Resistance Revision for IGCSE WJEC Physics | IGCSE WJEC 物理：电阻考点精讲

📚 Resistance Revision for IGCSE WJEC Physics | IGCSE WJEC 物理：电阻考点精讲

Understanding resistance is essential for mastering electric circuits in the IGCSE WJEC Physics syllabus. This article covers all the key concepts, from the definition of resistance and Ohm’s law to the factors that affect it, how resistors combine, and the behaviour of special components like thermistors and LDRs. Each section presents paired English and Chinese explanations to support both language learners and international students.

理解电阻是掌握 IGCSE WJEC 物理电学部分的核心。本文涵盖电阻的定义、欧姆定律、影响电阻的因素、电阻器的组合方式以及热敏电阻和光敏电阻等特殊元件的特性。每一部分都配有中英文对照讲解，帮助双语学习者和国际学生牢固掌握考点。

1. What is Resistance? | 什么是电阻？

Resistance is a measure of how much a component opposes the flow of electric current. The greater the resistance, the smaller the current for a given potential difference. Resistance is caused by collisions between the free electrons moving through a conductor and the vibrating positive ions of the metal lattice.

电阻衡量的是电路中某个元件对电流的阻碍程度。电阻越大，在给定电压下电流就越小。电阻的成因是移动中的自由电子与金属晶格中振动的正离子之间的碰撞。

Resistance is defined by the equation R = V / I, where R is the resistance in ohms (Ω), V is the potential difference in volts (V), and I is the current in amperes (A). One ohm is the resistance when a potential difference of one volt produces a current of one ampere.

电阻的定义式为 R = V / I，其中 R 是电阻（单位：欧姆 Ω），V 是电势差（单位：伏特 V），I 是电流（单位：安培 A）。当一伏特的电压使电路中产生一安培的电流时，该元件的电阻就是一欧姆。

Conductance is the reciprocal of resistance, but for IGCSE, the focus is always on resistance and how it limits current. Good conductors have very low resistance, while insulators have extremely high resistance.

电导是电阻的倒数，但在 IGCSE 阶段我们主要关注电阻及其如何限制电流。良导体电阻极低，而绝缘体的电阻则极高。

2. Ohm’s Law | 欧姆定律

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 relationship is written as V = I × R, or rearranged as I = V / R.

欧姆定律指出，对于恒温下的金属导体，通过它的电流与导体两端的电势差成正比。这个关系写作 V = I × R，或变形为 I = V / R。

A component that obeys Ohm’s law is called an ohmic conductor. Its current–voltage (I–V) graph is a straight line passing through the origin, showing a constant resistance. However, many components, such as filaments and semiconductors, do not follow Ohm’s law under all conditions; these are non‑ohmic conductors.

遵循欧姆定律的元件称为欧姆导体。其电流–电压（I–V）图像是一条过原点的直线，表明电阻恒定。然而许多元件，如灯丝和半导体，在一定条件下并不遵循欧姆定律，它们是非欧姆导体。

Always remember that Ohm’s law is only valid if temperature (and other physical conditions) remain constant. When current increases and heats up the wire, the resistance changes, and the I–V graph curves.

必须牢记：欧姆定律仅在温度（及其他物理条件）保持不变时才成立。当电流增大使导线发热时，电阻会改变，I–V 图就会弯曲。

3. Factors Affecting Resistance | 影响电阻的因素

The resistance of a wire depends on four main factors: length, cross‑sectional area, the material itself, and temperature. Understanding these factors helps in designing circuits and choosing the right components.

导线的电阻主要取决于四个因素：长度、横截面积、材料本身以及温度。了解这些因素有助于电路设计和元件的合理选用。

Length (L): Resistance is directly proportional to the length of the conductor. If the length doubles, the resistance doubles, because the electrons must travel twice as far and encounter twice as many collisions with ions.

长度（L）：电阻与导体长度成正比。若长度加倍，电阻也加倍，因为电子需要行进两倍的距离，与离子的碰撞次数也增加一倍。

Cross‑sectional area (A): Resistance is inversely proportional to the area. A thicker wire has more space for the electrons to flow, so the resistance is lower. If the area doubles, the resistance halves.

横截面积（A）：电阻与横截面积成反比。较粗的导线为电子流动提供了更大的空间，因而电阻更小。横截面积加倍时，电阻减半。

Material: Every material has a characteristic resistivity (ρ). Good conductors like copper have very low resistivity, while alloys like nichrome have higher resistivity, making them useful for heating elements.

