Electricity | 电学 - aleveler.com

📚 Electricity | 电学

This article provides a comprehensive review of the AQA A-Level Physics topic “Electricity”. It covers electric current, potential difference, resistance, resistivity, circuit analysis, Kirchhoff’s laws, EMF and internal resistance, and practical applications. Each concept is explained in both English and Chinese with exam-focused clarity.

本文系统梳理 AQA A-Level 物理“电学”板块的核心内容，涵盖电流、电势差、电阻、电阻率、电路分析、基尔霍夫定律、电动势与内阻，以及实际应用。每个概念均以中英双语呈现，紧扣考纲与考点。

1. Electric Current & Charge Conservation | 电流与电荷守恒

Electric current is defined as the rate of flow of charge. In metallic conductors, charge is carried by free electrons. The equation is I = ΔQ / Δt, where I is current in amperes (A), Q is charge in coulombs (C), and t is time in seconds (s).

电流定义为电荷流动的速率。在金属导体中，电荷由自由电子携带。其表达式为 I = ΔQ / Δt，其中 I 为电流，单位安培（A）；Q 为电荷量，单位库仑（C）；t 为时间，单位秒（s）。

I = ΔQ / Δt

Charge conservation requires that at any junction in a circuit, the total current entering equals the total current leaving. This is the foundation of Kirchhoff’s first law and is essential for analyzing complex circuits.

电荷守恒要求：电路中任一节点处，流入的总电流等于流出的总电流。这是基尔霍夫第一定律的基础，是分析复杂电路的关键。

One ampere equals one coulomb per second.
一安培等于每秒通过一库仑电荷。
Conventional current flows from positive to negative while electrons flow in the opposite direction.
传统电流方向从正极流向负极，而电子流动方向相反。
In a steady state, the current is the same at every point in a series circuit.
在稳定状态下，串联电路中各点的电流相同。

2. Potential Difference & Work Done | 电势差与做功

Potential difference (p.d.) is the energy transferred per unit charge between two points in a circuit. It is defined as V = W / Q, where W is energy in joules (J) and Q is charge in coulombs (C). The unit of p.d. is the volt (V), equal to one joule per coulomb.

电势差是电路中两点之间单位电荷所转移的能量。其定义为 V = W / Q，其中 W 为能量（焦耳，J），Q 为电荷量（库仑，C）。电势差的单位是伏特（V），1 伏特等于 1 焦耳每库仑。

V = W / Q

It is crucial to distinguish p.d. from EMF. The p.d. across a component represents the electrical energy converted to other forms (e.g., heat, light) per unit charge. EMF, discussed later, is the energy supplied to each coulomb by a source.

必须区分电势差与电动势。元件两端的电势差表示单位电荷在该元件上由电能转化为其他形式能量（如热能、光能）的多少。而电动势将在后文讨论，它是电源提供给每库仑电荷的能量。

3. Resistance & Ohm’s Law | 电阻与欧姆定律

Resistance is the opposition to the flow of electric current. It is defined as the ratio of p.d. to current: R = V / I. The unit of resistance is the ohm (Ω), where 1 Ω = 1 V A⁻¹.

电阻是对电流流动的阻碍。其定义为电势差与电流之比：R = V / I。电阻单位为欧姆（Ω），且 1 Ω = 1 V A⁻¹。

R = V / I

Ohm’s law states that for a metallic conductor at constant temperature, the current is directly proportional to the p.d. across it. This means the resistance remains constant under fixed physical conditions.

欧姆定律指出：对于温度恒定的金属导体，通过导体的电流与其两端的电势差成正比。这意味着在固定物理条件下，电阻保持恒定。

Ohmic conductors obey Ohm’s law at constant temperature.
欧姆导体在恒温下遵守欧姆定律。
Non-ohmic components, such as filament lamps and diodes, have a changing resistance.
非欧姆元件（如白炽灯和二极管）的电阻会发生变化。
Resistance depends on length, cross-sectional area, temperature and material.
电阻取决于长度、横截面积、温度和材料。

4. Resistivity & Conductivity | 电阻率与导电性

Resistivity ρ is an intrinsic property of a material that quantifies how strongly it opposes current flow. It is given by ρ = R·A / L, where R is resistance, A is cross-sectional area (m²), and L is length (m). The unit of resistivity is ohm-metre (Ω·m).

