📚 Electric Current | 电流 考点精讲
Electric current is one of the most fundamental concepts in A-Level Physics. It describes the rate at which charge flows through a conductor and underpins everything from simple circuits to complex electronics. In the CCEA specification, you are expected to understand both the macroscopic definition of current and its microscopic origins, as well as how to apply related principles to solve circuit problems. This revision guide breaks down all the essential points you need for the exam.
电流是 A-Level 物理中最基本的概念之一，描述电荷流过导体的速率，是简单电路乃至复杂电子学的基础。在 CCEA 考试大纲中，你既要掌握电流的宏观定义，也要理解其微观起源，并能应用相关原理解决电路问题。这篇精讲为你拆解所有必考点。
1. Definition of Current | 电流的定义
Electric current, symbol I, is defined as the net rate of flow of charge past a point in a circuit. Mathematically, it is the amount of charge ΔQ passing a cross-section in time Δt.
电流用符号 I 表示，定义为电荷流过电路中某一点的净速率。数学上，它是时间 Δt 内通过某一截面的电荷量 ΔQ。
I = ΔQ / Δt
The SI unit of current is the ampere (A), where 1 A is equivalent to 1 coulomb per second. Since charge is carried by discrete particles such as electrons, a current of 1 A corresponds to about 6.25 × 1018 electrons passing a point each second.
电流的国际单位是安培 (A)，1 A 等于 1 库仑每秒。由于电荷是由像电子这样的离散粒子携带的，1 A 电流相当于每秒大约有 6.25 × 1018 个电子通过某点。
2. Direction of Current: Conventional vs Electron Flow | 电流的方向：传统方向与电子流动
Historically, current was defined as the flow of positive charge, meaning conventional current points from the positive terminal to the negative terminal of a battery. In metallic conductors, however, the actual charge carriers are free electrons, which move in the opposite direction. You must be able to distinguish between conventional current and electron flow in exam explanations.
历史上，电流被定义为正电荷的流动，即传统电流的方向是从电池的正极指向负极。然而在金属导体中，实际载流子是自由电子，它们沿相反方向运动。考试中你必须要能区分传统电流方向和电子流动方向。
Despite this convention, all mathematical relationships using I assume the flow of positive charge. When describing processes like electrolysis, both positive and negative ions can contribute to the current, and the net current is the sum of their effects.
尽管有此惯例，所有使用 I 的数学关系都假定为正电荷的流动。在描述像电解这样的过程时，正负离子都会对电流有贡献，净电流是两种离子作用的叠加。
3. Microscopic Model of Current | 电流的微观模型
To explain current in metals, we use the free electron model. The current can be expressed in terms of the number density of charge carriers n, the cross-sectional area A, the drift velocity vd, and the charge on each carrier q.
为了解释金属中的电流，我们使用自由电子模型。电流可以用载流子数密度 n、横截面积 A、漂移速度 vd 和每个载流子的电荷量 q 来表示。
I = nAvdq
For a typical copper wire, n is about 1029 m-3, and the electron charge q is 1.60 × 10-19 C. Even for large currents, the drift velocity is surprisingly small – often less than 1 mm s-1. This equation highlights that the current can be altered by changing the wire’s thickness or the material’s carrier density.
对于典型的铜导线，n 大约为 1029 m-3，电子电荷 q 为 1.60 × 10-19 C。即使电流很大，漂移速度也惊人地小——通常小于 1 mm s-1。这个方程突出表明，通过改变导线的粗细或材料的载流子密度，可以改变电流。
The difference between the almost instantaneous transmission of an electrical signal and the slow drift speed can be confusing; remember that it is the electric field that propagates near the speed of light, pushing electrons all along the wire at once.
电信号几乎瞬间传递与缓慢的漂移速度之间容易混淆；要记住，以接近光速传播的是电场，它同时推动导线所有位置的电子。
4. Charge Conservation and Kirchhoff’s First Law | 电荷守恒与基尔霍夫第一定律
Kirchhoff’s first law states that at any junction in an electrical circuit, the total current entering the junction equals the total current leaving it. This is a direct consequence of the conservation of charge – charge cannot accumulate or disappear at a point.
基尔霍夫第一定律指出，在电路的任一节点处，流入节点的总电流等于流出节点的总电流。这是电荷守恒的直接结果——电荷不能在一点处积累或消失。
Σ Iin = Σ Iout
When applying this law, assign directions to all currents before calculation. If a calculated current comes out negative, it simply means the actual direction is opposite to your initial assumption. This law is essential for analysing parallel circuits and complex networks.
