📚 Electric Current: WJEC A-Level Physics Revision | 电流：WJEC A-Level 物理考点精讲
An electric current is a flow of charged particles. In WJEC Physics, you must understand how current is defined, what drives it, and how it behaves in different circuits. This revision guide covers all essential concepts: from the basic equation I = Q / t to complex applications like Kirchhoff’s laws and internal resistance. Each section pairs key points in English with a Chinese translation to help you master the topic thoroughly.
电流是电荷的定向运动。在 WJEC 物理中，你需要掌握电流的定义、驱动力以及在不同电路中的行为。本复习指南涵盖所有核心概念：从基础公式 I = Q / t 到基尔霍夫定律和内电阻等复杂应用。每个要点均以中英双语对照展开，助你透彻掌握这一主题。
1. Definition of Electric Current | 电流的定义
Electric current is the rate of flow of charge. If a net charge ΔQ passes through a cross-section of a conductor in time Δt, the current I is given by I = ΔQ / Δt. The SI unit of current is the ampere (A), which is equivalent to one coulomb per second.
电流是电荷流动的速率。若在时间 Δt 内有净电荷 ΔQ 通过导体的某一横截面，则电流 I 由 I = ΔQ / Δt 定义。电流的国际单位是安培 (A)，即 1 库仑每秒。
In a series circuit, the current is the same at every point. This arises from charge conservation: charge cannot be created or destroyed, so the amount of charge entering a point per second must equal the amount leaving it.
在串联电路中，各点的电流处处相等。这是由电荷守恒导致的：电荷不能被创生或消灭，因此每秒流入某点的电荷量必然等于流出的电荷量。
The direction of conventional current is taken as the direction of positive charge flow. In metallic wires, electrons actually move in the opposite direction, but all equations use conventional current. WJEC always emphasizes that current arrows point from high to low potential.
约定电流的方向为正电荷流动的方向。在金属导线中，电子实际运动方向相反，但所有公式均采用约定电流。WJEC 始终强调电流箭头由高电位指向低电位。
I = ΔQ / Δt
2. Charge Carriers and Conduction | 电荷载流子与导电机制
Charge carriers are the mobile particles that transport charge. In metals, the carriers are delocalised electrons moving through a lattice of positive ions. In electrolytes, both positive and negative ions move. In semiconductors, electrons and positive holes contribute to conduction.
电荷载流子是运载电荷的可移动粒子。在金属中，载流子是穿过正离子晶格运动的离域电子。在电解质中，正、负离子同时移动。在半导体中，电子和空穴共同导电。
The number density n of charge carriers is a critical parameter. For a typical copper wire, n ≈ 8.5 × 10²⁸ m⁻³. A high number density means many free electrons are available, enabling large currents even with slow drift speeds.
载流子的数密度 n 是一个关键参数。对典型的铜导线，n 约为 8.5×10²⁸ m⁻³。高数密度意味着有大量自由电子可供导电，从而使漂移速度很慢时也能形成大电流。
The sign of the charge carrier q is positive for holes or positive ions and negative for electrons. In the drift velocity equation, we always use the magnitude of electronic charge e = 1.60 × 10⁻¹⁹ C for electrons, and adjust the direction according to conventional current.
电荷载流子的电量 q 对空穴或正离子为正，对电子为负。在漂移速度公式中，电子总使用元电荷的大小 e = 1.60×10⁻¹⁹ C，而方向则按约定电流处理。
3. The Drift Velocity Equation (I = nAvq) | 漂移速度公式 I = nAvq
If a conductor has cross-sectional area A, number density n of charge carriers each carrying charge q, and the carriers have an average drift velocity v, the resulting current is I = n A v q. This is a fundamental equation in WJEC electricity.