电阻率 ρ 是材料本身的性质，用于量化材料对电流的阻碍强度。其表达式为 ρ = R·A / L，其中 R 为电阻，A 为横截面积（m²），L 为长度（m）。电阻率的单位是欧姆·米（Ω·m）。

ρ = R·A / L

For a wire of length L and uniform cross-sectional area A, resistance increases with length and decreases with area. This is why copper cables used in power transmission are thick: to reduce resistance and hence energy loss.

对于长度为 L、横截面积均匀为 A 的导线，电阻随长度增加而增大，随横截面积增大而减小。这就是输电用铜缆较粗的原因：减小电阻从而减少能量损耗。

Material	Resistivity/Ω·m (approx.)
Copper	1.7 × 10⁻⁸
Constantan	4.9 × 10⁻⁷
Silicon (semiconductor)	~ 6.4 × 10²

For a metallic conductor, resistivity increases with temperature because lattice ions vibrate more vigorously, scattering electrons more frequently.

对金属导体而言，电阻率随温度升高而增大，因为晶格离子振动加剧，更频繁地散射电子。

5. I–V Characteristics | I–V 特性曲线

The I–V characteristic of a component is a graph showing how the current through it varies with the p.d. across it. Different components have distinctive I–V graphs.

元件的 I–V 特性曲线是描述通过其电流随两端电势差变化的图像。不同元件具有各自典型的 I–V 曲线。

Ohmic conductor: a straight line through the origin; the gradient gives 1/R.
欧姆导体：过原点的直线，斜率为 1/R。
Filament lamp: as current increases, temperature rises, resistance increases, causing the curve to flatten.
白炽灯：电流增大时温度升高，电阻增大，曲线趋于平缓。
Semiconductor diode: negligible current in reverse bias; rapidly increasing current after a threshold forward voltage (~0.7 V for silicon).
半导体二极管：反向偏置时电流几乎为零；正向电压超过阈值（硅约 0.7 V）后电流快速增大。

When interpreting I–V graphs, remember that the ratio V/I gives resistance at a specific point, while the gradient at that point gives the differential resistance ΔV/ΔI. These two are equal only for ohmic conductors.

在解读 I–V 曲线时需注意：某点的 V/I 比值给出该点的电阻，而该点的切线斜率给出微分电阻 ΔV/ΔI。只有欧姆导体两者相同。

6. Series & Parallel Circuits | 串联与并联电路

In series circuits, components are connected end-to-end, so the same current flows through each component. The total p.d. is the sum of individual p.d.s, and the total resistance is the sum of individual resistances.

在串联电路中，元件首尾相接，因此通过每个元件的电流相同。总电压等于各元件电压之和，总电阻等于各元件电阻之和。

R_total = R₁ + R₂ + R₃ + …

In parallel circuits, components are connected across the same two points. Each component experiences the same p.d., and the total current is the sum of the branch currents. The total resistance is given by:

在并联电路中，各元件连接在相同两点之间，每个元件两端电压相同，总电流等于各支路电流之和。总电阻满足：

1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + …

It is important to note that the total resistance in a parallel combination is always smaller than the smallest individual resistance. Adding more parallel branches always decreases the total resistance.

需特别注意：并联组合的总电阻总是小于其中最小的那个电阻。并联支路越多，总电阻越小。

7. 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. This is a direct 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。这是电荷守恒的直接推论。

Kirchhoff’s second law (loop rule) states that the algebraic sum of the EMFs around any closed loop equals the algebraic sum of the p.d.s across the components in that loop. This follows from energy conservation.

基尔霍夫第二定律（回路定律）指出：沿任一闭合回路，电动势的代数总和等于各元件上电压的代数总和。这是能量守恒的体现。

Σ EMF = Σ IR (around a closed loop)

When applying Kirchhoff’s laws, always assign a conventional current direction first. If the final value is negative, the actual direction is the opposite of your assumption.

