Practical Circuits
A-Level Physics Topic 10 20:35 English narration · English + 中文 subtitles burned in
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Here is an old battery, and a voltmeter says it is still full: nine volts.
这是一块旧电池，电压表说它电量仍然充足：九伏。
Yet connect it to a bulb, and the bulb barely glows.
可是把它接到灯泡上，灯泡却几乎不亮。
How can a full battery be so weak?
一块满电的电池怎么会这么弱？
The secret is hidden inside.
秘密藏在内部。
Every battery has its own resistance, buried within it.
每块电池内部都埋着它自己的电阻。
With no current flowing, you read the full voltage.
没有电流流过时，你读到的是完整的电压。
But the moment current flows, that inner resistance steals some of it — and in an old battery, it steals almost everything.
但电流一流过，那个内部电阻就偷走其中一部分—— 而在旧电池里，它几乎把全部都偷走。
The battery is not empty; it is choked from the inside.
电池不是空的；它是从内部被扼住了。
Real circuits are more than a battery and a bulb.
真实的电路不只是一块电池和一个灯泡。
Today: electromotive force and internal resistance, Kirchhoff's two great laws, resistors in series and parallel, and the clever potential divider.
今天：电动势与内阻、基尔霍夫的两大定律、 串联与并联的电阻，以及巧妙的分压器。
Let's begin.
让我们开始吧。
In the lab you often build on a breadboard — a board with rows of holes that connect components without soldering.
在实验室里，你常常在面包板上搭建电路——一块带有成排小孔的板，不用焊接就能连接元件。
You measure currents and potential differences with a multimeter.
你用万用表测量电流和电势差。
The red and black probes touch the points you care about, and the reading tells you what is really happening in the circuit.
红黑表笔触到你关心的点，读数告诉你电路里真正在发生什么。
Practical circuits start here: real components, real meters, and the symbols we are about to learn.
实用电路从这里开始：真实的元件、真实的仪表，以及我们即将学习的符号。
First, the language of circuits: their symbols.
首先，电路的语言：电路符号。
A cell, with its long and short lines.
电池，有长短两条线。
A resistor, a rectangle.
电阻，一个矩形。
A bulb, a cross in a circle.
灯泡，圆圈里一个叉。
A switch that opens and closes.
开关，能断开和闭合。
A voltmeter, which measures voltage across a component, and an ammeter, which measures the current through it.
电压表，测量元件两端的电压； 电流表，测量流过它的电流。
Learn to read a circuit diagram, and you can read any circuit.
学会读电路图，你就能读懂任何电路。
The syllabus asks you to recognise and draw every standard symbol: cell and battery, switch, fixed and variable resistor, lamp, diode and light-emitting diode, capacitor, inductor, thermistor, light-dependent resistor, fuse, earth, junction, motor, ammeter, voltmeter and galvanometer.
考纲要求你认识并会画每一个标准符号：电池与电池组、开关、 定值与可变电阻、灯、二极管与发光二极管、电容器、电感器、 热敏电阻、光敏电阻、保险丝、接地、节点、电动机、电流表、电压表和检流计。
A battery is drawn as two or more cells in a row.
电池组画成两个或多个电池连成一排。
A variable resistor has an arrow through it.
可变电阻穿过一个箭头。
The diode has a triangle pointing to a bar — current only one way.
二极管是一个指向横杠的三角形——电流只能单向通过。
Learn the grid; the exam will expect you to sketch any of them cleanly.
把这张图记牢；考试会要求你干净地画出其中任何一个。
Placement matters.
位置很重要。
An ammeter goes in series with the component whose current you want — so the same current flows through the meter.
电流表串联在你要测电流的元件上——这样同一电流流过仪表。
A voltmeter goes in parallel across the component — so it samples the potential difference without breaking the path.
电压表并联在元件两端——这样它读取电势差而不打断通路。
An ideal ammeter has zero resistance and does not steal current.
理想电流表电阻为零，不偷走电流。
An ideal voltmeter has infinite resistance and draws no current.
理想电压表电阻无穷大，不吸取电流。
Real meters are close enough for school work, but the ideal rules keep your reasoning clean.