材料：每种材料都有特定的电阻率（ρ）。铜等良导体的电阻率极低，而镍铬合金等合金的电阻率较高，适合用作加热元件。

Temperature: For a metallic conductor, resistance increases with temperature. Heating causes the positive ions in the lattice to vibrate more vigorously, increasing the frequency of collisions and making it harder for electrons to pass through. For semiconductors and thermistors, resistance typically decreases as temperature rises.

温度：对于金属导体，电阻随温度升高而增大。升温使晶格中的正离子振动加剧，碰撞频率增加，电子更难通过。对于半导体和热敏电阻，电阻通常随温度升高而减小。

4. Resistivity and the Resistance Formula | 电阻率与电阻公式

The resistance of a uniform conductor can be calculated using the formula R = ρL / A, where ρ is the resistivity of the material in ohm‑metres (Ω⋅m), L is the length in metres (m), and A is the cross‑sectional area in square metres (m²).

均匀导体的电阻可用公式 R = ρL / A 计算，其中 ρ 是材料的电阻率（单位：欧姆·米 Ω⋅m），L 是长度（单位：米 m），A 是横截面积（单位：平方米 m²）。

Resistivity is a property of the material itself and does not depend on the dimensions of the sample. For IGCSE WJEC, you are not required to perform complex calculations with resistivity, but you should understand the proportionalities: R ∝ L and R ∝ 1/A.

电阻率是材料本身的属性，与试样的尺寸无关。IGCSE WJEC 不要求进行复杂的电阻率计算，但你需要理解比例关系：R ∝ L 和 R ∝ 1/A。

This formula explains why long, thin wires have high resistance, and short, thick wires have low resistance. It also shows why you should use thick cables for high‑current appliances to reduce energy lost as heat.

该公式解释了为什么长而细的导线电阻大，而短而粗的导线电阻小。这也说明了为什么大功率电器需使用粗电缆，以减少热损耗。

5. Resistors in Series | 电阻的串联

When resistors are connected in series, the same current passes through each resistor, but the total potential difference is shared across them. The total (equivalent) resistance R_total is simply the sum of the individual resistances.

电阻串联时，通过每个电阻的电流相同，但总电压在各电阻间分配。总（等效）电阻 R_total 等于各电阻之和。

R_total = R₁ + R₂ + R₃ + …

Adding more resistors in series always increases the total resistance because the current must flow through each one in turn, and the conducting path becomes effectively longer.

串联更多的电阻总会使总电阻增加，因为电流必须依次流过每一个电阻，导电通路相当于变长了。

Series circuits are often used when you want to share voltage, for example in potential divider circuits or when connecting several low‑voltage bulbs to a higher‑voltage supply, provided the currents match.

串联电路常用于需要分压的场合，例如分压器电路，或将几个低压灯泡接到电压较高的电源上（前提是电流匹配）。

6. Resistors in Parallel | 电阻的并联

When resistors are connected in parallel, the potential difference across each resistor is the same, but the total current is divided among the branches. The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.

电阻并联时，每个电阻两端的电压相同，但总电流分配于各支路。总电阻的倒数等于各电阻倒数之和。

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …

For the special case of two parallel resistors, the total resistance can be found using the product‑over‑sum formula: R_total = (R₁ × R₂) / (R₁ + R₂). However, it is safer to use the reciprocal formula to avoid mistakes, especially with three or more resistors.

对于两个电阻并联的特殊情况，可用“积除以和”公式：R_total = (R₁ × R₂) / (R₁ + R₂)。但对于三个或以上电阻，最好使用倒数求和公式以避免错误。

Adding more resistors in parallel decreases the total resistance because additional paths are created for the current. The total resistance of a parallel combination is always less than the smallest individual resistance.

并联更多电阻会降低总电阻，因为为电流提供了额外的通路。并联组合的总电阻始终小于其中最小的单个电阻。

7. Current–Voltage Characteristics | 电流–电压特性

The I–V characteristic of a component is a graph showing how the current through it varies with the applied potential difference. The shape of the graph reveals whether the component is ohmic or non‑ohmic, and how its resistance changes.

元件的 I–V 特性图反映了通过它的电流如何随端电压变化。图形的形状可以表明该元件是欧姆导体还是非欧姆导体，以及其电阻如何变化。

Ohmic conductor (e.g., a metal wire at constant temperature): straight line through origin, constant gradient. Resistance is constant, equal to 1/gradient.

