IGCSE Physics: Resistance Key Points | IGCSE 物理：电阻考点精讲

📚 IGCSE Physics: Resistance Key Points | IGCSE 物理：电阻考点精讲

Resistance is a core concept in IGCSE Physics that links voltage, current and the properties of materials. Understanding how to calculate resistance, how it varies in different components, and how resistors behave in circuits is essential for both theory papers and practical experiments. This revision guide covers every key point you need, from Ohm’s law to I-V characteristics and energy transfer in resistors.

电阻是 IGCSE 物理中连接电压、电流和材料属性的核心概念。掌握电阻的计算方法、不同元件中电阻的变化方式以及电阻在电路中的行为，对于理论考试和实验操作都至关重要。本文梳理了从欧姆定律到 I-V 特性以及电阻能量转移的全部考点，助你高效复习。

1. What is Resistance? | 什么是电阻？

Resistance is a measure of how much a component opposes the flow of electric current. It is given the symbol R and is measured in ohms (Ω). The resistance of a component can be determined using the ratio of the potential difference (voltage) across it to the current flowing through it: R = V / I. A high resistance means the component allows only a small current for a given voltage.

电阻衡量元件对电流的阻碍程度，符号为 R，单位是欧姆（Ω）。元件的电阻可通过其两端的电势差（电压）与通过它的电流之比来计算：R = V / I。高电阻意味着在给定电压下电流较小。

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. In other words, the resistance remains constant as long as the temperature does not change. The relationship is expressed by the equation:

V = I × R

where V is the potential difference in volts (V), I is the current in amperes (A), and R is the resistance in ohms (Ω).

欧姆定律指出，对于温度恒定的金属导体，通过它的电流与两端的电势差成正比。也就是说，只要温度不变，电阻保持恒定。这个关系用公式表示为：V = I × R，其中 V 为电压（伏特），I 为电流（安培），R 为电阻（欧姆）。

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

The resistance of a wire depends on four main factors:

Length (L): resistance increases with length; R ∝ L
Cross-sectional area (A): resistance decreases as area increases; R ∝ 1/A
Material: each material has a characteristic resistivity
Temperature: for most metal conductors, resistance increases when temperature rises

导线的电阻主要取决于四个因素：长度（L）：电阻与长度成正比；横截面积（A）：电阻与面积成反比；材料：不同材料有不同的电阻率；温度：大多数金属导体的电阻随温度升高而增大。

In contrast, insulators and semiconductors (like thermistors) often show a decrease in resistance with increasing temperature. The change in resistance with temperature is put to use in many sensing circuits.

与此相反，绝缘体和半导体（如热敏电阻）的电阻通常随温度升高而降低。电阻随温度变化的特性被广泛应用于传感电路中。

4. Resistivity | 电阻率

Resistivity (ρ) is a material property that quantifies how strongly a material opposes current flow. The resistance of a uniform wire is given by:

R = ρ L / A

where ρ is the resistivity (unit: ohm metre, Ω·m), L is the length, and A is the cross-sectional area. A low resistivity means the material is a good conductor.

电阻率（ρ）是表征材料阻碍电流能力的物理量。均匀导线的电阻由下式给出：R = ρ L / A，其中 ρ 为电阻率（单位：欧姆·米，Ω·m），L 为长度，A 为横截面积。电阻率越低，材料的导电性越好。

5. Resistors in Series | 串联电阻

When resistors are connected in series, the total resistance is simply the sum of the individual resistances:

R_total = R₁ + R₂ + R₃ + …

The current is the same through each resistor, while the total voltage from the source is divided among them. For example, a 4 Ω and a 6 Ω resistor in series give a total resistance of 10 Ω.

电阻串联时，总电阻等于各个电阻之和：R_total = R₁ + R₂ + R₃ + …。流过每个电阻的电流相同，而电源的总电压分配在各个电阻上。例如，一个 4 Ω 和一个 6 Ω 的电阻串联，总电阻为 10 Ω。

6. Resistors in Parallel | 并联电阻

For resistors in parallel, the total resistance is found from the reciprocal formula:

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

The voltage across each parallel resistor is the same, while the total current splits between the branches. For two resistors, a shortcut is R_total = (R₁ × R₂) / (R₁ + R₂). For example, a 4 Ω and a 12 Ω resistor in parallel give a total resistance of (4×12)/(4+12) = 48/16 = 3 Ω.