若导体横截面积为 A，数密度为 n 的载流子各携带电荷 q，且载流子的平均漂移速度为 v，则产生的电流为 I = n A v q。这是 WJEC 电学中的一个基本公式。
Derivation: in time Δt, a charge carrier moves a distance v Δt, so the volume of carriers passing a point is A v Δt. The total charge passing is n q A v Δt, and dividing by Δt gives I = n A v q.
推导：在 Δt 时间内，一个载流子移动了 v Δt 距离，因此通过某点的载流子体积为 A v Δt。通过的总电荷量为 n q A v Δt，除以 Δt 即得 I = n A v q。
I = n A v q
Despite the enormous number density in copper, the typical drift speed of electrons for household currents is only about 10⁻⁴ m s⁻¹, much slower than the propagation of the electric field (≈ 3×10⁸ m s⁻¹). The slow drift does not hinder rapid signal transmission.
尽管铜的载流子数密度极大，但家用电流下电子的典型漂移速度仅约为 10⁻⁴ m s⁻¹，远慢于电场传播速度（约 3×10⁸ m s⁻¹）。缓慢的漂移并不妨碍信号的高速传递。
4. Potential Difference and Electromotive Force | 电位差与电动势
The potential difference (p.d.) V between two points is the energy transferred per unit charge moving between those points. V = W / Q, measured in volts (J C⁻¹). A voltmeter measures p.d. across a component.
两点之间的电位差（电压）V 是单位电荷在这两点间移动时转移的能量。V = W / Q，单位为伏特 (J C⁻¹)。伏特计用于测量元件两端的电压。
Electromotive force (e.m.f.) ε is the energy supplied per unit charge by a source such as a battery or generator. It is not a force but an energy per charge; the term ‘electromotive force’ is historical.
电动势 (ε) 是电池或发电机等电源提供给每单位电荷的能量。它不是力，而是单位电荷的能量；“电动势”一词为历史沿用。
The total e.m.f. in a closed loop equals the sum of the potential differences. This is the basis of Kirchhoff’s voltage law. In a simple circuit, ε = Vexternal + Vinternal if internal resistance is present.
闭合回路中的总电动势等于各段电位差之和。这是基尔霍夫电压定律的基础。在简单电路中，若存在内阻，则有 ε = V外 + V内。
5. Resistance and Resistivity | 电阻与电阻率
Resistance R of a component is defined by R = V / I, where V is the p.d. across it and I the current through it. The SI unit of resistance is the ohm (Ω). A component has a resistance of 1 Ω if a p.d. of 1 V drives a current of 1 A.
元件的电阻 R 定义为 R = V / I，V 为其两端电压，I 为通过它的电流。电阻的国际单位是欧姆 (Ω)。若 1 V 的电压产生 1 A 电流，则该元件具有 1 Ω 的电阻。
Resistivity ρ is a material property: ρ = R A / L, where A is cross-sectional area and L is length. Good conductors have low resistivity; insulators have extremely high resistivity. The unit of resistivity is Ω m.
电阻率 ρ 表征材料属性：ρ = R A / L，A 为横截面积，L 为长度。良导体电阻率低，绝缘体电阻率极高。电阻率单位是 Ω m。
ρ = R A / L
In WJEC problems, you may need to calculate resistance from resistivity or compare how resistance changes with dimensions. Keeping A and ρ constant, resistance is proportional to L; keeping L and ρ constant, resistance is inversely proportional to A.
在 WJEC 题目中，你可能需要根据电阻率计算电阻，或比较尺寸变化时电阻如何变化。保持 A 和 ρ 不变，电阻正比于 L；保持 L 和 ρ 不变，电阻反比于 A。
6. Ohm’s Law and I-V Characteristics | 欧姆定律与 I-V 特性曲线
Ohm’s law states that for a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it: V ∝ I. A resistor that obeys this law is called an ohmic conductor.
欧姆定律指出，对于温度恒定的金属导体，通过它的电流与它两端的电位差成正比：V ∝ I。遵循这一定律的电阻器称为欧姆导体。
The I-V graph for an ohmic resistor is a straight line through the origin. A filament lamp does not obey Ohm’s law because its resistance increases as the temperature rises; its I-V graph curves with decreasing gradient at higher voltages.