实际仪表对中学实验已经够用，但理想规则让你的推理保持干净。
A battery does work to push charge all the way around a circuit.
电池做功，把电荷推着绕电路走一整圈。
The energy it gives to each unit of charge is called the electromotive force, or e.m.f.
它给予每单位电荷的能量，叫做电动势。
Despite the name, it is not a force — it is energy per charge, measured in volts.
尽管名字里有"力"，它并不是一个力——它是每电荷的能量，用伏特量度。
The e.m.f. is the total energy the source provides.
电动势是电源提供的总能量。
The potential difference is the energy delivered to one part of the circuit.
电势差是传递给电路某一部分的能量。
E.m.f. is the whole; potential difference is a share.
电动势是整体；电势差是其中的一份。
Both quantities are measured in volts, but they differ in energy direction.
两个量都用伏特量度，但能量方向不同。
The e.m.f. is energy put into the circuit by the source — chemical to electrical in a battery, mechanical to electrical in a generator.
电动势是电源把能量送入电路—— 电池里是化学能变电能，发电机里是机械能变电能。
The potential difference is energy taken out of the electrical form — electrical to thermal in a resistor, to light in a lamp, to kinetic in a motor.
电势差是能量从电能形式被取走——电阻里变热能，灯里变光，电动机里变动能。
So e.m.f. is the source writing energy in; potential difference is a component writing energy out.
所以电动势是电源把能量写进去；电势差是元件把能量写出来。
Same units, opposite energy flow.
单位相同，能量流向相反。
The examiner's wording is fixed, so learn it: e.m.f. is the energy transferred per unit charge by the source in driving charge round a complete circuit; p.d. is the energy transferred per unit charge from electrical to other forms.
考官的措辞是固定的，所以要背下来： 电动势，是电源在驱动电荷绕完整电路一周的过程中，每单位电荷所转移的能量； 电势差，是每单位电荷从电能转化为其他形式的能量。
Complete circuit is the phrase that separates them.
「完整电路」这个词是区分两者的关键。
Now the twist.
现在是转折。
A real source has internal resistance, hidden inside it.
一个真实的电源有内阻，藏在它内部。
As current flows, some energy is wasted there — inside the battery itself.
电流流过时，一部分能量就在那里被浪费掉—— 在电池自己内部。
So the voltage you actually get at the terminals is the e.m.f., minus the voltage lost across the internal resistance.
所以你在两极实际得到的电压，是电动势减去在内阻上损失的电压。
That lost part is the current, times the internal resistance.
损失的那部分等于电流乘以内阻。
The bigger the current, the more you lose.
电流越大，损失越多。
That is why our old battery failed: its internal resistance had grown huge.
这就是我们那块旧电池失灵的原因：它的内阻变得巨大。
Three special cases of the same formula.
同一公式的三种特殊情况。
On open circuit — no current, I equals zero — the terminal potential difference equals the e.m.f.
开路时——没有电流，电流为零——端电势差等于电动势。
You read the full voltage with a voltmeter alone.
只用电压表，你读到完整电压。
With a larger load current, the terminal potential difference falls: more of the e.m.f. is dropped inside as I r.
负载电流越大，端电势差越低：更多的电动势以电流乘内阻的形式 降在内部。
On short circuit, the external resistance goes to zero, so the current is e.m.f. over r — a large current — and all the energy turns to heat inside the source.
短路时，外电阻趋于零，所以电流等于电动势除以内阻——很大的电流—— 全部能量都在电源内部变成热。
That is dangerous, and it is why shorting a battery is forbidden.
这很危险，所以禁止把电池短路。
When the outside circuit changes, argue through the current rather than guessing.
外电路变化时，要顺着电流推，而不是猜。
Lower the external resistance and the current increases, so the lost volts I r increase, so the terminal p.d. decreases — and the other way round when the external resistance rises.
外电阻变小，电流增大，于是内阻上的损失电压 I r 增大，端电压就下降—— 外电阻变大时反过来。
Cells joined together: in series the e.m.f.s add and the internal resistances add, so three cells of e.m.f. epsilon and internal resistance r give three epsilon and three r; a cell put in the wrong way round subtracts its e.m.f. while still adding its internal resistance.
