📚 Electric Current Key Points for IB CCEA Physics | IB CCEA 物理：电流 考点精讲
Electric current is one of the most fundamental concepts in electricity, forming the backbone of circuit analysis in both IB and CCEA Physics. This article distils the essential points you must master: from the definition of current and its microscopic origin to the application of Kirchhoff’s laws. Each section is designed to align closely with examination requirements, helping you build a rigorous and confident understanding.
电流是电学中最基础的概念之一，也是 IB 和 CCEA 物理电路分析的基石。本文提炼了必须掌握的核心考点：从电流的定义及其微观本质，到基尔霍夫定律的应用。每节内容紧密贴合考纲要求，助你建立严谨而自信的知识体系。
1. Definition of Electric Current | 电流的定义
Electric current is the rate of flow of electric charge past a given cross-section of a conductor. In the SI system, current is a base quantity and its unit is the ampere (A). One ampere is defined as the flow of one coulomb of charge per second. Mathematically, it is expressed as I = ΔQ/Δt, where ΔQ is the net charge passing through the cross-section in time Δt.
电流是指单位时间内通过导体某一横截面的电荷量。在国际单位制中，电流是一个基本物理量，单位为安培（A）。1 安培定义为每秒流过 1 库仑的电荷。数学上表示为 I = ΔQ/Δt，其中 ΔQ 是 Δt 时间内通过截面的净电荷量。
2. Conventional Current vs Electron Flow | 常规电流与电子流动方向
Historically, current was defined as the flow of positive charge from the positive to the negative terminal of a source. This is called conventional current. In metallic conductors, however, the actual charge carriers are negatively charged electrons, which drift from the negative to the positive terminal. When solving circuits, always use conventional current direction unless instructed otherwise. In electrolytes or semiconductors, both positive and negative ions or holes may contribute to current.
历史上，电流被定义为正电荷从电源正极流向负极，称之为常规电流方向。然而在金属导体中，实际的载流子是带负电的电子，它们从负极漂移到正极。分析电路时，除非另有说明，统一采用常规电流方向。在电解液或半导体中，正负离子或空穴都可能参与导电。
3. Drift Velocity and the Microscopic Model | 漂移速度与微观模型
Inside a metal wire, free electrons move randomly at high speeds due to thermal energy, but this random motion does not produce a net current. When an electric field is applied, electrons acquire a small average velocity opposite to the field direction; this is called the drift velocity, v. It is typically of the order of 10⁻⁴ m s⁻¹. The current results from the uniform drift of a huge number of charge carriers along the conductor.
在金属导线内部，自由电子因热运动而高速随机运动，但这种随机运动不产生净电流。当施加电场时，电子获得一个与电场方向相反的微小平均速度，称为漂移速度 v，其数量级通常仅为 10⁻⁴ m/s。电流正是由大量载流子沿导体的有序漂移产生的。
4. Equation I = nAvq | 公式 I = nAvq
The current through a conductor can be expressed in terms of microscopic quantities: I = n A v q, where n is the number density of charge carriers (number per unit volume), A is the cross-sectional area of the conductor, v is the drift speed, and q is the charge on each carrier (e.g., for electrons, q = e = 1.60 × 10⁻¹⁹ C). This equation shows that for a given material and conductor at constant temperature, I ∝ v. Altering the cross‑section, doping level, or material changes n and therefore impacts current.
导体中的电流可用微观量表示为 I = n A v q，其中 n 是载流子数密度（单位体积内的数目），A 是导体横截面积，v 是漂移速率，q 是每个载流子的电荷量（如对于电子，q = e = 1.60 × 10⁻¹⁹ C）。该公式表明，在材料和温度不变时，I ∝ v。改变横截面积、掺杂水平或材料会影响 n，从而影响电流。
5. Potential Difference and Electromotive Force | 电势差与电动势
Potential difference (p.d.) between two points is the work done per unit charge to move a charge between those points. It is measured in volts (V). Electromotive force (e.m.f.) of a source is the total energy per unit charge supplied to the charges as they pass through the source. It is also measured in volts but refers to the source’s ability to drive current around a complete circuit. In an ideal source with no internal resistance, terminal p.d. equals e.m.f., but in real sources internal resistance causes a drop.
两点间的电势差（p.d.）是将单位电荷从一点移动到另一点所做的功，单位为伏特（V）。电源的电动势（e.m.f.）是电荷通过电源时每单位电荷获得的全部能量，单位也是伏特，但它表征电源驱动电流在全电路中循环的能力。在无内阻的理想电源中，路端电压等于电动势；但在实际电源中，内阻会引起电压降。
6. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance (R) is the ratio of potential difference across a component to the current flowing through it: R = V / I. The unit is the ohm (Ω). 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. This means V ∝ I, and the resistance remains constant. Components that obey this law are called ohmic conductors; those that do not are non‑ohmic (e.g., a filament lamp or a diode).
