Edexcel物理 GCSE 电路 电流 电阻 电功率
Edexcel 的 GCSE Physics（1PH0）把电学整块放在 Topic 10 Electricity and circuits，考在 Paper 2 上。两卷各 1 小时 45 分钟、各 100 分、各占总成绩一半，Paper 1 走 Topic 1 到 7，Paper 2 走 Topic 8 到 15 并把 Topic 1 的关键概念带回来复用，电学的出现频率因此很高。Edexcel 的物理卷首会附一份公式表，电位差、电流、电阻与功率的关系都印在上面，但单位换算、公式变形与读数判断不会替你完成。下面按官方 spec 的条目顺序走一遍电流与电荷、电位差与电阻、串并联规律、I-V 核心实验、热敏与光敏元件、电功率与电能、市电安全与输电。每一节都给公式、单位、一组带数字的算例，以及阅卷时最容易扣分的位置。
Electricity and circuits sits in Topic 10 of the Edexcel GCSE Physics specification, first taught from September 2016 with the first exams in 2018, and it is examined in Paper 2. Both papers run for 1 hour 45 minutes and carry 100 marks, so the electrical content carries half the qualification, with Foundation tier covering grades 1 to 5 and Higher tier covering 4 to 9; the equations sheet printed with the paper gives the relationships, yet converting units and rearranging formulas remains the student's job. The sections below follow the specification order, pairing each idea with its formula, its units and a worked number, and they close on the wording examiners reward in explanations.
Topic 10 在 Paper 2 的位置与分值结构
Edexcel GCSE Physics 的卷面结构是固定的，Paper 1 用 1PH0/1F 与 1PH0/1H 两个代号，考 Topic 1 到 7，Paper 2 用 1PH0/2F 与 1PH0/2H，考 Topic 8 到 15 外加 Topic 1 的关键概念。两卷各 100 分、各占最终成绩的 50%，题型混有选择题、短答、计算与 6 分长答。Foundation 的目标区间是 1 到 5 级，Higher 是 4 到 9 级，同一知识点在两个层级的问法深度不同。电学内容集中在 Topic 10，静态电是 Topic 11，磁场与电动机效应是 Topic 12，三块都在 Paper 2 里出现。Ofqual 对科学类 GCSE 的评分目标口径大致是知识与理解约 40%、应用约 40%、分析与评价约 20%，电学计算往往同时占住前两块。很多学生以为背下公式就等于拿分，实际上 6 分题考的是把因果链写成完整句子。
The structure of Edexcel GCSE Physics is fixed: Paper 1 assesses Topics 1 to 7 while Paper 2 assesses Topics 8 to 15 and returns to the key concepts of Topic 1; each paper carries 100 marks and 50% of the final grade. Foundation tier targets grades 1 to 5 and Higher tier grades 4 to 9, so the same content is questioned at different depths; electricity and circuits is Topic 10, static electricity Topic 11 and magnetism with the motor effect Topic 12, all three in Paper 2. Ofqual splits the science assessment objectives at roughly 40% knowledge, 40% application and 20% analysis, and calculations that also demand an explanation are where those objectives overlap.
电流与电荷 Q = It
电流是电荷的流动速率，1 安培等于每秒通过 1 库仑电荷，写成 Q = I t，其中 Q 的单位是库仑、I 是安培、t 是秒。金属导体里真正移动的是自由电子，漂移方向从负极指向正极，而约定的电流方向从正极到负极，这条错位每年都让学生画错方向。电流表必须串联在被测支路里，理想电流表内阻接近零，串进去不会改变电流大小。算例：电流 0.5 A 持续 120 秒，通过的电量是 0.5 x 120 = 60 C。若换成 250 mA 持续 40 秒，要先把 250 mA 换成 0.25 A，再算 0.25 x 40 = 10 C。学生最常把毫安直接当安培代入，结果整整大了 1000 倍，而这一步的错误在 3 分计算题里就是全错。
Current is the rate of flow of charge, one ampere being one coulomb passing a point each second, so Q = It links coulombs, amperes and seconds. Inside a metal the carriers are free electrons drifting from the negative terminal to the positive one, while conventional current is drawn the other way round; an ammeter therefore goes in series, and its near-zero resistance leaves the current unchanged. Converting milliamperes before substituting is the step students skip most often, and a factor of 1000 is enough to lose every mark on a three-mark calculation.
