A2 Physics: Electric Current – Exam Essentials | A2 物理：电流

📚 A2 Physics: Electric Current – Exam Essentials | A2 物理：电流 – 考点精讲

Electric current is a fundamental concept in A2 Physics, linking charge, energy and circuit laws. Mastering current involves understanding its definition, microscopic origin, behaviour in different components, and the key laws such as Ohm’s law, Kirchhoff’s rules and power relationships. This article distills the essential points you need for your A2 exam.

电流是 A2 物理中的核心概念，它将电荷、能量与电路定律联系起来。掌握电流需要理解其定义、微观起源、在不同元件中的行为，以及欧姆定律、基尔霍夫定则和功率关系等关键规律。本文提炼了 A2 考试所需的核心考点。

1. Definition of Current | 电流的定义

Electric current I is the rate of flow of electric charge. If a charge ΔQ passes through a cross-section of a conductor in time Δt, the current is given by:

电流 I 是电荷流动的速率。若在时间 Δt 内有电荷 ΔQ 通过导体的某一横截面，则电流为：

I = ΔQ / Δt

Current is a scalar quantity, though we often assign a direction (conventional current flows from positive to negative). The SI unit of current is the ampere (A), which is equivalent to C s⁻¹.

电流是标量，但通常我们规定方向（传统电流从正极流向负极）。电流的国际单位是安培 (A)，等于 C s⁻¹。

In metallic conductors, the charge carriers are free electrons, each carrying a charge of magnitude e = 1.60 × 10⁻¹⁹ C. One ampere corresponds to the flow of approximately 6.25 × 10¹⁸ electrons per second.

在金属导体中，载流子是自由电子，每个电子所带电荷的大小为 e = 1.60 × 10⁻¹⁹ C。1 A 的电流相当于每秒流过约 6.25 × 10¹⁸ 个电子。

2. Conservation of Charge & Kirchhoff’s First Law | 电荷守恒与基尔霍夫第一定律

Charge is conserved; it cannot be created or destroyed. This principle leads directly to Kirchhoff’s first law (the junction rule):

电荷守恒，既不能被创造也不会被消灭。这一原理直接导出基尔霍夫第一定律（节点定律）：

Σ Iᵢₙ = Σ Iₒᵤₜ

At any junction in an electrical circuit, the sum of currents entering the junction equals the sum of currents leaving the junction. This law is a consequence of charge conservation and is essential for analysing parallel circuits.

在电路中的任一节点，流入节点的电流总和等于流出节点的电流总和。这一定律是电荷守恒的推论，对于分析并联电路至关重要。

3. Microscopic Model of Current | 电流的微观模型

For a conductor with charge carriers moving with an average drift velocity v, each carrying charge q, the current can be expressed in terms of microscopic quantities:

对于载流子以平均漂移速度 v 运动的导体，每个载流子携带电荷 q，电流可以用微观量表示：

I = n A v q

where n is the number density of charge carriers (number per unit volume) and A is the cross-sectional area. For electrons in a copper wire, q = e, and n is typically about 8.5 × 10²⁸ m⁻³.

其中 n 是载流子的数密度（单位体积内的数目），A 是横截面积。对铜导线中的电子而言，q = e，n 大约为 8.5 × 10²⁸ m⁻³。

Deriving ΔQ = n A v q Δt shows that the drift velocity is surprisingly small; in a typical circuit, v is of the order of mm s⁻¹, while the electric signal propagates almost at the speed of light.

由 ΔQ = n A v q Δt 可推导出漂移速度非常小；在典型电路中，v 约为 mm s⁻¹ 数量级，而电信号几乎以光速传播。

4. Potential Difference and Electromotive Force | 电势差与电动势

The potential difference (p.d.) V between two points is the energy transferred per unit charge when charge flows between them. Electromotive force (e.m.f.) ε of a source is the total energy supplied per unit charge, including energy lost inside the source.

两点间的电势差 V 是单位电荷在两点间流动时所转移的能量。电源的电动势 ε 是每单位电荷提供的总能量，包括电源内部损失的能量。

Symbolically: V = W / Q and ε = E_total / Q. Both are measured in volts (V), equivalent to J C⁻¹.

符号表示为：V = W / Q，ε = E_total / Q。两者均以伏特 (V) 为单位，等同于 J C⁻¹。

5. Resistance and Ohm’s Law | 电阻与欧姆定律

Resistance R is defined by R = V / I, where V is the potential difference across a component and I is the current through it. The unit is the ohm (Ω).

电阻 R 的定义式为 R = V / I，其中 V 是元件两端的电势差，I 是通过它的电流。单位是欧姆 (Ω)。

Ohm’s law states that, for a metallic conductor kept at constant temperature, the current is directly proportional to the applied potential difference, so R is constant. Ohm’s law is not a universal law; it applies only to ‘ohmic’ conductors.

欧姆定律指出，对于温度保持恒定的金属导体，电流与所加电势差成正比，因此 R 为常数。欧姆定律不是普适定律，仅适用于“欧姆导体”。

Ohmic conductors have a linear I–V graph passing through the origin. Non-ohmic components include filament lamps, diodes and thermistors.

欧姆导体的 I–V 特性图为过原点的直线。非欧姆元件包括灯丝灯泡、二极管和热敏电阻。

6. Resistivity and Conductivity | 电阻率与电导率

The resistance of a uniform wire is directly proportional to its length L and inversely proportional to its cross-sectional area A. The constant of proportionality is the resistivity ρ of the material:

均匀导线的电阻与其长度 L 成正比，与横截面积 A 成反比。比例常数即材料的电阻率 ρ：

R = ρ L / A

Resistivity has the unit Ω m and depends on the material and temperature. Conductivity σ is the reciprocal of resistivity, σ = 1 / ρ, with units (Ω m)⁻¹ or S m⁻¹.