欧姆导体的 I-V 曲线是一条通过原点的直线。白炽灯丝不符合欧姆定律，因为温度升高时电阻增大；其 I-V 曲线在较高电压处斜率下降，呈现弯曲。
For a semiconductor diode, the I-V characteristic shows very high resistance in reverse bias and low resistance above a threshold voltage (about 0.7 V for silicon) in forward bias. These non-ohmic behaviours are essential for WJEC exam analysis.
半导体二极管的 I-V 特性显示反向偏置时电阻极高，正向偏置且超过阈值电压（硅管约 0.7 V）后电阻很低。这些非欧姆行为是 WJEC 考试分析的重点。
V = I R
7. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s first law, the junction rule, is based on conservation of charge: the sum of currents entering a junction equals the sum of currents leaving it. Mathematically, Σ Iin = Σ Iout, or Σ I = 0 when inflows are taken as positive and outflows as negative.
基尔霍夫第一定律（节点定律）基于电荷守恒：流入某节点的电流之和等于流出该节点的电流之和。数学表达为 Σ I入 = Σ I出，或规定流入为正、流出为负时，Σ I = 0。
Kirchhoff’s second law, the loop rule, follows from energy conservation: the sum of the e.m.f.s around any closed loop equals the sum of the potential drops (IR) across components in that loop. Σ ε = Σ I R.
基尔霍夫第二定律（回路定律）基于能量守恒：任一闭合回路中，电动势的代数和等于各元件上电位降 (IR) 的代数和。即 Σ ε = Σ I R。
Σ I = 0
Σ ε = Σ I R
These laws allow you to find unknown currents and voltages in complex circuits by writing simultaneous equations. In WJEC exams, systematic application of the sign conventions is crucial.
利用这两条定律，通过列方程组可以求出复杂电路中的未知电流和电压。在 WJEC 考试中，严格遵循符号约定至关重要。
8. Series and Parallel Circuits | 串联与并联电路
In a series circuit, components are connected end-to-end, so the same current flows through each. The total p.d. across the series combination is the sum of the individual p.d.s: Vtotal = V1 + V2. The equivalent resistance is Rtotal = R1 + R2.
在串联电路中，元器件首尾相接，因此通过每个元件的电流相同。串联组合两端的电压为各电压之和：V总 = V1 + V2。等效电阻为 R总 = R1 + R2。
In a parallel circuit, components share the same p.d. across their branches. The total current from the source is the sum of the branch currents: Itotal = I1 + I2. The reciprocal of the equivalent resistance is 1/Rtotal = 1/R1 + 1/R2.
在并联电路中，各支路两端电压相同。电源提供的总电流为各支路电流之和：I总 = I1 + I2。等效电阻的倒数等于各电阻倒数之和：1/R总 = 1/R1 + 1/R2。
These relationships can be derived from Kirchhoff’s laws. In WJEC problems, always identify whether components are in series or parallel, then apply the appropriate voltage and current rules while keeping track of common nodes.
这些关系可由基尔霍夫定律推导。在 WJEC 题目中，首先判断元器件是串联还是并联，然后运用对应的电压和电流规律，同时关注公共节点。
Parallel circuits provide lower overall resistance and allow independent operation of devices. The total resistance of a parallel network is always less than the smallest individual resistance.
并联电路整体电阻更小，且各器件可独立工作。并联网络的总电阻始终小于其中最小的单个电阻。
9. Energy and Power in Circuits | 电路中的能量与功率
When a charge Q moves through a p.d. V, it gains or loses energy ΔE = Q V. Since current I = Q / t, the power P dissipated or supplied is P = I V. This power can be expressed in alternative forms using Ohm’s law: P = I² R and P = V² / R.
