，随横截面积减小。
Twice as long is twice the resistance; twice the area is half.
长度加倍，电阻加倍；横截面积加倍，电阻减半。
Think of water in a pipe.
想想水管：又长又细就难走。
The material enters through its resistivity.
材料通过电阻率起作用。
One catch: resistivity rises with temperature, so a hot lamp filament has more resistance, and its graph bends.
还有一点要注意：电阻率随温度升高而增大， 所以灯丝变热后电阻更大，它的图线就会弯曲。
Every resistor turns electrical energy into heat, and power says how fast.
每个电阻都把电能变成热，而功率说明这个过程有多快。
Power is the current times the potential difference across the element.
功率等于电流乘以元件两端的电势差。
Ohm's law lets you write it two other ways: current squared times resistance, or voltage squared divided by resistance.
利用欧姆定律，它还可以写成另外两种形式： 电流的平方乘以电阻，或者电压的平方除以电阻。
Choose the form that uses the numbers you have.
选用你已经知道的量的那一个。
Two amperes through a six ohm resistor: twelve volts across it, so twenty-four watts.
两安培的电流通过六欧姆的电阻：它两端是十二伏，所以功率是二十四瓦。
A favourite exam question: which bulb is brightest?
考试最爱问：哪个灯泡最亮？
A bulb is a resistor that glows, and brightness follows power — so rank bulbs by power, never by resistance.
灯泡就是会发光的电阻，亮度取决于功率—— 所以要按功率排序，绝不能只看电阻。
In a series string every bulb carries the same current, so use current squared times resistance: the largest resistance is brightest.
串联时每个灯泡通过的电流相同， 所以用电流的平方乘以电阻：电阻最大的最亮。
In parallel every bulb gets the full voltage, so the smallest resistance is brightest.
并联时每个灯泡都得到完整的电压，所以电阻最小的最亮。
It all depends on how the parts are wired.
一切都取决于元件是怎么连接的。
In series there is one path, so the same current flows through every element in turn.
串联只有一条路径，所以同一个电流依次通过每个元件。
In parallel the path splits, so the current divides between the branches — but every branch has the same potential difference.
并联时路径分开，电流在各支路之间分配——但每条支路两端的电势差相同。
Same current in series; same voltage in parallel.
串联同电流，并联同电压。
Any group of resistors can be replaced by one equivalent resistor.
任何一组电阻都可以用一个等效电阻来代替。
In series the resistances simply add.
串联时电阻直接相加。
In parallel the reciprocals add, and the answer is always smaller than the smallest resistor.
并联时倒数相加，结果总是比其中最小的电阻还要小。
Think about why: another parallel branch is another path for charge, so more current flows for the same voltage — which means less resistance.
想一想为什么： 多一条并联支路，就多一条让电荷通过的路径，同样的电压下电流更大—— 这就意味着电阻更小。
Reduce a network step by step until one resistor is left.
分析电路时，一步一步化简，直到只剩下一个电阻。
Let's do one properly.
我们认真做一道。
A twelve volt battery drives a four ohm resistor and a twelve ohm resistor in parallel.
一个十二伏的电池驱动一个四欧姆电阻和一个十二欧姆电阻并联。
Find the total current, and each branch current.
求总电流，以及每个电阻中的电流。
Pause here and try it yourself.
先暂停，自己试一试。
First combine them: one quarter plus one twelfth is one third, so the equivalent resistance is three ohms — smaller than either.
首先把它们合并：四分之一加十二分之一等于三分之一，所以等效电阻是三欧姆—— 比其中任何一个都小。
Then the total current: twelve volts divided by three ohms is four amperes.
然后求总电流：十二伏除以三欧姆等于四安培。
Finally split it.
最后分流。
Both resistors have the full twelve volts, so the four ohm carries three amperes and the twelve ohm carries one.
两个电阻两端都是完整的十二伏，所以四欧姆的通过三安培， 十二欧姆的通过一安培。
So far every battery, wire and meter has been ideal.
到目前为止，我们的电池、导线和电表都是理想的。
Real ones are not.
真实的并不是。
A real battery has a small internal resistance.
