📚 A-Level CIE Physics: Electric Current Key Points | A-Level CIE 物理：电流 考点精讲
Electric current is one of the most fundamental concepts in A-Level Physics. Understanding current as the rate of flow of charge, its microscopic origin, and the behaviour of components in circuits is essential for solving problems in electricity. This revision guide covers all the key points you need for the CIE A-Level 9702 syllabus, from basic definitions to Kirchhoff’s laws and potential dividers.
电流是 A-Level 物理中最基础的概念之一。将电流理解为电荷的流动速率、弄清其微观成因以及电路中元件的行为，是解决电学问题的关键。本篇复习指南涵盖了 CIE A-Level 9702 考纲的所有核心考点，从基本定义到基尔霍夫定律和分压器，一应俱全。
1. Definition of Electric Current | 电流的定义
Electric current is defined as the rate of flow of electric charge. The instantaneous current I is given by I = ΔQ / Δt, where ΔQ is the net charge passing through a cross-sectional area in time Δt. The SI unit of current is the ampere (A), where 1 A = 1 C s⁻¹. Current is a scalar quantity, but we often assign it a direction for circuit analysis.
电流定义为单位时间内通过导体横截面的电荷量。瞬时电流 I = ΔQ / Δt，其中 ΔQ 是在 Δt 时间内通过某一截面的净电荷量。电流的国际单位是安培（A），1 A = 1 C s⁻¹。电流是标量，但在电路分析中我们常给它规定一个方向。
I = ΔQ / Δt
2. Charge Carriers and Conventional Current Direction | 电荷载流子与常规电流方向
In metallic conductors, the charge carriers are free electrons, which move from the negative terminal to the positive terminal of a power supply. However, the conventional current direction is defined as the direction of flow of positive charge, i.e. from positive to negative. This convention is used in all circuit diagrams and equations. In electrolytes and semiconductors, positive ions or holes can also contribute to current.
在金属导体中，电荷载流子是自由电子，它们从电源负极流向正极。但常规电流方向被定义为正电荷流动的方向，即从正极到负极。这一规定在所有电路图和公式中沿用。在电解液和半导体中，正离子或空穴也能对电流作出贡献。
3. Microscopic Model: I = nAve | 微观模型 I = nAve
The current in a conductor can be expressed in terms of the microscopic motion of charge carriers. The equation is I = n A v e, where n is the number density of free charge carriers (m⁻³), A is the cross-sectional area (m²), v is the mean drift velocity (m s⁻¹), and e is the elementary charge (1.60 × 10⁻¹⁹ C). This formula shows that for a given current, a larger cross-sectional area results in a smaller drift velocity.
导体中的电流可以用电荷载流子的微观运动来描述。公式为 I = n A v e，其中 n 是自由电荷载流子的数密度（m⁻³），A 是横截面积（m²），v 是平均漂移速度（m s⁻¹），e 是元电荷（1.60 × 10⁻¹⁹ C）。该式表明，对于给定的电流，横截面积越大，漂移速度越小。
I = n A v e
4. Potential Difference and EMF | 电势差与电动势
Potential difference (p.d.) between two points is the energy transferred per unit charge when charge moves between them. It is measured in volts (V); 1 V = 1 J C⁻¹. Electromotive force (emf) of a source is the energy supplied per unit charge to drive charge around a complete circuit. While p.d. is associated with the conversion of electrical energy into other forms, emf is linked to the conversion of other forms into electrical energy.
两点间的电势差（p.d.）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）是驱动电荷绕完整回路一周所供给的单位电荷能量。电势差涉及电能转化为其他形式的能，而电动势则关联其他形式的能转化为电能。
5. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance R is defined as R = V / I, where V is the potential difference across a component and I is the current through it. Ohm’s law states that for a metallic conductor at constant temperature, the current is directly proportional to the applied p.d., i.e. V ∝ I, and thus resistance is constant. Components obeying this law are called ohmic conductors. The unit of resistance is the ohm (Ω).
电阻 R 定义为 R = V / I，其中 V 是元件两端的电势差，I 是通过元件的电流。欧姆定律指出，对于温度恒定的金属导体，电流与所加电势差成正比，即 V ∝ I，因此电阻恒定。遵守该定律的元件称为欧姆导体。电阻的单位是欧姆（Ω）。
R = V / I
6. Resistivity | 电阻率
The resistance of a uniform wire depends on its length L, cross-sectional area A, and the material’s resistivity ρ: R = ρ L / A. Resistivity is a material property, measured in ohm metres (Ω m). It is temperature-dependent; for metals, resistivity increases with temperature. Conductivity is the reciprocal of resistivity.