欧姆导体（如恒温下的金属导线）：过原点的直线，斜率恒定。电阻恒定，等于斜率的倒数。

Filament lamp: as the current increases, the wire heats up, and resistance rises. The I–V graph curves, with a decreasing gradient. At higher voltages, the line becomes less steep, showing a larger resistance.

白炽灯丝：电流增大导致灯丝发热，电阻上升。I–V 图弯曲，斜率减小。电压较高时，曲线变得更平缓，表明电阻变大。

Diode: a diode allows current in one direction only. The forward I–V graph shows almost no current until the threshold voltage (≈0.6 V for silicon) is reached, after which current rises steeply. In the reverse direction, current is negligible (except at very high reverse breakdown).

二极管：只能单向导通。正向 I–V 图显示，在达到阈值电压（硅管约为 0.6 V）之前几乎没有电流，随后电流急剧上升。反向时电流几乎为零（极高反向击穿电压除外）。

You should be able to sketch and interpret these graphs and link the shape to resistance changes. In a filament lamp, the gradient at any point gives the reciprocal of the resistance at that voltage.

你需要能够绘制并解释这些图像，并将形状与电阻变化联系起来。对于灯丝，曲线上任一点的斜率等于该电压下电阻的倒数。

8. Variable Resistors and Potentiometers | 可变电阻与电位器

A variable resistor (rheostat) allows you to change the resistance in a circuit manually. It typically consists of a coil of resistance wire and a sliding contact. Moving the slider changes the length of wire in the circuit, thus varying the resistance.

可变电阻（变阻器）可以手动改变电路中的电阻。它通常由一个电阻丝线圈和一个滑动触点构成。移动滑块可改变接入电路中的导线长度，从而改变电阻。

Variable resistors are used for dimming lights, controlling volume, adjusting motor speed, and acting as potential dividers. In a potential divider arrangement, the variable resistor is connected across a fixed voltage, and the output is taken between the wiper and one end.

可变电阻用于调光、音量控制、电机调速以及充当分压器。在分压器配置中，可变电阻接在一个固定电压上，从滑动端与一端之间取出输出电压。

At IGCSE level, you should be able to explain how turning a knob or sliding a contact alters the balance of voltage across components and how this can make a lamp brighter or dimmer.

在 IGCSE 水平，你需要能够解释旋钮或滑片如何改变各元件上的电压分配，以及如何使灯泡变亮或变暗。

9. Thermistors | 热敏电阻

A thermistor is a temperature‑dependent resistor. There are two types: negative temperature coefficient (NTC) thermistors, whose resistance decreases as temperature rises, and positive temperature coefficient (PTC) thermistors, whose resistance increases with temperature. NTC thermistors are the most commonly examined.

热敏电阻是一种对温度敏感的电阻器。有两种类型：负温度系数（NTC）热敏电阻，其电阻随温度升高而减小；正温度系数（PTC）热敏电阻，电阻随温度升高而增大。NTC 热敏电阻最常见于考试中。

In a typical sensing circuit, a thermistor is placed in a potential divider with a fixed resistor. When the temperature changes, the share of the voltage across the thermistor also changes. This voltage can be used to trigger an alarm or switch a heating system on or off.

在典型的传感电路中，热敏电阻与一个固定电阻组成分压器。当温度变化时，热敏电阻两端的电压份额也随之改变。此电压可用于触发告警或控制加热系统的开关。

NTC thermistors are widely used in electronic thermometers, fire alarms, and temperature‑controlled circuits. The graph of resistance against temperature is a curve that drops steeply at lower temperatures and flattens out as temperature rises further.

NTC 热敏电阻广泛应用于电子温度计、火灾报警器和温控电路。其电阻–温度关系曲线在低温时陡降，随温度进一步升高而趋于平缓。

10. Light‑Dependent Resistors (LDRs) | 光敏电阻

A light‑dependent resistor (LDR) changes its resistance based on the intensity of light falling on it. In darkness, an LDR has a very high resistance (often several megaohms); in bright light, its resistance drops significantly (to a few hundred ohms or less).