应用该定律时，在计算前要先为所有电流设定方向。如果算出的电流为负值，仅表示实际方向与你最初假设的方向相反。该定律对分析并联电路和复杂网络至关重要。
5. Direct Current and Alternating Current | 直流电与交流电
Direct current (DC) flows steadily in one direction around a circuit, typically produced by batteries and cells. Alternating current (AC), in contrast, periodically reverses direction, and in the UK mains supply it changes direction 50 times per second (50 Hz).
直流电 (DC) 在电路中沿一个方向稳定流动，通常由电池产生。而交流电 (AC) 则会周期性地反向，英国的市电以每秒 50 次 (50 Hz) 的频率改变方向。
For AC circuits, we often use root-mean-square (rms) values of current and voltage to compare with equivalent DC effects. The peak current I0 and rms current Irms are related by Irms = I0 / √2 for sinusoidal waveforms. CCEA questions may ask you to interpret oscilloscope traces of AC signals.
对于交流电路，我们常用电流和电压的方均根值 (rms) 来与等效的直流效果比较。对于正弦波形，峰值电流 I0 与方均根电流 Irms 满足关系 Irms = I0 / √2。CCEA 考题可能会要求你解释交流信号的示波器波形。
6. Measuring Current – The Ammeter | 测量电流 – 安培表
An ammeter must be connected in series with the component whose current you wish to measure, so that the same current passes through both. An ideal ammeter has zero internal resistance to avoid affecting the circuit, but real ammeters have very low resistance.
安培表必须与被测元件串联，以便相同的电流流过它们。理想安培表内阻为零，以免影响电路，但真实安培表内阻非常低。
Incorrect placement, such as connecting an ammeter in parallel with a component, can cause a large current to flow through the meter, potentially damaging it. Always double-check your practical circuit diagrams: ammeters in series, voltmeters in parallel.
错误的连接，例如将安培表与元件并联，会导致大电流流过电表，可能损坏它。一定要反复检查实验电路图：安培表串联，伏特表并联。
7. Potential Difference and Electromotive Force | 电位差与电动势
Potential difference (p.d.), or voltage, between two points is the energy transferred per unit charge as charge moves between those points. It is measured in volts (V), where 1 V = 1 J C-1. Electromotive force (emf) ε of a source is the energy supplied per unit charge to drive charge around a complete circuit.
两点间的电位差 (p.d.) 或电压，是单位电荷在两点间移动时转移的能量，单位为伏特 (V)，1 V = 1 J C-1。电源的电动势 (emf) ε 是驱动电荷绕完整电路一周所提供给每单位电荷的能量。
V = W / Q
While emf is measured across the terminals of a source when no current flows (open circuit), the terminal p.d. drops when a current is drawn due to internal resistance. You should be able to distinguish these clearly in descriptions and calculations.
电动势是在无电流（开路）时测量电源两端的电压，而端电压在有电流输出时会因内阻而下降。你要能在描述和计算中清晰地区分两者。
8. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance R is a measure of the opposition to current flow, defined by R = V / I, provided temperature and other physical conditions remain constant. For an ohmic conductor, the current through it is directly proportional to the applied potential difference, yielding a straight-line I-V graph through the origin.
电阻 R 是对电流阻碍作用的量度，定义为 R = V / I，前提是温度和其他物理条件保持不变。对于欧姆导体，通过它的电流与所加电位差成正比，得到一条过原点的直线 I-V 图像。
Non-ohmic components such as filament lamps and diodes show non-linear behaviour. A filament lamp’s resistance increases with current because the filament heats up, while a diode allows current in only one direction above a threshold voltage. These characteristics are commonly examined in CCEA practicals.
非欧姆元件，如灯丝灯泡和二极管，表现出非线性特征。灯丝灯泡的电阻随电流增大而增加，因为灯丝发热；而二极管仅在高于阈值电压的正向方向上允许电流通过。这些特性是 CCEA 实验考试中常见的考点。
| Component | I-V Characteristic |
|---|---|
| Ohmic resistor (constant temperature) | Straight line through origin |
| Filament lamp | Curve with decreasing gradient (resistance rises) |
| Semiconductor diode | Negligible current in reverse bias; exponential rise in forward bias after ~0.6 V |
9. Resistivity and the Factors Affecting Resistance | 电阻率与影响电阻的因素
The resistance of a uniform wire depends on its length L, cross-sectional area A, and the resistivity ρ of the material. Resistivity is an intrinsic property that quantifies how strongly a material opposes current flow.