电位差、电阻与 V = IR
电位差是每库仑电荷在两点之间转移的能量，一伏特等于一焦耳每库仑，电压表必须并联在元件两端。电阻是元件对电流的阻碍，单位欧姆，题目里的连接导线通常忽略不计，但偏长的导线与偏细的导线会被特意拿来设问。欧姆定律写成 V = I R，变形得到 R = V / I 与 I = V / R，三种写法要能随手切换。算例：12 V 电源接在 4 欧姆的固定电阻上，电流是 12 / 4 = 3 A。算例：某灯泡两端电压 0.40 V 时电流 0.10 A，用 R = V / I 得到 4 欧姆。常见的错误是把 I = R / V 写反，或者忘记电阻只在恒温的固定电阻上才与电压成正比，灯丝与二极管都不满足这一条件。
Potential difference measures the energy transferred per unit charge between two points, one volt being one joule per coulomb, and a voltmeter is connected in parallel across the component. Resistance describes how strongly a component opposes current and is measured in ohms; V = IR rearranges into R = V/I and I = V/R, and moving between the three forms should take no thought. Calling a filament lamp proportional is the mistake that follows from ignoring temperature, because only a fixed resistor at constant temperature keeps its resistance steady.
串联与并联的电流电压规律
串联电路只有一条路径，各处电流相同，总电压等于各元件电压之和，总电阻等于各电阻相加。6 欧姆与 3 欧姆串联得到 9 欧姆，接在 12 V 电源上电流是 12 / 9 = 1.33 A，两个电阻上的电压分别是 8 V 与 4 V，加起来正好是电源电压。并联电路里各支路两端电压相同且等于电源电压，支路电流相加得到干路电流，等效电阻比任一支路都小。6 欧姆与 3 欧姆并联，用 1 / R = 1 / 6 + 1 / 3 得到 2 欧姆，干路电流变成 12 / 2 = 6 A。家庭插座采用并联，是因为每条支路能独立开关。错得最多的是把并联电阻直接相加，得到比任一支路都大的答案。
A series circuit offers one path, so the current is the same everywhere, the voltages add to the supply voltage and the resistances simply add; six ohms and three ohms in series give nine ohms, which draws 1.33 A from a 12 V supply and splits into 8 V and 4 V. In parallel the voltage across each branch matches the supply and the branch currents add, leaving a combined resistance smaller than either branch; the same pair in parallel gives two ohms and 6 A in the main circuit. Adding parallel values as if they were in series is the error that wastes most marks, and it always produces an answer larger than the smallest branch.
电路图符号与电表接法
Edexcel 的电路图题按符号规范给分，电池、电阻、灯丝灯泡、二极管、开关、电流表、电压表、热敏电阻与光敏电阻各有固定画法，连线要求横平竖直。电流表串在待测支路，电压表并在待测元件两端，两只表的正负接线柱都要与电源方向一致。二极管符号的三角形指向电流允许通过的方向，画反之后整个电路的分析都会跟着错。审题时先看清问的是通过哪个元件的电流，还是哪两点之间的电压，再决定表的位置。阅卷时凡是把电压表串在干路上的答案，读数一栏基本拿不到分。这一步最容易在故障判断题里丢分，因为那类题要求写出电流几乎为零、电压表内阻很大这样的因果句。
Circuit diagrams earn marks for correct symbols and tidy right-angled connections; the battery, resistor, filament lamp, diode, switch, ammeter, voltmeter, thermistor and light-dependent resistor each have one accepted symbol. An ammeter is wired in series with the component under test and a voltmeter in parallel across it, with both sets of terminals following the supply direction, because an ideal ammeter has almost no resistance while a voltmeter has a great deal. Strange readings usually mean a meter in the wrong place, and a voltmeter placed in series leaves so little current that a lamp stays dark.
