📚 Resistance | 电阻
Resistance is one of the most fundamental concepts in electricity. It describes how much a component or material opposes the flow of electric charge. In GCSE OCR Physics, understanding resistance is closely linked with Ohm’s law, circuit analysis, and practical investigations of wires and components.
电阻是电学中最基本的概念之一。它描述了某个元件或材料对电荷流动的阻碍程度。在 GCSE OCR 物理中，理解电阻与欧姆定律、电路分析以及对导线及元件的实验探究紧密相连。
1. What is Resistance? | 什么是电阻？
Resistance (symbol: R) is a measure of how difficult it is for current to pass through a component. It is defined by the ratio of the potential difference (V) across the component to the current (I) flowing through it. The unit of resistance is the ohm (Ω).
电阻（符号：R）是用来衡量电流通过一个元件时困难程度的物理量。它由元件两端的电势差（V）与流过其中的电流（I）的比值来定义。电阻的单位是欧姆（Ω）。
A component has a resistance of 1 ohm when a potential difference of 1 volt produces a current of 1 ampere through it. The defining equation is:
当 1 伏特的电势差在元件中产生 1 安培的电流时，该元件的电阻为 1 欧姆。定义方程为：
R = V / I
This relationship applies to all components, but only ohmic components keep R constant when temperature is unchanged.
这一关系适用于所有元件，但只有在温度不变的情况下，欧姆元件才会保持 R 不变。
2. Ohm’s Law | 欧姆定律
Ohm’s law states that the current through an ohmic conductor is directly proportional to the potential difference across it, provided that its temperature remains constant. Mathematically,
欧姆定律指出：在温度保持不变的条件下，流过欧姆导体的电流与其两端的电势差成正比。数学表达式为：
V = I × R
If you double the voltage across a fixed resistor, the current doubles. A graph of V against I for an ohmic conductor is a straight line passing through the origin, meaning its resistance is constant.
如果你将固定电阻两端的电压加倍，电流也会加倍。对于欧姆导体，V-I 图是一条通过原点的直线，这意味着它的电阻是恒定的。
It is crucial to remember that many real components, such as lamps and diodes, are non-ohmic because their resistance changes with temperature or applied voltage.
要记住，许多真实的元件，如灯泡和二极管，并不是欧姆导体，因为它们的电阻会随温度或所加电压的改变而改变。
3. Factors Affecting Resistance | 影响电阻的因素
The resistance of a wire or conductor is determined by four main factors. Every student should be able to explain and predict the effect of each one.
导线或导体的电阻主要由四个因素决定。每位学生都应能够解释和预测每一个因素的影响。
1. Length (L): For a uniform wire, resistance is directly proportional to its length. R ∝ L. A longer wire provides more obstacles for the drifting electrons, increasing the number of collisions with metal ions.
1. 长度（L）：对于均匀导线，电阻与其长度成正比（R ∝ L）。导线越长，为漂移电子提供的障碍物越多，与金属离子碰撞的次数就增多。
2. Cross-sectional area (A): Resistance is inversely proportional to the cross-sectional area. R ∝ 1/A. A thicker wire has more space for electrons to flow, so fewer collisions occur per unit length.
2. 横截面积（A）：电阻与横截面积成反比（R ∝ 1/A）。较粗的导线有更多的空间让电子流动，因此单位长度内发生的碰撞更少。
3. Material: Different materials have different numbers of free charge carriers and different ionic structures. Metals like copper have very low resistivity, while insulators have extremely high resistivity.
3. 材料：不同材料具有不同数量的自由电荷载流子和不同的离子结构。铜等金属的电阻率非常低，而绝缘体的电阻率极高。
4. Temperature: For most metal conductors, resistance increases with temperature. As temperature rises, metal ions vibrate more vigorously, making it harder for electrons to pass through. In some materials like semiconductors, resistance decreases with temperature.
4. 温度：对大多数金属导体而言，电阻随温度升高而增大。温度上升时，金属离子振动更加剧烈，使电子更难通过。而在半导体等材料中，电阻会随温度升高而减小。
4. Resistivity and the Wire Resistance Formula | 电阻率与导线电阻公式
The resistance of a uniform wire can be calculated using its resistivity (ρ), length (L) and cross-sectional area (A). Resistivity is a property of the material itself, independent of the wire’s dimensions.