电荷 Q 通过电位差 V 时获得或失去的能量为 ΔE = Q V。因 I = Q / t，消耗或提供的功率 P = I V。利用欧姆定律可推得两种等价形式：P = I² R 及 P = V² / R。
P = I V = I²R = V²/R
The unit of power is the watt (W), equivalent to J s⁻¹. The energy transferred over time t is E = I V t. This is the basis for the kilowatt-hour (kWh) unit used in electricity meters; 1 kWh = 3.6 × 10⁶ J.
功率的单位是瓦特 (W)，即 J s⁻¹。在时间 t 内转移的能量为 E = I V t。电表中使用的千瓦时 (kWh) 即以此为基础：1 kWh = 3.6×10⁶ J。
In a resistor, electrical energy is converted entirely into heat (Joule heating). This is why resistors get warm. In a motor or lamp, part of the energy is converted into mechanical work or light.
在电阻中，电能全部转化为热量（焦耳热），因此电阻会发热。在电动机或灯泡中，部分电能转化为机械能或光能。
10. Internal Resistance and EMF | 内电阻与电动势
All real sources of e.m.f., such as batteries, have some internal resistance r. The terminal voltage V across the battery is less than its e.m.f. ε when it delivers a current I: V = ε − I r.
所有实际电源（如电池）均具有一定的内电阻 r。当电池提供电流 I 时，端电压 V 小于其电动势 ε：V = ε − I r。
You can determine ε and r experimentally by measuring V and I for different load resistances and plotting a straight-line graph. Rearranging gives V = −r I + ε, so a graph of V against I has gradient −r and intercept ε on the voltage axis.
可以通过改变负载电阻来测量不同电流时的端电压，绘出直线图测出 ε 和 r。将公式改写为 V = −r I + ε，则 V 对 I 作图斜率为 −r，纵轴截距为 ε。
When a cell is short-circuited (R = 0), the terminal voltage is zero and the current is Imax = ε / r. This large current can damage the cell; practical circuits avoid short circuits by using fuses.
当电池短路 (R = 0) 时，端电压为零，电流达到最大值 Imax = ε / r。这种大电流可能损坏电池；实际电路中常通过保险丝避免短路。
In WJEC numerical problems, always distinguish between terminal voltage and e.m.f. – especially when calculating power delivered to an external load.
在 WJEC 计算题中，务必区分端电压与电动势，尤其是在求解输送给外部负载的功率时。
11. Experimental Skills and WJEC Exam Tips | 实验技能与 WJEC 考试技巧
WJEC requires you to draw circuit diagrams with conventional symbols (cells, resistors, lamps, diodes, voltmeters, ammeters). Always label components and indicate the direction of conventional current with arrows.
WJEC 要求能够使用标准电气符号绘制电路图（电池、电阻、灯泡、二极管、伏特计、安培计）。务必标注元器件，并用箭头标明约定电流方向。
When setting up a potential divider or using a rheostat, understand how to vary the p.d. or current smoothly. The potential divider circuit is widely used to supply a variable p.d. from 0 up to the source voltage.
在搭建分压电路或使用变阻器时，务必理解如何平滑调节电压或电流。分压电路被广泛用于提供 0 到电源电压之间的可变电压。
In I-V characteristic experiments, a protective resistor should be included to limit current, and readings should be taken both for increasing and decreasing voltage to check for hysteresis in filament lamps.
进行 I-V 特性实验时，应串联保护电阻以限制电流；对白炽灯还应分别记录升高和降低电压时的读数，以观察迟滞现象。
Show your working in all calculations: write down the relevant formula, substitute values with units, and give your final answer to an appropriate number of significant figures – usually 2 or 3 in WJEC papers.
所有计算题都应展示完整推导过程：写出相关公式，代入数据（带单位），最终答案取合适的有效数字位数——WJEC 试卷中通常为 2 或 3 位。
Vout = (R2/(R1+R2)) × Vin
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