电池组合起来：串联时电动势相加、内阻也相加， 所以三个电动势为 ε、内阻为 r 的电池给出三 ε 和三 r； 而一个接反的电池，它的电动势要减掉，内阻却照样要加上。
Here is the lab circuit for finding e.m.f. and internal resistance.
这是求电动势和内阻的实验电路。
A cell is drawn as e.m.f. E in series with its own internal resistance r, both inside a dashed box.
电池画成电动势 E 与自身内阻 r 串联，两者都在虚线框内。
Outside: a voltmeter across the terminals, an ammeter, and a variable resistor that lets you change the external load.
外面：两极间的电压表、电流表，以及可改变外负载的可变电阻。
Change the load, read V and I, and you gather the data for the graph we meet next.
改变负载，读出电压和电流，就得到我们接下来要看的图的数据。
The dashed box reminds you that r is not a separate component you can unplug — it lives inside the source.
虚线框提醒你：内阻不是一个可以拔掉的单独元件——它住在电源内部。
Plot terminal potential difference against current.
把端电势差对电流作图。
You get a straight line starting at E on the voltage axis and sloping down.
你会得到一条直线，从电压轴上的 E 出发，向下倾斜。
The y-intercept is the e.m.f. — the open-circuit voltage.
纵截距就是电动势——开路电压。
The gradient is minus r — so the steeper the fall, the larger the internal resistance.
斜率是负的内阻——下降越陡，内阻越大。
From V equals epsilon minus I r, a graph of V against I is a straight line of gradient minus r.
由电压等于电动势减去电流乘内阻，电压对电流的图就是斜率为负内阻的直线。
That is how you measure r without opening the battery: change the load, plot, read the slope.
这就是你不用拆开电池也能测内阻的方法：改变负载，作图，读斜率。
Worked example.
例题。
A cell of e.m.f. one point five volts and internal resistance zero point five zero ohms is connected to a two point five ohm resistor.
一块电动势一点五伏特、内阻零点五零欧姆的电池，接到一个二点五欧姆的电阻上。
The e.m.f. drives the current through both resistances, so I equals epsilon over R plus r.
电动势推动电流穿过两个电阻，所以电流等于电动势除以外电阻加内阻。
That is one point five over two point five plus zero point five zero, which is zero point five zero amps.
那就是一点五除以二点五加零点五零，等于零点五零安培。
Then the terminal potential difference is epsilon minus I r: one point five minus zero point five zero times zero point five zero, which is one point two five volts.
然后端电势差是电动势减去电流乘内阻：一点五减去零点五零乘零点五零，等于一点二五伏特。
Always add r to R before you find the current.
求电流之前，一定要把内阻加到外电阻上。
Power splits the same way.
功率也这样分开。
The power given to the outside load is the terminal voltage times the current — that is epsilon minus I r, all times I.
送给外负载的功率是端电压乘以电流——也就是电动势减去电流乘内阻，再乘电流。
The power lost inside is I squared r — heat wasted in the electrolyte or windings.
内部损耗的功率是电流的平方乘内阻——电解液或绕组里浪费的热。
The total power from the source is epsilon times I.
电源给出的总功率是电动势乘电流。
Check: the two parts add to the total.
核对：两部分加起来等于总数。
When r is large, most of the power is lost inside — exactly what happens in a dying battery that feels warm but barely lights a bulb.
当内阻很大时，大部分功率损耗在内部——这正是一块快没电的电池摸起来温热却几乎点不亮灯泡的情况。
That split gives the efficiency of the source directly: useful power out over total power in is V I over epsilon I, which is just V over epsilon, and that equals R over R plus r.
这个功率分配直接给出电源的效率： 有用输出功率除以总输入功率，是 V I 除以 ε I，也就是 V 除以 ε， 而它等于 R 除以 R 加 r。
So a large load resistance wastes little energy inside the source, and a load equal to the internal resistance — the condition for maximum power transfer — is only fifty per cent efficient.