均匀导线的电阻可以利用其电阻率（ρ）、长度（L）和横截面积（A）来计算。电阻率是材料本身的特性，与导线的尺寸无关。
R = ρL / A
The unit of resistivity is ohm metre (Ω·m). In GCSE OCR Physics, you do not need to memorise resistivity values, but you must know how R depends on L and A. For example, if a wire is stretched to twice its original length and its volume stays constant, its cross-sectional area halves, so its resistance increases by a factor of four.
电阻率的单位是欧姆·米（Ω·m）。在 GCSE OCR 物理中，你不需要记住具体的电阻率数值，但必须知道 R 是如何依赖于 L 和 A 的。例如，若导线被拉伸至原长的两倍且体积不变，横截面积会减半，因此电阻将增加为原来的四倍。
5. Resistors in Series | 串联电阻
When resistors are connected end to end, they are in series. The total resistance is the sum of the individual resistances.
当电阻器首尾相连时，它们就是串联连接。总电阻等于各个电阻之和。
Rtotal = R1 + R2 + R3 + …
In a series circuit, the current is the same everywhere. Adding more resistors in series always increases the total resistance because there are more obstacles for the current to overcome. The combined resistance is always larger than the largest individual resistor.
在串联电路中，各处的电流都相同。串联更多的电阻器总会增加总电阻，因为电流需要克服的阻碍更多。总电阻始终大于其中最大的分电阻。
6. Resistors in Parallel | 并联电阻
For resistors connected in parallel, the total resistance is less than the smallest individual resistance. The currents have multiple paths, making it easier for charge to flow.
对于并联连接的电阻器，总电阻小于最小的分电阻。电流有多条路径，使电荷更容易流动。
1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3 + …
This reciprocal relationship means that adding a resistor in parallel provides an additional path and reduces the overall resistance. For two identical resistors R in parallel, the total resistance is R/2.
这种倒数关系意味着并联增加一个电阻器就提供了一条额外的通路，从而降低了总电阻。对于两个阻值相同的电阻器 R 并联，总电阻为 R/2。
7. I-V Characteristics of an Ohmic Conductor | 欧姆导体的 I-V 特性
An ohmic conductor, such as a metal wire at constant temperature, shows a straight-line I-V graph passing through the origin. The current is directly proportional to the voltage. The gradient of the I-V graph is constant and equals 1/R if current is on the y-axis. Reversing the polarity of the supply gives a symmetric straight line through the third quadrant.
欧姆导体（如恒温下的金属导线）的 I-V 特性图为一条通过原点的直线。电流与电压成正比。若将电流放在 y 轴，I-V 图的斜率恒定，等于 1/R。将电源极性反转后，会得到一条穿过第三象限的对称直线。
In practical measurements, you use a voltmeter in parallel with the component and an ammeter in series. The resistance calculated from R = V/I remains constant for all values of V and I.
在实际测量中，你将电压表与被测元件并联，电流表与之串联。通过 R = V/I 算出的电阻在所有 V 和 I 的取值下均保持不变。
8. I-V Characteristics of a Filament Lamp | 灯丝的 I-V 特性
A filament lamp does not obey Ohm’s law because its resistance increases as the filament gets hotter. When you increase the potential difference, the current rises, heating the filament to a high temperature. The metal ions vibrate more vigorously, causing greater resistance.
灯丝灯泡并不遵循欧姆定律，因为随着灯丝温度升高，其电阻会增大。当你增大电势差时，电流上升，灯丝被加热至高温。金属离子振动更加剧烈，导致电阻增大。
On an I-V graph, the curve passes through the origin but bends towards the voltage axis, showing a decreasing slope. The slope is steepest near the origin where the filament is cool and resistance is lowest. Because the filament behaves the same way regardless of current direction, the graph is symmetric about the origin.
在 I-V 图上，曲线经过原点但向电压轴弯曲，斜率逐渐减小。原点附近灯丝是冷的，电阻最小，因此斜率最陡。由于灯丝在电流方向改变时表现相同，图形关于原点对称。
9. I-V Characteristics of a Diode | 二极管的 I-V 特性
A diode is a non-ohmic component that allows current to flow easily in one direction (forward bias) and has very high resistance in the reverse direction. For a silicon diode, a forward voltage of about 0.6–0.7 V is needed before significant current flows. Above this threshold, current rises sharply.
二极管是一种非欧姆元件，它允许电流沿一个方向（正向偏置）轻易流过，而在反方向具有极高的电阻。对于硅二极管，需要大约 0.6–0.7V 的正向电压才会产生明显电流。超过该阈值后，电流急剧上升。
In reverse bias, the diode has extremely high resistance, so only a tiny leakage current flows until the breakdown voltage is reached (which is not studied at GCSE). The I-V graph shows a near-zero current for negative voltages and a steep upward curve for positive voltages above the threshold.
