📚 Current Electricity: Key Points for Edexcel A-Level Physics | A-Level Edexcel物理：电流考点精讲
This article covers the essential concepts of current electricity for the Edexcel A-Level Physics syllabus. Students will learn about charge carriers, current, potential difference, resistance, Ohm’s law, resistivity, circuits, Kirchhoff’s laws, internal resistance, potential dividers, and more. Clear explanations, formulas, graphs, and practical insights are provided to help you master this topic.
本文涵盖Edexcel A-Level物理教学大纲中电流部分的核心概念。学生将学习电荷载子、电流、电势差、电阻、欧姆定律、电阻率、电路、基尔霍夫定律、内阻、分压器等内容。提供清晰的解释、公式、图表和实验见解，帮助您掌握该主题。
1. Electric Current and Charge | 电流与电荷
Electric current is the rate of flow of electric charge. In a metal conductor, the moving charges are negatively charged electrons, but conventionally the direction of current is taken as the direction in which positive charge carriers would move.
电流是电荷流动的速率。在金属导体中，运动的电荷是带负电的电子，但电流的约定方向是正电荷载子运动的方向。
I = ΔQ / Δt
where I is current in amperes (A), ΔQ is the charge in coulombs (C) passing a cross-section, and Δt is the time interval in seconds (s). The ampere is one of the base SI units.
其中I是电流，单位为安培(A)；ΔQ是通过横截面的电荷量，单位为库仑(C)；Δt是时间间隔，单位为秒(s)。安培是SI基本单位之一。
Charge is quantised: the charge on a proton is +e, and on an electron is -e, where e ≈ 1.60 × 10⁻¹⁹ C. The net charge in an isolated system is always conserved.
电荷是量子化的：质子的电荷为 +e，电子的电荷为 -e，其中 e ≈ 1.60 × 10⁻¹⁹ C。孤立系统中的净电荷总是守恒的。
2. Potential Difference and Electromotive Force | 电势差与电动势
The potential difference (p.d.) between two points is the energy transferred per unit charge moving between those points. It is defined by V = W/Q, where W is the work done or energy transferred in joules, and Q is the charge.
两点之间的电势差是单位电荷在两点间移动时传递的能量。定义为 V = W/Q，其中 W 是做功或能量转换，单位为焦耳，Q 是电荷量。
V = W / Q
Electromotive force (e.m.f., ε) of a source is the energy supplied by the source per unit charge passing through it. It is measured in volts, and represents the total energy per coulomb made available, including energy dissipated inside the source.
电源的电动势(ε)是电源每单位电荷通过时提供的能量。以伏特为单位，表示每库仑可用的总能量，包括在电源内部耗散的能量。
While p.d. is the energy transferred to a component per unit charge, e.m.f. is the energy supplied by the source per unit charge. When no current flows, the terminal p.d. equals the e.m.f.
电势差是每单位电荷传递给元件的能量，而电动势是电源每单位电荷提供的能量。在没有电流流动时，端电压等于电动势。
3. Ohm’s Law and I-V Characteristics | 欧姆定律与I-V特性
Ohm’s law states that for a metallic conductor at constant temperature, the current flowing is directly proportional to the potential difference across it. The constant ratio is the resistance R, defined as R = V/I.
欧姆定律指出，对于恒温下的金属导体，流过导体的电流与它两端的电势差成正比。该恒定比值即为电阻R，定义为 R = V/I。
R = V / I
A component that obeys Ohm’s law is called an ohmic conductor. Its I-V graph is a straight line through the origin. A filament lamp is non-ohmic: its resistance increases with current because the heating raises temperature, increasing the metal’s resistivity. A semiconductor diode has very low resistance in one direction (forward bias) and very high resistance in the reverse direction, showing a non-linear characteristic.
满足欧姆定律的元件称为欧姆导体，其I-V图线是一条通过原点的直线。灯丝是非欧姆的：其电阻随电流增大而增大，因为发热使温度升高，金属的电阻率增加。半导体二极管在一个方向（正向偏置）电阻极低，在反向偏置时电阻极大，呈非线性特性。
| Component 元件 | I-V Relationship I-V关系 | Graph Shape 图形 |
|---|---|---|
| Ohmic conductor (固定电阻) | I ∝ V, R constant | Straight line through origin 过原点直线 |
| Filament lamp 灯丝 | R increases with V (heating) | Curve flattening out 曲线变平 |
| Semiconductor diode 二极管 | Conducts in one direction only | Very steep after threshold voltage 阈值后极陡 |
4. Resistance and Resistivity | 电阻与电阻率
The resistance of a uniform wire depends on its length L, cross-sectional area A, and the material’s resistivity ρ. Resistivity is a material property that quantifies how strongly the material opposes current flow. The formula is R = ρL/A.