电阻（R）是元件两端电势差与流经它的电流之比：R = V / I，单位为欧姆（Ω）。欧姆定律指出，在温度保持不变的条件下，金属导体中的电流与其两端的电势差成正比，即 V ∝ I，电阻为定值。遵循该定律的元件称为欧姆导体，不遵循的则为非欧姆导体（例如灯丝灯泡或二极管）。
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 current. The resistance of a uniform wire of length L and cross‑sectional area A is given by R = ρL / A. The SI unit of resistivity is Ω m. Conductivity (σ) is the reciprocal of resistivity: σ = 1 / ρ. Metals like copper have very low resistivity (~1.7 × 10⁻⁸ Ω m), making them excellent conductors. Resistivity increases with temperature for metals, but decreases for semiconductors.
电阻率（ρ）是材料的内在属性，用来衡量其阻碍电流的强弱。长度为 L、横截面积为 A 的均匀导线电阻为 R = ρL / A，电阻率单位为 Ω m。电导率（σ）是电阻率的倒数：σ = 1 / ρ。铜等金属的电阻率很低（约 1.7 × 10⁻⁸ Ω m），是优良导体。金属的电阻率随温度升高而增大，而半导体则相反。
8. I-V Characteristics of Components | 元件的 I-V 特性
The current‑voltage graph is a powerful tool for identifying the behaviour of circuit elements. For a fixed resistor at constant temperature, the I-V graph is a straight line through the origin (ohmic). For a filament lamp, the graph curves as resistance increases with temperature. For a diode, current is extremely small in reverse bias and rises sharply in forward bias above a threshold voltage (~0.7 V for silicon). Knowing these shapes is essential for examination questions on component identification.
电流‑电压特性图是识别元件行为的有力工具。对于恒定温度下的固定电阻，I-V 图为一条过原点的直线（欧姆性）；对于灯丝灯泡，图线弯曲，因为温度升高导致电阻增大；对于二极管，反偏时电流极小，正偏且超过阈值电压（硅管约 0.7 V）后电流急剧上升。熟悉这些曲线形状是解答元件识别类考题的关键。
| Component | I-V Shape | Key Feature |
|---|---|---|
| Ohmic resistor | Straight line through origin | Constant resistance |
| Filament lamp | Curve flattening at high V | Resistance increases with T |
| Diode | Negligible current in reverse; steep rise in forward | Threshold voltage |
表格对照常见元件的 I-V 特性，帮你快速梳理。
9. Kirchhoff’s Current Law (KCL) | 基尔霍夫电流定律
KCL states that at any junction in an electrical circuit, the total current entering the junction equals the total current leaving the junction. This is a direct consequence of the conservation of charge. In equation form: Σ Iin = Σ Iout. When solving circuits, assign a direction to each current and treat currents entering as positive and leaving as negative (or vice‑versa), ensuring the algebraic sum is zero.
基尔霍夫电流定律指出，在电路的任一节点上，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体现。公式形式为 Σ I入 = Σ I出。解题时，为每个电流设定方向，可规定流入为正、流出为负（或相反），使代数和为零。
10. Kirchhoff’s Voltage Law (KVL) | 基尔霍夫电压定律
KVL states that the sum of the electromotive forces (e.m.f.) around any closed loop in a circuit is equal to the sum of the potential drops (IR) in that loop. This follows from the conservation of energy. In symbols: Σ ε = Σ I R. To apply KVL, pick a loop direction, assign positive signs to e.m.f.s that aid the traversal direction, and equate them to the sum of I R terms, taking care of signs for voltage rises and drops.
基尔霍夫电压定律指出，电路中任一闭合回路的电动势（e.m.f.）代数和等于该回路中各电阻上电压降（IR）的代数和。这是能量守恒的体现。公式为 Σ ε = Σ I R。应用时，选择回路方向，将相助的电动势记为正，并将其与各 IR 项的和相等，注意电压升和降的符号规则。
11. Power Dissipation in Circuits | 电路中的功率耗散
The power P dissipated in a circuit component is the rate at which it converts electrical energy into other forms. It is given by P = I V, where V is the potential difference across the component and I is the current through it. Using Ohm’s law, this can be rewritten for a resistor as P = I² R or P = V² / R. These expressions are vital for analysing energy transfer and for questions on heating effects, efficiency, and fuse rating.
电路中元件耗散的功率 P 是它把电能转化为其他形式能量的速率。公式为 P = I V，其中 V 是元件两端电压，I 是流经的电流。结合欧姆定律，对电阻元件可改写为 P = I² R 或 P = V² / R。这些形式在分析能量转换、热效应、效率和保险丝额定值问题时至关重要。
12. Practical Measurement of Current | 电流的实际测量
Current is measured using an ammeter, which must be connected in series with the component under test. An ideal ammeter has zero internal resistance so that it does not affect the circuit. In practice, digital multimeters have very low resistance. To measure current in a branch, break the circuit and insert the ammeter. Always start with the highest range to avoid damaging the meter. In examinations, you may be asked to draw circuits with ammeters or explain why they are placed in series.
电流使用安培表测量，安培表必须与被测元件串联。理想安培表内阻为零，以免影响电路。实际的数字万用表电阻非常小。要测量某支路的电流，需断开电路并串入安培表。务必从最高量程开始，防止损坏仪表。考试中可能要求绘制含有安培表的电路图，或解释其为何串联连接。
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