所以负载电阻很大时，电源内部浪费的能量很少； 而负载等于内阻时——也就是最大功率传输的条件——效率只有百分之五十。
To solve any circuit, we lean on two laws.
要解任何电路，我们都依靠两条定律。
The first: at any junction, the total current flowing in equals the total current flowing out.
第一条：在任何一个节点，流入的总电流等于流出的总电流。
Charge cannot pile up or vanish — so whatever arrives must leave.
电荷不能堆积也不能消失——所以到来的必须离开。
This is Kirchhoff's first law, and it is simply the conservation of charge, written for a wire.
这就是基尔霍夫第一定律， 它其实就是为导线写下的电荷守恒。
Here is the first law with numbers.
这是带数字的第一定律。
A three amp current from the battery arrives at a junction and splits into a two amp branch and a one amp branch.
从电池来的三安电流到达一个节点，分成二安的支路和一安的支路。
Three amps in equals two amps plus one amp out.
三安流入等于二安加一安流出。
Further on, the branches recombine: two plus one becomes three again before returning to the battery.
再往前，支路重新汇合：二加一又变成三，然后回到电池。
For any junction, write I one equals I two plus I three when currents two and three leave and current one arrives.
对任何节点，当电流二和三离开、电流一到达时，写成电流一等于电流二加电流三。
Charge per second in equals charge per second out.
每秒流入的电荷等于每秒流出的电荷。
The second law follows the energy.
第二条定律追随能量。
Go around any closed loop, and add up every rise and drop in voltage: they must sum to zero.
绕任何一个完整的回路走一圈，把电压的每一次升高和降低加起来： 它们必须总和为零。
The energy the source gives is exactly the energy used by the components around the loop.
电源给出的能量，正好等于回路上各元件用掉的能量。
So the sum of the e.m.f.s equals the sum of the potential differences.
所以电动势之和等于电势差之和。
This is Kirchhoff's second law — the conservation of energy, around a loop.
这就是基尔霍夫第二定律——回路上的能量守恒。
When you apply the second law, pick a direction round the loop first.
应用第二定律时，先选定绕回路的方向。
Take an e.m.f. as positive when your loop direction goes from the negative terminal to the positive terminal of the source — climbing the potential hill the source builds.
当你的回路方向从电源负极走向正极时， 把电动势取为正——爬上电源建立的电势山。
Take a potential difference as positive when your loop direction is the conventional current direction through the resistor — going downhill, losing potential.
当你的回路方向就是电阻中的常规电流方向时，把电势差取为正——下山，失去电势。
With a consistent choice, the signed sum is zero, and you get one clean equation per independent loop.
选择一致时，带符号的总和为零，每个独立回路就得到一个干净的方程。
These laws give us two shortcuts.
这两条定律给了我们两个捷径。
Resistors in series, one after another, carry the same current, and their resistances simply add.
串联的电阻，一个接一个，通过相同的电流， 它们的电阻直接相加。
Resistors in parallel, side by side, share the same voltage — and here the inverses add, so the combined resistance is always less than the smallest one.
并联的电阻，并排放置，共享相同的电压—— 这时相加的是倒数，所以合电阻总是比最小的那个还小。
Series to add resistance, parallel to lower it.
串联增大电阻，并联减小电阻。
Look carefully at series.
仔细看串联。
Two resistors R one and R two carry the same current I.
两个电阻 R 一和 R 二通过相同的电流 I。
The total potential difference is V one plus V two, and each is I times its resistance, so the e.m.f. equals I times R one plus R two.
总电势差是 V 一加 V 二，每一个都是电流乘各自的电阻，所以电动势等于电流乘 R 一加 R 二。
That is why the equivalent resistance is just the sum.
这就是为什么等效电阻就是它们的和。
A series combination is always larger than any single resistor in it.
串联组合总是比其中任何一个电阻都大。
Chain resistors when you need more resistance or when you want to split a voltage between them.
当你需要更大电阻，或想在电阻之间分压时，就把电阻串起来。
Now parallel.
现在看并联。
The same potential difference V sits across both branches.
相同的电势差 V 跨在两条支路上。
The total current splits: I equals V over R one plus V over R two.