电阻并联时，总电阻的倒数等于各电阻倒数之和：1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + …。每个并联电阻两端的电压相等，总电流则分配到各支路。对于两个电阻，可简化为 R_total = (R₁ × R₂) / (R₁ + R₂)。例如，一个 4 Ω 和一个 12 Ω 的电阻并联，总电阻为 (4×12)/(4+12) = 3 Ω。

7. I-V Characteristics: Ohmic Conductor | 欧姆导体的 I-V 特性

An ohmic conductor follows Ohm’s law. Its current-voltage (I-V) graph is a straight line passing through the origin, showing that current is directly proportional to voltage. The resistance is constant and can be found from the inverse of the gradient (or from R = V/I at any point). A fixed metal resistor at constant temperature is a typical example.

欧姆导体遵循欧姆定律，其电流-电压（I-V）图是一条通过原点的直线，表明电流与电压成正比。电阻恒定，可通过斜率倒数求出（或用任意一点的 R = V/I 计算）。恒温下的固定金属电阻就是一个典型例子。

8. I-V Characteristics: Filament Lamp | 灯丝的 I-V 特性

A filament lamp does not obey Ohm’s law because its temperature changes significantly. As the current increases, the filament heats up, causing its resistance to rise. The I-V graph is a curve that gets less steep at higher voltages, indicating increasing resistance. The graph is symmetric for positive and negative voltages.

灯丝不遵循欧姆定律，因为其温度变化显著。随着电流增大，灯丝温度升高，电阻增加。其 I-V 图是一条曲线，在较高电压处斜率减小，表明电阻变大。正负电压下图形是对称的。

9. I-V Characteristics: Diode | 二极管的 I-V 特性

A diode allows current to flow easily in one direction (forward bias) but has very high resistance in the opposite direction (reverse bias). In forward bias, a small voltage (about 0.6–0.7 V for a silicon diode) is needed before the current rises sharply. The I-V graph shows almost zero current in reverse bias until breakdown, and a steep rise in forward bias above the threshold.

二极管只允许电流沿一个方向轻易通过（正向偏置），反向时电阻极高。正向偏置下，需要一个小电压（硅二极管约 0.6–0.7 V）才能使电流急剧上升。其 I-V 图显示反向时电流几乎为零（直至击穿），正向超过阈值后电流陡升。

10. Variable Resistor and Potentiometer | 可变电阻与电位器

A variable resistor (rheostat) allows the resistance in a circuit to be changed by moving a sliding contact along a resistive track. It can be used to control the current in a circuit. A potentiometer is connected as a voltage divider: the two end terminals are connected across a supply, and the sliding contact provides an adjustable output voltage between zero and the full supply voltage.

可变电阻（滑动变阻器）通过移动滑动触点在电阻丝上的位置来改变电路中的电阻，常用于控制电流。电位器则用作分压器：两个固定端接电源，滑动触点输出可在零和电源电压之间变化的可调电压。

11. Light-Dependent Resistor (LDR) and Thermistor | 光敏电阻与热敏电阻

An LDR (light-dependent resistor) has a resistance that decreases as the light intensity falling on it increases. In the dark its resistance is very high; in bright light it becomes low. A thermistor is a temperature-sensitive resistor. Most common types have a negative temperature coefficient (NTC), meaning resistance decreases as temperature rises.

光敏电阻（LDR）的阻值随照射光强的增加而减小。黑暗时电阻很高，强光下电阻很低。热敏电阻是一种对温度敏感的电阻器，常见为负温度系数（NTC）型，即温度升高时电阻降低。

Both are widely used in sensor circuits—for example, an LDR in a light-operated switch, or a thermistor in a temperature alarm. They are often connected in series with a fixed resistor to form a potential divider.

两者广泛应用于传感器电路，例如光敏电阻用于光控开关，热敏电阻用于温度报警。它们常与固定电阻串联组成分压电路。

12. Energy Transfer and Power in Resistors | 电阻中的能量转移与功率

When a current passes through a resistor, electrical energy is converted into thermal energy (heat). The power (energy per second) dissipated is given by:

P = I × V = I² × R = V² / R

where P is in watts (W). The total energy transferred over a time t is E = P × t = I² R t = V I t. This heating effect is the basis of devices like electric heaters and fuses. A fuse uses a thin wire that melts and breaks the circuit if the current exceeds a safe value.

当电流通过电阻时，电能转化为内能（热）。耗散的功率（每秒能量）由下式给出：P = I × V = I² × R = V² / R，单位为瓦特（W）。在时间 t 内转移的总能量为 E = P × t = I² R t = V I t。这种热效应是电热器和熔断器的基础。保险丝中用一根细丝，在电流超过安全值时熔断，从而断开电路。

Calculating the correct fuse rating involves choosing a value slightly above the normal operating current of the appliance, so that the fuse protects the device without blowing during normal use.

选择合适保险丝额定值时，应选略高于电器正常工作电流的规格，以保证正常使用时不熔断，同时起到保护作用。

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IGCSE Physics: Resistance Key Points | IGCSE 物理：电阻 考点精讲