在反向偏置下，二极管的电阻极高，因此只有极小的漏电流，直至达到击穿电压（GCSE 阶段不涉及）。I-V 图上，负电压时电流几乎为零，正电压超过阈值后曲线急剧上升。
10. Variable Resistors and Potential Dividers | 可变电阻与分压器
A variable resistor (rheostat) allows you to change the resistance in a circuit by moving a sliding contact. It is used to control current or adjust potential difference. By increasing the length of the resistive track in the circuit, the resistance increases, which reduces the current.
可变电阻（滑动变阻器）让你可以通过移动滑动触点在电路中改变电阻。它被用来控制电流或调节电势差。通过增加电路中电阻轨道的接入长度，电阻增大，从而减小了电流。
A potential divider typically uses two fixed resistors or a sensor with a variable resistor to split a supply voltage. The voltage across one resistor R1 in a series circuit with R2 is given by:
分压器通常使用两个固定电阻，或者传感器与可变电阻配合，来分配电源电压。在串联电路中，R1 两端的电压由下式给出：
Vout = Vin × R1 / (R1 + R2)
This concept is widely applied in circuits with thermistors and LDRs, where a change in resistance leads to a change in output voltage.
这一概念广泛应用于含有热敏电阻和光敏电阻的电路中，电阻的变化会导致输出电压的变化。
11. Practical: Investigating Resistance of a Wire | 实验：探究导线的电阻
A common GCSE required practical is to investigate how the resistance of a metal wire depends on its length. You set up a circuit with the wire connected via crocodile clips, a voltmeter in parallel with the wire, an ammeter in series, and a low-voltage power supply. Record V and I for different lengths, keeping the wire uncoiled and straight on a metre ruler.
GCSE 常见的必做实验是探究金属导线的电阻如何随其长度变化。你搭建的电路包括通过鳄鱼夹连接的导线、与导线并联的电压表、串联的电流表以及低压电源。用米尺将导线拉直，在不同长度下记录 V 和 I。
Calculate R = V/I for each length. Plot a graph of resistance against length. You should obtain a straight line through the origin, confirming R ∝ L. Safety points include keeping the current low to avoid overheating the wire and using sharp probes to make good contact.
对每个长度计算 R = V/I。绘制电阻与长度的关系图。你应该得到一条通过原点的直线，从而验证 R ∝ L。安全要点包括保持低电流以避免导线过热，以及使用尖锐探头以保证良好接触。
Alternatively, you can investigate how cross-sectional area affects resistance by using different thickness wires of the same material and length. Plot R against 1/A to show proportionality.
此外，你也可以通过使用相同材料、相同长度但不同粗细的导线来探究横截面积对电阻的影响。绘制 R 与 1/A 的图线可展示正比关系。
12. Exam Tips and Summary | 考试技巧与总结
Always write down the appropriate formula first when solving a problem. For ohmic conductors, use V = I × R. For series and parallel circuits, be careful with the rules: current splits in parallel but is the same in series; voltage adds in series but is the same across parallel branches.
解题时，务必先写出合适的公式。对于欧姆导体，使用 V = I × R。对于串并联电路，注意规则：并联电路中电流分流而串联电路中电流相等；串联电路中电压相加而并联支路两端电压相同。
Key points to remember:
需要记住的关键点：
1. Resistance is the ratio V/I, but only constant for ohmic components. 2. R = ρL/A links resistance to physical dimensions. 3. In series, total resistance is always larger; in parallel, it is always smaller. 4. I-V graphs reveal whether a component is ohmic or non-ohmic. 5. A filament lamp’s resistance increases because its temperature increases, not because of any special property of the metal.
1. 电阻是 V/I 的比值，但仅对欧姆元件保持不变。 2. R = ρL/A 将电阻与物理尺寸相联系。 3. 串联时总电阻总是更大；并联时总电阻总是更小。 4. I-V 图揭示了元件是欧姆还是非欧姆。 5. 灯丝灯泡电阻增大是因为温度升高，而不是因为金属本身有什么特殊性质。
In calculations, always check that you have converted units correctly: length in metres, area in square metres. For common errors, students often forget to square the radius when calculating area from diameter, or they add resistances in parallel incorrectly.
在计算中，务必检查单位是否正确换算：长度用米，面积用平方米。常见错误包括：学生由直径计算面积时忘记将半径平方，或者错误地计算并联电阻的倒数之和。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导