均匀导线的电阻取决于其长度 L、横截面积 A 以及材料的电阻率 ρ。电阻率是一个内禀性质，量化材料对电流阻碍的强弱程度。
R = ρL / A
Resistivity is measured in ohm metres (Ω m). Good conductors like copper have very low resistivity (~1.7 × 10-8 Ω m), while insulators have extremely high values. The equation shows that doubling the length doubles the resistance, while doubling the cross-sectional area halves it. This relationship is vital for explaining the behaviour of variable resistors and sensor circuits.
电阻率的单位是欧姆·米 (Ω m)。像铜这样的良导体电阻率非常低（~1.7 × 10-8 Ω m），而绝缘体的电阻率极高。该方程表明，长度加倍会导致电阻加倍，而截面积加倍则会使电阻减半。这种关系对于解释可变电阻器和传感器电路的行为至关重要。
10. Electrical Power and Energy Dissipation | 电功率与能量耗散
The power P transferred in a circuit component is the rate at which it converts electrical energy into other forms. It is given by the product of current and potential difference.
电路元件中转化的功率 P 是它把电能转化为其他形式的速率，由电流与电位差的乘积给出。
P = IV
Using Ohm’s law, this can also be written as P = I2R and P = V2/R. The form P = I2R is particularly useful for calculating the heating effect (Joule heating) in a resistor or transmission cable, where power loss increases with the square of the current. This is why electricity is transmitted at very high voltages – for a given power, a higher voltage means lower current and less I2R loss.
利用欧姆定律，它还可以写成 P = I2R 和 P = V2/R。P = I2R 的形式对于计算电阻器或输电电缆中的热效应（焦耳热）特别有用，这里功率损耗随电流的平方增大。这也是为什么电力要以极高电压传输的原因——在给定功率下，电压越高，电流越小，I2R 损耗也就越少。
11. Internal Resistance of a Source | 电源的内部电阻
Every real power source, whether a cell, battery, or power supply, possesses some internal resistance r. When a current I flows, energy is dissipated inside the source, and the terminal p.d. is less than the emf.
每一个真实的电源，无论是电池还是电源供应器，都具有一定的内阻 r。当有电流 I 流过时，能量在电源内部耗散，端电压就会小于电动势。
ε = I(R + r)
The ‘lost volts’ inside the source is Ir, so the terminal p.d. V = ε – Ir. A graph of terminal p.d. against current yields a straight line with gradient -r and y-intercept ε. This is a classic required practical in CCEA, often using a variable resistor to vary the current.
电源内部的“损失电压”为 Ir，因此端电压 V = ε – Ir。端电压对电流作图得到一条斜率为 -r、y 轴截距为 ε 的直线。这是 CCEA 中一项典型的必做实验，通常使用可变电阻来改变电流。
12. Key Exam Tips and Common Mistakes | 考试要点与常见错误
When solving current problems, always check whether you are working with conventional current or electron flow, particularly in questions about charged particles in electric or magnetic fields. In circuit calculations, use Kirchhoff’s laws systematically and label all branch currents before writing equations.
解决电流问题时，始终要注意你正在使用传统电流方向还是电子流动方向，特别是在涉及带电粒子在电场或磁场中运动的问题里。在电路计算中，要系统地使用基尔霍夫定律，并在列方程之前标出所有支路电流。
Remember that an ammeter is a low-resistance device; do not place it in parallel. For internal resistance experiments, the voltmeter must be connected directly across the cell terminals. When comparing resistances using I-V graphs, a steeper gradient means a lower resistance, not higher – check whether axes are current vs voltage or voltage vs current.
记住安培表是低电阻设备，不要把它并联。在做内阻实验时，伏特表必须直接连接在电池两端。用 I-V 图像比较电阻时，更陡的斜率意味着更低的电阻，而不是更高——要检查坐标轴是电流-电压还是电压-电流。
Finally, practise using the drift velocity equation I = nAvdq in different contexts, such as explaining why a thinner wire heats up more for the same current. Mastery of these core ideas will give you a solid foundation for the electricity section of your CCEA A-Level Physics exam.
最后，要多练习在不同情境下使用漂移速度方程 I = nAvdq，例如解释为什么在相同电流下更细的导线会发热更严重。掌握这些核心概念，将为你的 CCEA A-Level 物理考试中的电学部分打下坚实基础。
Published by TutorHao | Physics Revision Series | aleveler.com
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