应用基尔霍夫定律时，先设定一个传统电流方向。若最终计算值为负，说明实际方向与假设方向相反。

8. EMF & Internal Resistance | 电动势与内阻

The electromotive force (EMF) ε of a source is the electrical energy transferred to each unit of charge passing through the source. It is measured in volts. A real battery has an internal resistance r, causing a loss of p.d. inside the battery when current flows.

电源的电动势 ε 是电源向通过其的每一单位电荷提供的电能，单位是伏特。实际电池具有内阻 r，当电流流过时，电池内部会产生电压损失。

The terminal p.d. V across a battery is given by:

电池两端的端电压 V 由下式给出：

V = ε − Ir

When charging a battery, the terminal p.d. becomes V = ε + Ir. When the external resistance R is connected, the current can be calculated as:

给电池充电时，端电压变为 V = ε + Ir。当接入外部电阻 R 时，电流可表示为：

I = ε / (R + r)

The maximum power transfer to the load occurs when R = r. This is known as the maximum power transfer theorem and is a common exam question.

当负载电阻 R 等于内阻 r 时，负载获得最大功率。这称为最大功率传输定理，是常见考点。

9. Potential Divider | 电势分压器

A potential divider uses two or more resistors in series to produce a desired output voltage from a larger input voltage. The output voltage across one resistor is proportional to its resistance fraction of the total.

电势分压器利用两个或多个串联电阻，从一个较大的输入电压中产生所需的输出电压。某一电阻两端的输出电压与它在总电阻中所占比例成正比。

V_out = V_in × R₂ / (R₁ + R₂)

Potential dividers are used in sensor circuits. For example, a thermistor (temperature-dependent resistor) in a potential divider produces a changing output voltage that can be used to trigger a heating or cooling system. Similarly, a light-dependent resistor (LDR) is used in automatic lighting circuits.

分压器常用于传感器电路。例如，热敏电阻（随温度变化的电阻）在分压器中产生随温度变化的输出电压，可用于触发热水器或冷却系统。类似地，光敏电阻（LDR）可用于自动照明电路。

When a thermistor heats up, its resistance decreases, so the p.d. across it decreases.
热敏电阻受热时阻值减小，因此其两端电压降低。
When an LDR is illuminated, its resistance decreases, increasing the p.d. across the fixed resistor.
光敏电阻受光照时阻值减小，导致固定电阻两端的电压升高。

10. Potentiometer & Practical Applications | 电位计与实际应用

A potentiometer is a variable potential divider. It consists of a resistive track and a sliding contact. It can be used to continuously vary the p.d. supplied to a circuit component, such as adjusting the brightness of a lamp or the speed of a motor.

电位计是一种可变分压器，由电阻轨道和滑动触点组成。它可用于连续调节电路中元件两端的电压，例如调节灯泡亮度或电机转速。

In a balanced potentiometer circuit, when the galvanometer shows zero deflection, the p.d. across a known length of the slide wire equals the EMF being compared. This allows precise measurement of an unknown EMF without drawing current from the source.

在平衡的电位计电路中，当检流计读数为零时，滑线某段长度对应的电压等于待测电动势。这可以在不从电源取电流的情况下精确测量未知电动势。

Usage	Key circuit component
Temperature sensor	Thermistor + potential divider
Light sensor	LDR + potential divider
EMF measurement	Balanced potentiometer
Variable lamp brightness	Rheostat / potentiometer

All electrical components in real life have limitations: fuses protect against overcurrent, circuit breakers provide resettable protection, and earthing prevents dangerous voltages on metal casings. Understanding electricity at this level helps you interpret how these safety devices function.

现实中所有电气元件都有其限流与保护机制：保险丝防止过流，断路器提供可复位保护，接地可防止金属外壳出现危险电压。从这一层面理解电学，有助于你明白这些安全装置的工作原理。

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Electricity | 电学