电阻率的单位为 Ω m，取决于材料和温度。电导率 σ 是电阻率的倒数，σ = 1 / ρ，单位为 (Ω m)⁻¹ 或 S m⁻¹。

Good conductors like copper have low ρ (~1.7 × 10⁻⁸ Ω m), while insulators have extremely high ρ.

优良导体如铜的 ρ 很低（~1.7 × 10⁻⁸ Ω m），而绝缘体的 ρ 极高。

7. I–V Characteristics | I–V 特性曲线

Examining the I–V graph of a component reveals whether it is ohmic and how its resistance changes with current or voltage.

分析元件的 I–V 图可以判断其是否为欧姆元件，以及其电阻如何随电流或电压变化。

Fixed resistor at constant temp: straight line through origin; constant resistance.

恒温固定电阻器：通过原点的直线；电阻恒定。

Filament lamp: curve with decreasing gradient as V increases; as current raises temperature, resistance increases.

灯丝灯泡：曲线斜率随电压增大而减小；电流使温度升高，电阻增大。

Semiconductor diode: negligible current for reverse bias; in forward bias, negligible current until the threshold voltage (~0.7 V for silicon) is reached, after which current rises steeply.

半导体二极管：反向偏置时电流可忽略；正向偏置时，在达到阈值电压（硅管约0.7 V）之前电流极小，之后电流急剧上升。

8. Electrical Power and Energy | 电功率与电能

The power P dissipated or transferred in a component is the rate at which it converts electrical energy. Using V = W / Q and I = Q / t, we obtain:

元件中消耗或转换的功率 P 是其转换电能的速率。由 V = W / Q 和 I = Q / t 可得：

P = I V

For a purely resistive load, Ohm’s law allows two equivalent forms:

对于纯电阻负载，结合欧姆定律可得另外两个等价形式：

P = I² R and P = V² / R

The unit of power is the watt (W); energy transferred E = P t is measured in joules (J). In domestic electricity, energy is often expressed in kilowatt-hours (kWh).

功率的单位是瓦特 (W)；所转移的能量 E = P t 以焦耳 (J) 为单位。在家庭用电中，能量常以千瓦时 (kWh) 表示。

9. Internal Resistance and Terminal p.d. | 内阻与端电压

Real sources such as batteries and power supplies have internal resistance r. When a current I flows, the terminal potential difference V (the voltage across the external circuit) is less than the e.m.f. ε:

真实电源如电池和电源供应器都具有内阻 r。当有电流 I 流过时，端电压 V（外电路两端的电压）低于电动势 ε：

V = ε − I r

Writing the total circuit resistance as R + r, we have ε = I (R + r). The lost volts inside the source equal I r. The maximum current (short-circuit current) occurs when R = 0: I_sc = ε / r.

将电路总电阻写作 R + r，有 ε = I (R + r)。电源内部损失的电压为 I r。当 R = 0 时出现最大电流（短路电流）：I_sc = ε / r。

Measuring V for different values of I and plotting V against I gives a straight line with gradient −r and y-intercept ε.

通过测量不同 I 对应的 V，并绘制 V–I 图，可得到斜率为 −r、y轴截距为 ε 的直线。

10. Temperature Dependence of Resistance & Superconductivity | 电阻随温度的变化与超导

For metals, resistivity increases approximately linearly with temperature: ρ_T = ρ₀ [1 + α (T − T₀)], where α is the temperature coefficient of resistance. This is because ionic vibrations scatter the conduction electrons more as thermal energy increases.

对于金属，电阻率随温度近似线性增加：ρ_T = ρ₀ [1 + α (T − T₀)]，其中 α 为电阻温度系数。这是因为随着热能增加，离子振动对传导电子的散射增强。

Thermistors are semiconductor devices; NTC thermistors show a sharp drop in resistance as temperature rises, making them useful in temperature sensors.

热敏电阻是半导体器件；NTC 热敏电阻的电阻随温度升高急剧下降，因而常用于温度传感器。

Superconductivity: certain materials, when cooled below a critical temperature T_c, exhibit exactly zero resistivity. This means a current can flow indefinitely without energy loss, leading to powerful electromagnets and MRI scanners.

超导：某些材料在冷却至临界温度 T_c 以下时，电阻率变为零。这意味着电流可以无损地持续流动，催生了强电磁铁和 MRI 扫描仪等应用。

11. Summary of Key Formulas | 关键公式总结

Formula	Description \| 说明
I = ΔQ / Δt	Definition of current \| 电流定义
Σ Iᵢₙ = Σ Iₒᵤₜ	Kirchhoff’s first law \| 基尔霍夫第一定律
I = n A v q	Microscopic current \| 微观电流
V = W / Q	Potential difference \| 电势差
R = V / I	Resistance definition \| 电阻的定义
R = ρ L / A	Resistivity formula \| 电阻率公式
P = I V = I²R = V²/R	Electrical power \| 电功率
V = ε − I r	Terminal p.d. with internal resistance \| 含内阻的端电压
ρ_T = ρ₀ [1 + α (T − T₀)]	Temperature variation of resistivity \| 电阻率随温度变化

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A2 Physics: Electric Current – Exam Essentials | A2 物理：电流 – 考点精讲