真实电池内部有一点内阻。
Once current flows, the terminal voltage drops below the electromotive force.
一旦有电流，端电压就会低于电动势。
That is why an old battery can read twelve volts and still fail to start a car.
这就是为什么一节旧电池仍能显示十二伏，却发动不了汽车。
Meters matter too.
电表也一样重要。
An ammeter measures current, so wire it in series; a voltmeter measures potential difference, so wire it in parallel.
电流表测量电流，所以要串联接入；电压表测量电势差，所以要并联接入。
Ideal meters have zero and infinite resistance; a real, nonideal one always disturbs what it measures.
理想电表的电阻分别是零和无穷大——而真实的电表总会干扰它所测量的量。
Two rules solve every circuit, and both are conservation laws in disguise.
两条定律可以解出任何电路，而且它们其实都是守恒定律。
The junction rule: the current into any junction equals the current out, because charge cannot pile up.
节点定律：流入任一节点的电流等于流出的电流，因为电荷不会在某一点堆积。
The loop rule: go around a closed loop and the potential differences add to zero.
回路定律：沿任意闭合回路走一圈，各元件上的电势差之和为零。
You gain voltage at the battery and lose it across each resistor, arriving back where you started.
经过电池时电势升高，经过每个电阻时电势下降，最后回到出发点。
Picture a graph of electric potential against position: up at the battery, down at each resistor.
可以想象一张电势随位置变化的图：在电池处上升，在每个电阻处下降。
Now bring in capacitors.
现在把电容也加进来。
They combine too, but the rules are swapped.
它们同样可以合并，但规则正好相反。
Capacitors in parallel simply add — you are effectively making the plates bigger.
并联的电容直接相加——相当于把极板做得更大。
Capacitors in series add as reciprocals, so the total is smaller than the smallest.
串联的电容按倒数相加， 所以总电容比其中最小的还要小。
And in series each capacitor holds the same charge, because the charge pushed onto one plate is pulled off its neighbour.
而且串联时每个电容带的电荷量相同， 因为推到一块极板上的电荷，正是从相邻极板上被拉走的。
Put a resistor and a capacitor together and you get a circuit that takes time.
把一个电阻和一个电容放在一起，你就得到一个需要时间的电路。
Watch it charge.
看它充电。
At first the capacitor fills quickly.
一开始电容充得很快。
Then the voltage across it grows and pushes back, so the current falls and the filling slows, levelling off at the supply voltage.
随后它两端的电压升高并产生反向作用， 于是电流减小，充电变慢，最后逐渐趋于电源电压。
Nothing here is sudden.
这里没有任何突变。
So how long does it take?
那么它要多久？
While it charges, the capacitor's voltage rises and the current falls, both exponentially.
充电时，电容器上的电压上升、电流下降，两者都按指数变化。
The time constant is the resistance times the capacitance.
时间常数等于电阻乘以电容。
In one time constant a charging capacitor reaches about sixty-three percent of its final voltage, and a discharging one falls to about thirty-seven percent.
经过一个时间常数，充电的电容达到最终电压的大约百分之六十三， 放电的电容降到大约百分之三十七。
Ten thousand ohms with one hundred microfarads gives one second.
一万欧姆配一百微法，时间常数是一秒。
Now learn the two limits.
再来记住两个极限。
At the first instant an uncharged capacitor behaves like a wire, so the current is greatest.
最初的一瞬间，未充电的电容表现得像一根导线，电流最大。
After a long time it behaves like a break.
经过很长时间之后，它就相当于断路。
Three habits that save marks.
三个能保住分数的习惯。
First, never mix the two rules of connection: same current in series, same voltage in parallel — write it down before you start the algebra.
第一，绝不要弄混两种连接方式：串联同电流，并联同电压—— 在动笔计算之前先把这句写下来。
Second, when a question asks which bulb is brightest, compare power, not resistance.
第二，当题目问哪个灯泡最亮时， 比较功率而不是电阻。
Third, in a capacitor circuit test the two limits first: at the start a wire, at the end a break.
第三，遇到含电容的电路，先检查两个极限： 开始时像导线，最后像断路。
Get those three, and this unit is yours.
做到这三点，这个单元就是你的了。