总电流分开： 电流等于 V 除以 R 一，加上 V 除以 R 二。
Factor out V, and you get one over R parallel equals one over R one plus one over R two.
提出 V，就得到并联电阻的倒数 等于各电阻倒数之和。
Two equal resistors R in parallel give R over two; N equal ones give R over N.
两个相等的电阻 R 并联得到 R 的一半；N 个相等的得到 R 除以 N。
A parallel combination is always smaller than any of its resistors — more paths mean easier flow for the current.
并联组合总是比其中任何一个电阻都小——路径越多，电流越容易流过。
Worked example.
例题。
A four point zero ohm resistor and a twelve ohm resistor are connected in parallel.
一个四点零欧姆的电阻和一个十二欧姆的电阻并联。
Find their combined resistance.
求它们的合电阻。
One over R equals one over four point zero plus one over twelve.
一除以 R 等于一除以四点零，加上一除以十二。
That is three twelfths plus one twelfth, which is four twelfths, or one third.
那是十二分之三加十二分之一，等于十二分之四， 也就是三分之一。
So R equals three point zero ohms.
所以 R 等于三点零欧姆。
Check: three is smaller than both four and twelve — as parallel always demands.
核对：三比四和十二都小——并联总是如此。
Invert each resistance, add, invert again.
把每个电阻取倒数，相加，再取倒数。
For a full network, follow five steps.
对完整网络，按五步走。
First, label every current with a symbol and a chosen direction — if a result comes out negative, the true direction is opposite.
第一，给每条电流标一个符号和选定的方向—— 若结果为负，真实方向相反。
Second, use Kirchhoff's first law at each junction to link the currents.
第二，在每个节点用基尔霍夫第一定律联系各电流。
Third, use Kirchhoff's second law around each independent loop to get equations in the potential differences.
第三，绕每个独立回路用基尔霍夫第二定律得到电势差方程。
Fourth, use V equals I R for each resistor.
第四，对每个电阻用电压等于电流乘电阻。
Fifth, solve the equations together.
第五，联立求解。
For symmetric networks, spot branches with equal currents — the branch with the most current dissipates the most power, since P equals I squared R.
对对称网络，找出电流相等的支路——电流最大的支路耗散功率最多，因为功率等于电流平方乘电阻。
Here is one of the most useful circuits: the potential divider.
这是最有用的电路之一：分压器。
Two resistors in series share the battery's voltage between them, in proportion to their resistances.
两个串联的电阻，把电池的电压按它们的电阻成比例地分配。
The output across one resistor is the input voltage, times that resistor, over the total.
一个电阻两端的输出，等于输入电压乘以那个电阻，再除以总电阻。
Change the ratio of the resistors, and you dial the output voltage up or down.
改变两个电阻的比例，你就能把输出电压调高或调低。
The diagram shows a source driving current I through R one and R two in series.
图中电源驱动电流 I 依次流过串联的 R 一和 R 二。
The total potential difference V splits into V one across R one and V two across R two.
总电势差 V 分成 R 一上的 V 一和 R 二上的 V 二。
The output is tapped across R two.
输出从 R 二两端引出。
Because the same current flows through both, V two over V one equals R two over R one — direct proportion.
因为同一电流流过两者，V 二比 V 一等于 R 二比 R 一——正比例。
A rheostat — a slider on a uniform-resistance wire — turns this into a smoothly variable divider: move the contact and the ratio changes continuously between zero and the full supply.
变阻器——均匀电阻丝上的滑片——把它变成平滑可调的分压器： 移动触点，比例就在零到全部电源电压之间连续变化。
Worked example.
例题。
A six point zero volt supply is connected across a two point zero kilohm resistor in series with a four point zero kilohm resistor.
一个六点零伏特的电源接在串联的二点零千欧电阻和四点零千欧电阻两端。
Find the output voltage tapped across the four point zero kilohm resistor.
求从四点零千欧电阻两端引出的输出电压。
V two equals V in times R two over R one plus R two.
