Electric Current: Key Concepts for IB & WJEC Physics | 电流 考点精讲

📚 Electric Current: Key Concepts for IB & WJEC Physics | 电流 考点精讲

Electric current is a fundamental concept in physics, essential for understanding circuits, energy transfer, and electromagnetism. For both IB and WJEC syllabuses, it is crucial to master the definition of current, its microscopic origins, and its behaviour in different materials and circuit configurations. This article provides a focused revision guide on electric current, highlighting key formulas, common pitfalls, and exam-ready explanations.

电流是物理学中的基本概念，对于理解电路、能量转换和电磁学至关重要。在 IB 和 WJEC 大纲中，掌握电流的定义、微观本质以及在不同材料和电路中的行为是关键。本文提供电流的考点精讲，重点突出核心公式、常见易错点以及考试级的解释。

1. Charge and Definition of Current | 电荷与电流的定义

Electric current is the rate of flow of electric charge. The charge is carried by charge carriers, such as electrons in a metal wire or ions in an electrolyte. If a net charge ΔQ passes through a cross-section of a conductor in a time interval Δt, the average current I is given by I = ΔQ / Δt. The SI unit of current is the ampere (A), where 1 A = 1 C s⁻¹. For a steady current, the instantaneous current equals the average current. In IB, you should recall that current is a scalar quantity, even though we assign a direction to it.

电流是电荷流动的速率。电荷由载流子携带，例如金属导线中的电子或电解液中的离子。如果在时间间隔 Δt 内有净电荷 ΔQ 通过导体的某一横截面，则平均电流 I 由 I = ΔQ / Δt 给出。电流的国际单位是安培 (A)，1 A = 1 C s⁻¹。对于恒定电流，瞬时电流等于平均电流。在 IB 中应记住电流是标量，尽管我们给它指定了方向。

2. Direction of Current: Conventional vs Electron Flow | 电流方向：常规电流与电子流

Historically, the direction of conventional current was defined as the direction in which positive charges would flow, from the positive terminal to the negative terminal of a power supply. In metallic conductors, the actual charge carriers are negatively charged electrons moving in the opposite direction. Thus, electron flow is from negative to positive, while conventional current is opposite. IB physics uses conventional current in circuit analysis unless specified. Beware of confusion: the arrow on a diode symbol points in the direction of allowed conventional current.

历史上，常规电流的方向被定义为正电荷流动的方向，即从电源的正极流向负极。在金属导体中，实际的载流子是带负电的电子，它们运动的方向与常规电流相反。因此，电子流是从负极到正极，而常规电流则相反。IB 物理在电路分析中默认使用常规电流（除非特别说明）。注意勿混淆：二极管符号上的箭头指向允许的常规电流方向。

3. Microscopic Model: I = nAvq | 微观模型：I = nAvq

For a conductor with charge carriers of drift velocity v, the current can be expressed as I = n A v q, where n is the number density of charge carriers (number per unit volume), A is the cross-sectional area, and q is the charge on each carrier. For electrons, q = -e, but often we use the magnitude e to find the magnitude of current. Derivation: in time Δt, carriers travel a distance vΔt, so the volume of carriers passing a point is A v Δt; multiply by n to get the number of carriers, then by q to get the charge. This gives ΔQ = n A v q Δt, and dividing by Δt gives the formula.

对于载流子漂移速度为 v 的导体，电流可表示为 I = n A v q，其中 n 是载流子的数密度（单位体积的个数），A 是横截面积，q 是每个载流子的电荷量。对于电子，q = -e，但通常用 e 的大小求电流的大小。推导：在 Δt 时间内，载流子移动距离 vΔt，因此经过某点的载流子体积为 A v Δt；乘以 n 得到载流子数目，再乘以 q 得到电荷量。由此得 ΔQ = n A v q Δt，除以 Δt 即得公式。

I = n A v_d q

4. Drift Velocity and Its Small Magnitude | 漂移速度及其微小量值

In a typical copper wire (n ≈ 8.5×10²⁸ m⁻³) carrying a current of 1 A with a cross-sectional area of 1 mm², the drift speed of electrons is only about 0.1 mm s⁻¹. This is extremely slow compared to the random thermal speeds of electrons (~10⁶ m s⁻¹). The slow drift is because the motion of electrons is a superposition of random thermal motion and a tiny average drift due to the electric field. The signal, however, propagates almost at the speed of light because the electric field sets up quickly throughout the circuit. Students often confuse drift velocity with the speed of the electrical signal; exam questions may test this distinction.