均匀导线的电阻取决于其长度 L、横截面积 A 和材料的电阻率 ρ，公式为 R = ρ L / A。电阻率是材料属性，单位为欧姆·米（Ω m）。电阻率随温度变化；金属的电阻率随温度升高而增大。电导率是电阻率的倒数。
R = ρ L / A
7. I-V Characteristics | I-V 特性曲线
The current–voltage relationship of a component is shown by its I-V characteristic graph. For an ohmic resistor, the graph is a straight line through the origin. A filament lamp shows a curve that flattens at higher voltages because its resistance increases with temperature. A semiconductor diode only conducts significantly when forward-biased above the threshold voltage (about 0.6 V for silicon), giving a steep rise; in reverse bias, current is negligible.
元件的电流–电压关系由其 I-V 特性曲线展示。欧姆电阻的特性线是一条过原点的直线。白炽灯的曲线在高电压时趋于平缓，因为温度升高导致电阻增大。半导体二极管仅在正向偏压超过阈值电压（硅管约 0.6 V）时才显著导通，电流急剧上升；反向偏置时电流可忽略不计。
8. Electrical Power and Energy | 电功率与电能
The power P dissipated in a circuit component is the rate at which it transfers energy: P = I V. Using Ohm’s law, we can also write P = I² R and P = V² / R. Energy transferred is E = P t = I V t, measured in joules (J). These expressions are used extensively in questions involving heating, efficiency, and cost of electricity.
电路元件耗散的功率 P 是其能量转换的速率：P = I V。结合欧姆定律，还可写成 P = I² R 和 P = V² / R。转移的能量为 E = P t = I V t，单位为焦耳（J）。这些公式广泛应用于涉及电热、效率以及电费计算的问题中。
P = I V P = I² R P = V² / R
9. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering any junction is zero: Σ I = 0. Equivalently, total current into a junction equals total current out. Kirchhoff’s voltage law (KVL) states that the sum of the emfs around any closed loop equals the sum of the potential differences: Σ ε = Σ V. These laws are essential for analysing complex circuits with multiple loops.
基尔霍夫电流定律（KCL）指出，流入任一节点的电流代数和为零：Σ I = 0。等价地说，流入一个节点的电流之和等于流出之和。基尔霍夫电压定律（KVL）指出，沿任一闭合回路，电动势的代数和等于电势降的代数和：Σ ε = Σ V。这两条定律是分析多回路复杂电路的基础。
Σ Iin = Σ Iout Σ ε = Σ V
10. Series and Parallel Circuits | 串联与并联电路
In a series circuit, current is the same everywhere, and the total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + …. The supply p.d. is shared across components. In a parallel circuit, the p.d. across each branch is the same, and the total resistance is given by 1 / Rtotal = 1 / R₁ + 1 / R₂ + …. Total current from the source equals the sum of branch currents.
在串联电路中，各处电流相等，总电阻等于各电阻之和：R总 = R₁ + R₂ + …。电源电压在各元件间分配。在并联电路中，各支路两端电压相等，总电阻由 1 / R总 = 1 / R₁ + 1 / R₂ + … 计算。电源输出的总电流等于各支路电流之和。
| Quantity | Series | Parallel |
|---|---|---|
| Current \\ 电流 | I = I₁ = I₂ = … | I = I₁ + I₂ + … |
| p.d. \\ 电压 | V = V₁ + V₂ + … | V = V₁ = V₂ = … |
| Resistance \\ 电阻 | R = R₁ + R₂ + … | 1/R = 1/R₁ + 1/R₂ + … |
11. Internal Resistance | 内阻
A real power source (e.g. a battery) has internal resistance r. When a current I flows, the terminal p.d. V is less than the emf ε due to lost volts across the internal resistance: V = ε – I r. This equation is crucial for questions on measuring emf and internal resistance, often using a variable resistor and plotting a graph of V against I to find ε (y-intercept) and r (negative gradient).
实际电源（如电池）具有内阻 r。当有电流 I 流过时，由于内阻上的损耗电压，端电压 V 会小于电动势 ε，关系式为 V = ε – I r。该方程对于测量电动势和内阻的实验题至关重要，通常通过可变电阻获得多组 V、I 值，绘制 V–I 图线，其中 y 轴截距为 ε，斜率绝对值为 r。
V = ε – I r
12. Potential Dividers | 分压器
A potential divider consists of two resistors in series across a supply voltage. The output voltage across one of the resistors is Vout = Vin × (R₂ / (R₁ + R₂)). By replacing one resistor with a sensor (e.g. an LDR or thermistor), the output voltage becomes dependent on light or temperature, forming the basis of many sensing circuits. The potentiometer is a variable potential divider.
分压器由两个串联电阻跨接在电源上构成。其中一个电阻两端的输出电压为 Vout = Vin × (R₂ / (R₁ + R₂))。若把其中一个电阻替换为传感器（如光敏电阻或热敏电阻），输出电压便取决于光照或温度，从而构成许多传感电路的基础。电位器即是一种可调分压器。
Vout = Vin × R₂ / (R₁ + R₂)
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