光敏电阻（LDR）的电阻随照射光强度的变化而变化。黑暗中，LDR 的电阻极高（常达数兆欧）；在强光下，其电阻会大幅下降（至几百欧或更低）。

LDRs are made from semiconductor materials such as cadmium sulphide. When photons hit the semiconductor, they provide enough energy to release more charge carriers, so conductance increases and resistance falls.

LDR 由硫化镉等半导体材料制成。光子撞击半导体时，能提供足够的能量释放出更多载流子，因此电导增加、电阻减小。

Typical applications include street lights that switch on automatically at dusk, burglar alarm sensors, and camera light meters. In a potential divider circuit with a fixed resistor, the voltage across the LDR changes according to the light level, which can then control a transistor or relay.

典型应用包括：黄昏自动亮起的路灯、防盗报警传感器和相机测光表。在与固定电阻构成的分压电路中，LDR 两端的电压随光照水平变化，进而可控制晶体管或继电器。

11. Practical Investigations | 实验探究

Investigating the resistance of a wire: You will often be asked to describe an experiment to find how the resistance of a wire depends on its length or thickness. Set up a circuit with a power supply, an ammeter in series, and a voltmeter in parallel with the wire under test. Vary the length (by moving a crocodile clip) or use different diameters, record V and I, and calculate R = V/I for each trial. Keep the current small to minimise heating effects.

探究导线电阻：常被要求描述一个实验，以找出导线电阻如何随长度或粗细变化。连接一个包含电源、串联电流表和并联在待测导线两端电压表的电路。通过移动鳄鱼夹改变长度，或使用不同直径的导线，记录 V 和 I，对每次测试计算 R = V/I。保持电流较小，以减小发热影响。

Plotting a graph of R against L should yield a straight line through the origin if temperature is constant, confirming R ∝ L. A graph of R against 1/A should also be linear, confirming R ∝ 1/A.

若温度恒定，绘制 R–L 图应得到一条过原点的直线，证实 R ∝ L。绘制 R–1/A 图也应呈线性，证实 R ∝ 1/A。

Investigating I–V characteristics: Use a similar setup but include a variable resistor or potential divider to vary the applied voltage smoothly. Take readings for both directions (reverse the connections) for a diode. For a filament lamp, increase voltage in small steps, allowing the lamp to warm up.

探究 I–V 特性：使用类似的装置，但加入可变电阻或分压器以平稳改变外加电压。对于二极管，需在两个方向（反接导线）读取数据。对于灯丝，以小步长逐渐升高电压，让灯丝充分升温。

12. Key Points and Common Misconceptions | 重点与常见误区

Resistance is not constant for all components. Only ohmic conductors have constant resistance. Filaments, diodes, thermistors, and LDRs change their resistance under different conditions. / 并非所有元件的电阻都是定值。 只有欧姆导体具有恒定电阻。灯丝、二极管、热敏电阻和 LDR 在不同条件下电阻会改变。
Temperature effect: In metals, resistance increases with temperature. In thermistors (NTC), resistance decreases with temperature. Do not confuse the two. / 温度效应： 金属中，电阻随温度升高而增大；而 NTC 热敏电阻的电阻随温度升高而减小。切勿混淆两者。
Series vs parallel: Series increases total resistance; parallel decreases total resistance. The parallel equivalent is always less than the smallest branch resistor. / 串联与并联： 串联增大总电阻；并联减小总电阻。并联等效电阻永远小于最小的支路电阻。
LDR and thermistor applications usually involve a potential divider, not just the sensor alone. The output voltage is taken from either the sensor or the fixed resistor, depending on whether you want voltage to rise or fall with the physical change. / LDR 与热敏电阻的应用 通常涉及分压器，而非单独使用传感器。根据你希望输出电压随物理量升高还是降低，可以从传感器或固定电阻两端取输出。
Ohm’s law V = I × R is always true for defining resistance, but the condition I ∝ V only holds when resistance is constant. / 欧姆定律 V = I × R 始终可用于定义电阻，但只有电阻恒定时 I ∝ V 才成立。

By mastering these concepts, you will be well prepared for both calculation questions and descriptive answers on resistance in the WJEC IGCSE Physics exam. Practice drawing diagrams and explaining the behaviour of components clearly and concisely.

掌握这些概念后，你将从容应对 WJEC IGCSE 物理考试中关于电阻的计算题与简答题。多加练习画图，并学会清晰、简洁地解释各元件的特性。

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Resistance Revision for IGCSE WJEC Physics | IGCSE WJEC 物理：电阻 考点精讲