V 二等于输入电压乘以 R 二除以 R 一加 R 二。
That is six point zero times four point zero over two point zero plus four point zero, which is six times four over six, which is four point zero volts.
那是六点零乘以四点零除以二点零加四点零，也就是六乘四除以六，等于四点零伏特。
The larger resistor takes the larger share of the voltage — here two thirds of six is four.
较大的电阻分到较大的电压份额——这里六的三分之二是四。
Now swap one resistor for a sensor, and the divider comes alive.
现在把其中一个电阻换成一个传感器，分压器就活了起来。
Use a light-dependent resistor: as darkness falls, its resistance climbs, and the output voltage swings — enough to switch a street lamp on at dusk.
用一个光敏电阻： 随着天色变暗，它的电阻升高，输出电压随之摆动——足以让路灯在黄昏点亮。
Use a thermistor, and the output tracks temperature — the heart of a thermostat.
用一个热敏电阻，输出就跟随温度变化——这是恒温器的核心。
A potential divider turns a change in the world into a change in voltage.
分压器把世界的变化，变成电压的变化。
A common arrangement: fixed resistor R in series with a thermistor S across a cell of e.m.f. E, with the output voltage taken across the thermistor.
常见接法：定值电阻 R 与热敏电阻 S 串联，跨接在电动势为 E 的电池两端，输出电压取自热敏电阻两端。
For a negative-temperature-coefficient thermistor, resistance falls as temperature rises.
对负温度系数热敏电阻，电阻随温度升高而下降。
So when it warms, the share of voltage across S falls, and the output drops.
所以升温时，S 上的电压份额下降，输出也下降。
Swap which resistor you tap across, and the output swings the other way.
改从另一个电阻两端引出，输出就朝反方向摆动。
Light-dependent resistors work the same way: resistance falls as light intensity rises, so brightness becomes a voltage.
光敏电阻同理： 电阻随光强升高而下降，于是亮度就变成了电压。
The voltage alone is not enough to light a lamp or run a heater.
电压本身还不足以点亮灯或驱动加热器。
Connect the output to a transistor base or a comparator, and the circuit becomes a switch.
把输出接到晶体管基极或比较器，电路就变成开关。
When the temperature or light level passes a threshold, the output crosses a set voltage and the transistor or comparator switches a load on or off.
当温度或光强越过阈值时，输出越过设定电压，晶体管或比较器就接通或切断负载。
That is how a dusk-to-dawn lamp and a simple thermostat both work: a sensor divider senses the world; a switching stage acts on the result.
黄昏到黎明的路灯和简单恒温器都这样工作：传感分压器感知世界；开关级按结果动作。
A potentiometer is a uniform resistance wire of length L zero with a sliding contact — the jockey.
电位差计是一段长度为 L 零的均匀电阻丝，带有滑动触头——游标。
A driver cell sends a steady current along the wire.
驱动电池沿电阻丝送出稳定电流。
Because resistance per unit length is uniform, the potential difference from one end to the jockey is proportional to the length x: V x equals V full times x over L zero.
因为单位长度电阻均匀，从一端到游标的电势差与长度 x 成正比： V x 等于全程电压乘以 x 除以 L 零。
Slide the jockey and you pick any voltage between zero and the full drop along the wire.
滑动游标，你就能在零到电阻丝全程压降之间选取任意电压。
That is a continuous potential divider made of wire.
这是用电阻丝做成的连续分压器。
The power of the potentiometer is the null method.
电位差计的威力在于零点法。
To compare two e.m.f.s — an unknown cell against a standard cell — connect each in turn through a galvanometer to the jockey.
要比较两个电动势——未知电池对标准电池—— 依次通过检流计把每个接到游标上。
Slide until the galvanometer reads zero: a null.
滑动直到检流计读数为零：零点。
At balance, no current flows through the cell being measured, because the potentiometer voltage exactly opposes its e.m.f.
平衡时，被测电池中没有电流流过，因为电位差计的电压正好抵消它的电动势。
The two balance lengths are in the ratio of the e.m.f.s: epsilon one over epsilon two equals l one over l two.