一根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。电阻率是量化材料阻碍电流强弱的性质。公式为 R = ρL/A。
R = ρL / A
Resistivity ρ has units Ω·m. For metals, resistivity increases with temperature because increased lattice vibrations scatter electrons more frequently. For semiconductors, resistivity often decreases with temperature as more charge carriers become available. A superconductor has zero resistivity below its critical temperature; once a current is set up, it persists without any p.d.
电阻率ρ的单位是Ω·m。对于金属，电阻率随温度升高而增大，因为晶格振动加剧使电子散射更频繁。对于半导体，由于更多载流子被激发，电阻率常随温度升高而降低。超导体在临界温度以下电阻率为零；一旦建立电流，无需电势差即可持续流动。
5. Drift Velocity | 漂移速度
In a conductor, free electrons move randomly at high speeds but have a slow average drift velocity when an electric field is applied. The current I is related to the drift velocity v by the equation I = nAvq, where n is the number density of charge carriers (m⁻³), A is cross-sectional area (m²), and q is the charge on each carrier (q = e for electrons, 1.60 × 10⁻¹⁹ C).
在电场作用下，导体中自由电子无规则高速运动，同时具有一个缓慢的平均漂移速度。电流I与漂移速度v的关系为 I = nAvq，其中 n 是载流子数密度(m⁻³)，A 是横截面积(m²)，q 是每个载流子的电荷（电子为 e = 1.60 × 10⁻¹⁹ C）。
I = nAvq
For a given current and material, reducing the cross-sectional area increases the drift velocity. In semiconductor devices, drift velocity considerations are essential for understanding switching speeds.
对于给定的电流和材料，减小横截面积会增大漂移速度。在半导体器件中，理解漂移速度对分析开关速度至关重要。
6. Electrical Power and Energy | 电功率与电能
Power P is the rate of energy transfer. For any electrical component, P = IV, where V is the potential difference across the component and I is the current through it. Using Ohm’s law for resistive loads, we also have P = I²R = V²/R.
电功率P是能量转换的速率。对任何电气元件，P = IV，V是元件两端的电势差，I是通过元件的电流。对于电阻性负载，结合欧姆定律可得 P = I²R = V²/R。
P = IV = I²R = V²/R
Energy transferred is E = Pt. In households, electrical energy is often measured in kilowatt-hours (kWh), where 1 kWh = 3.6 × 10⁶ J. Understanding power dissipation is important for selecting components with suitable power ratings to prevent overheating.
传递的能量 E = Pt。在家庭中，电能常用千瓦时(kWh)计量，1 kWh = 3.6 × 10⁶ J。了解功率耗散有助于选择合适额定功率的元件，防止过热。
7. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the current is the same everywhere, and the total resistance R_total is the sum of individual resistances: R_total = R₁ + R₂ + R₃ + … . The sum of the p.d.s across each component equals the e.m.f. of the source.
在串联电路中，各处电流相等，总电阻 R_total 等于各电阻之和：R_total = R₁ + R₂ + R₃ + …。各元件两端电势差之和等于电源的电动势。
R_total (series) = R₁ + R₂ + R₃
In a parallel circuit, the total current splits between branches; the sum of the branch currents equals the total current entering the junction. The total resistance for resistors in parallel is given by 1/R_total = 1/R₁ + 1/R₂ + … . The p.d. across each parallel branch is the same.
在并联电路中，总电流在各支路中分配；各支路电流之和等于流入节点的总电流。并联电阻的总电阻满足 1/R_total = 1/R₁ + 1/R₂ + …。每个并联支路两端的电势差相同。
1/R_total (parallel) = 1/R₁ + 1/R₂
Current dividers and voltage dividers are direct consequences of parallel and series combinations. These ideas are used extensively in sensor circuits.
分流器和分压器正是并联和串联组合的直接结果。这些思路广泛应用于传感器电路。
8. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s first law (junction rule) states that the total current entering a junction equals the total current leaving it: ΣI_in = ΣI_out. This is a consequence of charge conservation.
基尔霍夫第一定律（节点定律）指出，流入节点的总电流等于流出节点的总电流：ΣI_in = ΣI_out。这是电荷守恒的结果。
ΣI_in = ΣI_out
Kirchhoff’s second law (loop rule) states that in any closed loop of a circuit, the sum of the e.m.f.s equals the sum of the p.d.s across the resistances: Σε = ΣIR. This follows from energy conservation.
基尔霍夫第二定律（回路定律）指出，在电路的任何闭合回路中，电动势之和等于电阻上电势差之和：Σε = ΣIR。这是能量守恒的结果。
Σε = ΣIR
When solving complex circuits, assign current directions, apply the junction rule to reduce unknowns, and apply the loop rule for each independent loop. Solve the resulting simultaneous equations to find unknown currents and voltages.