核心实验：电阻、灯丝灯泡与二极管的 I-V 特性
Edexcel 在 Topic 10 里指定了一条核心实验，用可变电源或变阻器改变元件两端的电压，记录多组电压与电流并画出 I-V 图。固定电阻的图线是过原点的直线，电流与电压成正比，任取一点用 V / I 算出的电阻都相同。灯丝灯泡的图线同样过原点，但随电压升高逐渐变平，同一只灯泡在 0.10 A 时是 4 欧姆，在 0.40 A 时变成 8 欧姆。二极管的图线只在正向电压超过约 0.6 V 之后才明显抬头，反向几乎测不到电流，把电源正负极反接就能得到负向读数。实验要求正反两个方向都取点，只测正向的表格在评分方案里通常要扣分。读数要等指针稳定，灯泡过热带来的漂移会让相邻两点对不上，这一点可以写成误差来源。
The required practical in Topic 10 varies the potential difference across a component with a variable supply or a rheostat and collects several pairs of readings for an I-V graph. A fixed resistor gives a straight line through the origin, and every point on that line returns the same value when voltage is divided by current; a filament lamp curves over as it warms, so one lamp reads about four ohms at 0.10 A and about eight ohms at 0.40 A. A diode stays almost silent until the forward voltage passes roughly 0.6 V, which is why both polarities are tested and the negative readings plotted.
灯丝灯泡的电阻为什么会上升
金属导电靠自由电子在晶格之间穿行，温度升高时金属离子的振动幅度变大，电子与离子碰撞的机会增多，电阻因此上升。灯丝用钨做成，正常工作温度很高，冷态电阻比热态小得多，接通瞬间的电流也偏大。用实验数据看更直接：同一只灯泡在 0.10 A 时电压 0.40 V，电阻 4 欧姆；电流升到 0.40 A 时电压 3.2 V，电阻 8 欧姆。很多学生以为电阻随电压升高，准确的说法是电阻随温度升高，而温度升高来自电流做功。把电压变大导致电阻变大写进因果链，评分方案里通常一分不给；写成电流增大、灯丝温度升高、离子振动加剧、电阻上升，才能拿到全部要点。热敏电阻与光敏电阻的变化方向正好相反，它们的电阻随温度或光照下降。
Inside a metal the free electrons collide with ions whose vibrations grow with temperature, so a filament becomes more resistive as it heats; tungsten is far less resistive when cold, which is why the current surges at switch-on. The measurements show it plainly, since 0.40 V at 0.10 A gives four ohms while 3.2 V at 0.40 A gives eight ohms for the same filament. Thermistors and light-dependent resistors move the other way because their carriers are released rather than blocked, so higher voltage means higher resistance never earns the explanation mark.
热敏电阻与光敏电阻在分压电路里的用法
负温度系数热敏电阻在温度上升时电阻下降，光敏电阻在光照增强时电阻下降，两者都在 spec 的电路元件表里。Edexcel 常用分压电路考这两件元件：两个元件串联，输出取自其中一个，输出端电压等于输入端电压乘以该元件电阻占总电阻的比例。热敏电阻放在上端时，温度上升让它电阻变小，输出端电压随之下降，这个信号可以驱动恒温器切断加热。光敏电阻放在路灯电路里，天黑后光照减弱、电阻变大，分压输出升高，开关被触发。常见的错误是把 NTC 记成温度升高电阻升高，名字里带 negative 的元件变化方向都与温度相反。计算时先写总电阻再算电流，最后用 V = I R 求目标元件上的电压，比直接套分压公式更稳。
An NTC thermistor loses resistance as it warms up and an LDR loses resistance as light intensity rises; both symbols appear in the component list of the specification. A potential divider places them in series and takes the output across one of them, so the output voltage is the input voltage multiplied by that resistance fraction, which is how a thermostat decides to switch a heater off as the room warms. The familiar slip is describing an NTC device as one whose resistance rises with temperature, and the word negative in its name is the reminder that the change runs the opposite way.
电功率与电能计算
电功率写成 P = V I，变形后还有 P = I^2 R，后者用在电流与电阻已知而电压未知的场合。电能写成 E = P t，也可以写成 E = Q V，前者的单位是焦耳，后者把电荷与电位差直接连起来。算例：230 V 电压下通过 6 A 电流的电水壶，功率是 230 x 6 = 1380 W，也就是 1.38 kW。同一只水壶工作 3 分钟，先把时间换成 180 秒，电能是 1380 x 180 = 248400 J，约 248 kJ。换成千瓦时更直观，1.38 kW 持续 0.05 小时等于 0.069 kWh，而 1 kWh 正好是 3.6 兆焦。最常见的两个失分动作是把分钟直接代进以秒为单位的公式，以及把 W 与 kW 混着写进结果。
Electrical power follows P = VI, or P = I^2 R when current and resistance are known but voltage is not; energy transferred is then simply power multiplied by time. A 6 A kettle on the 230 V mains has a power of 1380 W, which is 1.38 kW, and three minutes is 180 seconds, so the energy comes to 248400 J or 0.069 kWh; one kilowatt-hour is 3.6 million joules. Leaving minutes in a formula that expects seconds, or writing watts where kilowatts belong, are the two slips that cost marks most often.