两个平衡长度之比等于电动势之比：电动势一比电动势二等于长度一比长度二。
The advantage: at balance the unknown cell gives no current, so its internal resistance does not affect the result.
优点是：平衡时未知电池不给出电流，所以它的内阻不影响结果。
You find a zero instead of measuring a current's value — that is a null method.
你找的是零点，而不是去测某个电流的数值——这就是零点法。
Why the null method is better than a voltmeter: at balance no current is drawn from the cell being measured, so there is no I r drop inside it, and the balance point therefore measures the e.m.f. and not the terminal p.d.
补偿法为什么比电压表好： 平衡时不从被测电池取用电流，所以它内部没有 I r 的压降， 因此平衡点测到的是电动势，而不是端电压。
Reading the balance point: anything that makes the p.d. being balanced larger moves the balance point further along the wire, and anything that makes the p.d. per unit length larger — a driver cell of greater e.m.f., or a wire of greater diameter taking a larger share — makes the balance length shorter.
读平衡点：任何让被平衡的电压变大的因素，都会把平衡点推得离起点更远； 而任何让单位长度上的电压变大的因素—— 电动势更大的驱动电池，或者直径更大、分到更大一份电压的电阻丝—— 都会让平衡长度变短。
Three marks to secure.
三个要拿稳的分。
First, terminal voltage is e.m.f. minus the drop across internal resistance.
第一，端电压等于电动势减去内阻上的电压降。
Second, Kirchhoff's laws are conservation of charge at junctions, and conservation of energy around loops.
第二，基尔霍夫定律是节点处的电荷守恒，以及回路上的能量守恒。
Third, in a potential divider, the voltage splits in proportion to the resistances.
第三，在分压器中，电压按电阻的比例分配。
Master these, and circuits are yours.
掌握这些，电路就是你的了。
The fixed-wording definitions, one answer only.
固定措辞的定义，只给一个答案。
E.m.f.: the energy transferred per unit charge by a source in driving charge round a complete circuit.
电动势：电源驱动电荷绕完整电路一周时，单位电荷所转移的能量。
P.d.: the energy transferred per unit charge from electrical energy to other forms.
电势差：单位电荷从电能转化为其他形式能量的量。
Internal resistance: the resistance to current inside a source, causing a p.d. of I r across it when a current flows.
内阻：电源内部对电流的阻碍，有电流时在电源上产生 I r 的电压降。
Terminal p.d.: e.m.f. minus I r.
端电压：电动势减去 I r。
Kirchhoff's first law: the sum of the currents into a junction equals the sum out of it — conservation of CHARGE.
基尔霍夫第一定律：流入节点的电流之和等于流出之和——电荷守恒。
Kirchhoff's second law: the sum of the e.m.f.s round a closed loop equals the sum of the p.d.s round it — conservation of ENERGY.
基尔霍夫第二定律：闭合回路中电动势之和等于电势差之和——能量守恒。
A potential divider: two or more resistors in series across a supply, giving across one of them a fraction of the supply p.d.
分压器：跨接在电源上的两个或更多串联电阻， 在其中一个上得到电源电压的一部分。
The traps.
陷阱。
Use epsilon equals I times R plus r; forgetting the internal resistance is the commonest error here.
要用 ε 等于 I 乘以 R 加 r；漏掉内阻是这里最常见的错误。
E.m.f. is energy per unit charge, not "the force that pushes the charge".
电动势是单位电荷的能量，不是「推动电荷的力」。
Pair each law with the right conservation law.
每条定律要配对正确的守恒定律。
Product over sum works for TWO parallel resistors only.
「积除以和」只适用于两个并联电阻。
Explain a sensor circuit as a chain — resistance, total resistance, current, I R across the fixed resistor, the rest across the sensor.
解释传感器电路要说成一条链—— 电阻、总电阻、电流、固定电阻上的 I R、剩下的落在传感器上。
A potentiometer at balance draws no current from the CELL BEING MEASURED; the driver cell always supplies the wire current.
电位差计在平衡时不从被测电池取电流；驱动电池始终在给电阻丝供电流。
And do not round a "show that" value before the last line.
另外「证明其为」类的题目，最后一行之前不要四舍五入。