在解决复杂电路时，先假设电流方向，用节点定律减少未知数，再对每个独立回路应用回路定律。解所得联立方程组，求出未知电流和电压。
9. Internal Resistance | 内阻
A real power source (battery, cell) has an internal resistance r. When a current I flows, the terminal p.d. V across the source is less than its e.m.f. ε: V = ε – Ir. The ‘lost volts’ Ir represent the energy per coulomb wasted inside the source as heat.
实际电源（电池）具有内阻r。当有电流I时，电源的端电压V小于其电动势ε：V = ε – Ir。’损失的电压’ Ir表示每库仑在电源内部以热量形式浪费的能量。
V = ε – Ir
The relationship ε = I(R + r) can be written for the whole circuit, where R is the external load resistance. By measuring terminal p.d. for different currents and plotting V against I, the gradient gives -r and the y-intercept gives ε. This experiment is a required practical.
对于完整电路，可写为 ε = I(R + r)，R是外接负载电阻。通过测量不同电流下的端电压，作V-I图线，其截距为ε，斜率的绝对值为内阻r。该实验是必做实验。
10. Potential Dividers | 分压器
A potential divider uses two resistors in series to produce a fraction of the input voltage. The output voltage across resistor R₂ is V_out = V_in × (R₂ / (R₁ + R₂)). This allows precise control of voltage without a variable power supply.
分压器用两个串联电阻产生输入电压的一部分。电阻R₂两端的输出电压为 V_out = V_in × (R₂ / (R₁ + R₂))。这样无需可调电源就能精确控制电压。
V_out = V_in × (R₂ / (R₁ + R₂))
Replacing one fixed resistor with a light-dependent resistor (LDR) or a thermistor creates a sensor circuit. For example, in a temperature-sensing divider, the thermistor’s resistance changes with temperature, altering V_out. These circuits are used in automatic lighting, thermostats, and many control applications.
用一个光敏电阻(LDR)或热敏电阻替换其中一个固定电阻，可构成传感器电路。例如，在温感分压器中，热敏电阻的阻值随温度变化，从而改变V_out。这类电路用于自动照明、恒温器和多种控制应用。
11. Experimental Determination of Resistivity and Internal Resistance | 电阻率与内阻的实验测定
Resistivity experiment: Measure the resistance R of a wire for different lengths L, keeping the temperature constant. The cross-sectional area A is found by measuring the diameter d with a micrometer, then A = π(d/2)². Plot R against L; the gradient equals ρ/A, so resistivity ρ = gradient × A. Main sources of uncertainty include zero error of the micrometer, heating of the wire, and contact resistance at connections.
电阻率实验：在不同长度L下测量导线的电阻R，保持恒温。用千分尺测量直径d，得到横截面积A = π(d/2)²。作R-L图，斜率为ρ/A，因此电阻率ρ = 斜率 × A。主要的不确定度来源包括千分尺的零误差、导线发热以及连接处的接触电阻。
Internal resistance experiment: Connect a cell to a variable resistor (or several fixed resistors) and measure the terminal p.d. V and current I. Use a voltmeter in parallel with the cell and an ammeter in series. Plot V against I; the equation V = ε – Ir gives a straight line with gradient -r and y-intercept ε. Using a switch to take readings quickly minimises heating effects. Repeating readings and using small intervals improves accuracy.
内阻实验：将电池与可变电阻（或多个固定电阻）连接，测量端电压V和电流I。电压表并联在电池两端，电流表串联。作V-I图线；由V = ε – Ir得一条直线，斜率为-r，y轴截距为ε。使用开关快速读数可减小发热效应。重复读数和使用小间隔可提高准确度。
12. Summary of Key Formulas and Graphs | 关键公式与图表总结
The central equations for current electricity, all expressed in SI units, are collected here for quick revision. Always ensure you can derive, rearrange, and apply them to unfamiliar contexts, such as designing sensor circuits or analysing compound circuits.
以下汇总了电流的核心公式（均使用SI单位），便于快速复习。请确保能够推导、变形并应用于陌生情境，比如设计传感器电路或分析复合电路。
| Formula 公式 | Description 说明 |
|---|---|
| I = ΔQ/Δt | Current = charge / time |
| V = W/Q | Potential difference = work / charge |
| R = V/I | Resistance (Ohm’s law for constant R) |
| R = ρL/A | Resistance in terms of resistivity |
| I = nAvq | Drift velocity relation |
| P = IV = I²R = V²/R | Power in electrical circuits |
| V = ε – Ir | Terminal p.d. with internal resistance |
| ΣI_in = ΣI_out | Kirchhoff’s 1st law (junction) |
| Σε = ΣIR | 更多咨询请联系16621398022（同微信）
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