在承载 1 A 电流、横截面积为 1 mm² 的典型铜导线 (n ≈ 8.5×10²⁸ m⁻³) 中，电子的漂移速率仅约 0.1 mm s⁻¹。这与电子随机热运动速度 (~10⁶ m s⁻¹) 相比极慢。漂移之所以缓慢，是因为电子的运动是随机热运动与电场导致的微小平均漂移的叠加。然而，信号几乎以光速传播，因为电场迅速在整个电路中建立。学生常将漂移速度与电信号速度混为一谈；考试可能考查这一区别。

5. Potential Difference and the Flow of Current | 电势差与电流的流动

For a current to flow in a conductor, a potential difference (p.d.) must be maintained across its ends. The p.d. provides the electric field that drives charge carriers through the material. In a circuit, a battery or power supply does work to separate charges, creating an electric field. When we connect a component across the battery, the field exerts a force on free charges, causing a net drift and hence a current. The energy transferred per unit charge is the potential difference. It’s important to distinguish that current does not get ‘used up’; charge is conserved, and current is the same at all points in a series circuit.

要使电流在导体中流动，必须在导体两端维持电势差。电势差提供电场，驱动载流子穿过材料。在电路中，电池或电源做功分离电荷，产生电场。当我们将元件跨接在电池两端时，电场对自由电荷施加力，导致净漂移并形成电流。每单位电荷转移的能量即电势差。务须区分：电流不会被“消耗掉”；电荷是守恒的，串联电路中各点电流相同。

6. Ohm’s Law and Resistance | 欧姆定律与电阻

Ohm’s law states that for many materials at constant temperature, the current I through a conductor is directly proportional to the potential difference V across it. The constant of proportionality is the resistance R, defined by V = I R. A component that obeys this linear relationship is called ohmic; examples include a metal wire at constant temperature. Non-ohmic components, like a filament lamp or a diode, have a V–I characteristic that is not a straight line. The resistance of a material depends on its geometry and resistivity, given by R = ρ L / A, where L is length, A is cross-sectional area, and ρ is resistivity.

欧姆定律指出，对于许多材料，在温度恒定的条件下，通过导体的电流 I 与导体两端的电势差 V 成正比。比例常数是电阻 R，定义为 V = I R。遵循这种线性关系的元件称为欧姆元件，例如恒温下的金属导线。非欧姆元件，如灯丝灯泡或二极管，其 V–I 特性不是直线。材料的电阻取决于其几何尺寸和电阻率：R = ρ L / A，其中 L 是长度，A 是横截面积，ρ 是电阻率。

R = ρ L / A

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

Resistivity ρ is an intrinsic property of a material that quantifies how strongly it opposes the flow of current. The SI unit is ohm-metre (Ω m). Conductors have low resistivity (e.g., copper ~ 1.7×10⁻⁸ Ω m), while insulators have very high resistivity. Semiconductors lie in between. Resistivity increases with temperature for metals because more lattice vibrations scatter the electrons, increasing resistance according to ρ = ρ₀[1 + α(T – T₀)], where α is the temperature coefficient of resistivity. In IB and WJEC, you may need to use this relationship to explain why filament lamps have a non-linear I–V characteristic. Conductivity σ is the reciprocal of resistivity: σ = 1/ρ.

电阻率 ρ 是材料固有的属性，量化了它对电流的阻碍程度。其国际单位是欧姆·米 (Ω m)。导体的电阻率低（例如铜 ~ 1.7×10⁻⁸ Ω m），而绝缘体的电阻率极高。半导体介于两者之间。金属的电阻率随温度升高而增加，因为更多的晶格振动散射电子，导致电阻增大：ρ = ρ₀[1 + α(T – T₀)]，其中 α 是电阻率的温度系数。在 IB 和 WJEC 中，可能需要利用此关系解释灯丝灯泡为何具有非线性的 I–U 特性。电导率 σ 是电阻率的倒数：σ = 1/ρ。

8. I–V Characteristics of Common Components | 常见元件的 I–V 特性曲线

Exam questions frequently ask you to sketch and interpret I–V graphs. For an ohmic resistor at constant temperature, the graph is a straight line through the origin, with slope = 1/R. A filament lamp shows a curve with decreasing slope (resistance increases) as the filament heats up. A semiconductor diode allows current to flow easily in one direction (forward bias) but has a very high resistance in reverse bias; its characteristic is highly non-linear. A thermistor’s resistance changes with temperature, and an LDR’s resistance changes with light intensity. Always label axes correctly: potential difference (V) on the x-axis and current (A) on the y-axis is typical for IB where current is plotted against voltage (I on vertical, V on horizontal). Be consistent with your syllabus.

考试题目常要求画出并解释 I–V 图。对于恒温下的欧姆电阻，其图形是一条过原点的直线，斜率 = 1/R。灯丝灯泡由于灯丝加热，其曲线斜率递减（电阻增大）。半导体二极管在正向偏置时容易导通电流，反向偏置时电阻极高；其特性高度非线性。热敏电阻的电阻随温度变化，光敏电阻 (

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