市电、三线插头与用电安全
英国市电是 230 V、50 Hz 的交流电，插座三根线分别是棕色火线、蓝色零线和黄绿相间的接地线。接地线接在电器的金属外壳上，内部线路一旦碰到外壳，电流顺着地线走掉，人手触碰外壳时不会有明显电流通过。保险丝装在火线一侧，电流超过额定值就熔断，让电器与火线断开。漏电保护器比较火线与零线的电流差，差值达到 30 mA 量级时在几十毫秒内跳闸。很多学生把保险丝画在零线上，这样断开之后电器内部仍带火线电位，安全逻辑并不成立。开关同样接在火线一侧，插头线头也不能露出太长，露出的铜丝碰到相邻接线柱就是短路。
The mains supply in the UK is 230 V alternating at 50 Hz, and a three-pin plug carries a brown live wire, a blue neutral wire and a green-and-yellow earth wire. The earth wire bonds to the metal case, so a fault touching the case sends current down the earth path instead of through the user, while the fuse in the live wire melts once the current passes its rating. An RCD compares live and neutral currents and trips within milliseconds when the difference reaches about 30 mA, whereas a fuse in the neutral wire would leave the appliance live after it blew.
输电与电能计费
电网把发电机、升压变压器、高压输电线、降压变压器和用户串成一条链，家庭端最终得到 230 V。输电采用高压的原因是同样功率下电压升高、电流减小，而电缆发热功率等于 I^2 R，电流减半发热就降到四分之一。算例：输电线电阻 2 欧姆、电流 20 A 时，线损是 400 x 2 = 800 W；电流降到 10 A，线损变成 100 x 2 = 200 W。常见的错误是把它解释成高压电线的电阻更小，电阻由材料与粗细决定，与电压无关。电费按千瓦时计费，用电度数等于功率的千瓦数乘以时间的小时数，假设电价 25 便士每千瓦时，1.38 kW 的水壶烧 0.05 小时约花 1.7 便士。阅卷时把减小电流以减少发热损失写成完整链条，比只写为了省电多拿两分。
The National Grid links generators, step-up transformers, high-voltage cables, step-down transformers and consumers, ending at 230 V in the home. Raising voltage lowers the current for the same power, and because cable heating follows I^2 R, halving the current cuts the loss to a quarter; a line of 2 ohms carrying 20 A wastes 800 W, while 10 A wastes only 200 W. Repeated as a reason for high-voltage transmission, cable resistance is the wrong explanation, since resistance depends on the material and thickness of the conductor rather than the voltage it carries.
常见失分点与三周复习顺序
单位换算是电学计算的第一道门槛，毫安换安培要除以 1000，千焦换焦耳要乘 1000，分钟换秒要乘 60。写计算题时先列公式再代入数字，Edexcel 的分值里通常有独立的过程分，只写答案拿不到满档。有效数字按题目要求处理，指定两位就写两位，没有指定时让结果的位数与题给数据一致。图线描述题要写清过原点的直线、电流与电压成正比，并补一句电阻保持恒定。6 分解释题需要完整因果链，堆词组不会有分。三周安排可以这样切：第一周过 Topic 10 的概念与 I-V 实验题，第二周集中做 V = I R 与 P = V I 的计算，第三周重做错题并练 6 分题的成句表达。错得最多的是把串联与并联的规律互换，做题前先在图旁标出电流相同还是电压相同再动手。
Unit conversion is the first gate in electrical calculations, since milliamperes are divided by 1000 and minutes multiplied by 60 before they enter a formula; writing the formula before substituting keeps the method marks a bare answer loses. Significant figures follow whatever the question asks, and where nothing is specified the answer should match the precision of the data given. A three-week plan works best when the first week covers Topic 10 concepts and I-V questions, the second drills V = IR alongside P = VI, and the third repeats wrong questions with six-mark explanations.
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