📚 Resistance in Electrical Circuits | 电路中的电阻
In KS3 Science and CIE Checkpoint Physics, resistance explains why some components make it harder for electric current to flow. Understanding resistance helps you predict how circuits behave and how energy is transferred. This article covers the key ideas, equations, factors and graphs you need for CIE-style questions.
在 KS3 科学和 CIE Checkpoint 物理中，电阻解释了为什么有些元件会让电流更难通过。理解电阻有助于预测电路行为以及能量如何转移。本文涵盖 CIE 风格题目中需要掌握的核心概念、公式、影响因素和图像。
1. What is Resistance? | 什么是电阻？
Resistance is a measure of how much a component opposes the flow of electric current. When electrons move through a wire or component, they collide with vibrating metal ions. These collisions slow the electrons down and transfer some electrical energy into heat.
电阻是衡量元件对电流阻碍作用大小的物理量。当电子通过导线或元件时，会与振动的金属离子碰撞。这些碰撞使电子减速，并把一部分电能转化为热能。
A high resistance means a small current for a given voltage. A low resistance means a larger current can flow more easily. Resistance is not a fault; it is a property of every material and component.
电阻大意味着在一定电压下电流较小。电阻小意味着电流更容易通过，电流较大。电阻不是故障，而是每种材料和元件都具有的性质。
2. Units and Circuit Symbols | 单位与电路符号
The SI unit of resistance is the ohm, written with the Greek letter omega (Ω). One ohm is the resistance when a voltage of one volt produces a current of one ampere.
电阻的国际单位是欧姆，用希腊字母 Ω 表示。当 1 伏特电压产生 1 安培电流时，电阻就是 1 欧姆。
In circuit diagrams, a fixed resistor is shown as a rectangle. A variable resistor is shown as a rectangle with an arrow passing through it. It is important to recognise these symbols in CIE questions.
在电路图中，固定电阻器用长方形表示。可变电阻器用一个带箭头的长方形表示。在 CIE 题目中识别这些符号非常重要。
You may also see resistance values written in kilohms (kΩ) or megohms (MΩ). For example, 1000 Ω is the same as 1 kΩ.
你可能还会看到电阻值用千欧 (kΩ) 或兆欧 (MΩ) 表示。例如，1000 Ω 等于 1 kΩ。
3. Conductors, Insulators and Semiconductors | 导体、绝缘体与半导体
Conductors such as copper and silver have very low resistance because they contain many free electrons. This allows current to flow easily. Insulators such as plastic and rubber have very high resistance because their electrons are tightly bound and cannot move freely.
铜和银等导体电阻很低，因为它们含有大量自由电子，电流容易通过。塑料和橡胶等绝缘体电阻很高，因为电子被紧紧束缚，不能自由移动。
Semiconductors such as silicon have resistance between conductors and insulators. In KS3 you mainly need to compare conductors and insulators and use them safely.
硅等半导体的电阻介于导体和绝缘体之间。在 KS3 阶段，你主要需要比较导体和绝缘体，并安全地使用它们。
4. Factors Affecting Resistance | 影响电阻的因素
The resistance of a wire depends on four main factors: length, cross-sectional area, material and temperature. A longer wire has greater resistance because electrons must travel through more vibrating ions.
导线的电阻取决于四个主要因素：长度、横截面积、材料和温度。导线越长，电阻越大，因为电子要经过更多振动的离子。
A thicker wire has lower resistance because there is a wider path for electrons, so more current can flow. For example, a thick copper cable has less resistance than a thin copper wire of the same length.
导线越粗，电阻越小，因为电子通道更宽，可以通过更多电流。例如，粗铜缆比相同长度的细铜线电阻更小。
Different materials have different resistivities; copper has lower resistance than iron. For most metals, increasing temperature increases resistance because ions vibrate more and collide with electrons more often.
不同材料具有不同的电阻率，铜的电阻比铁低。对大多数金属来说，温度升高会使电阻增大，因为离子振动更剧烈，与电子碰撞更频繁。
5. Current, Voltage and Ohm's Law | 电流、电压与欧姆定律
Ohm's law links current, voltage and resistance. It states that the current through a resistor is directly proportional to the voltage across it, provided temperature remains constant.
欧姆定律将电流、电压和电阻联系起来。它指出，在温度保持不变的条件下，通过电阻器的电流与它两端的电压成正比。
V = I × R
where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). You can rearrange this to find resistance or current.
其中 V 是电压，单位为伏特 (V)；I 是电流，单位为安培 (A)；R 是电阻，单位为欧姆 (Ω)。这个公式可以变形来求电阻或电流。
R = V ÷ I
I = V ÷ R
quantity you want to find. For example, covering V leaves I × R; covering R leaves V ÷ I.
可以用三角形法变形公式：遮住你想求的物理量。例如，遮住 V 得到 I × R；遮住 R 得到 V ÷ I。
6. Using the Formula R = V ÷ I: Worked Examples | 使用公式 R = V ÷ I：计算示例
A lamp has a voltage of 12 V across it and a current of 3 A flowing through it. Calculate its resistance.
一个灯泡两端电压为 12 V，通过它的电流为 3 A。计算它的电阻。
= V ÷ I. Substitute the values: R = 12 V ÷ 3 A = 4 Ω. The lamp has a resistance of 4 ohms.
解答：写出公式 R = V ÷ I。代入数值：R = 12 V ÷ 3 A = 4 Ω。灯泡的电阻为 4 欧姆。
A resistor has a resistance of 20 Ω and a current of 0.5 A. Calculate the voltage across the resistor.
一个电阻器的电阻为 20 Ω，通过它的电流为 0.5 A。计算电阻器两端的电压。
Solution: Use V = I × R. Substitute: V = 0.5 A × 20 Ω = 10 V. The voltage is 10 volts.
解答：使用 V = I × R。代入：V = 0.5 A × 20 Ω = 10 V。电压为 10 伏特。
7. Fixed and Variable Resistors | 固定电阻器与可变电阻器
Fixed resistors have a constant resistance. They are used to limit current or divide voltage in a circuit. Their resistance does not change when the voltage or current changes, as long as temperature is constant.
固定电阻器的电阻值是固定的，用于限制电流或分压。只要温度不变，它们的电阻不会随电压或电流的变化而改变。
Variable resistors, also called rheostats, allow you to change resistance by moving a slider or turning a knob. A variable resistor is useful in dimmer switches, volume controls and sensors. Increasing its resistance reduces the current, making a lamp dimmer or a sound quieter.
可变电阻器也叫变阻器，可以通过移动滑片或旋转旋钮改变电阻。可变电阻器用于调光开关、音量控制和传感器中。增大它的电阻会减小电流，使灯泡变暗或声音变小。
8. Measuring Resistance in Practice | 实际测量电阻
in series to measure current, and a voltmeter is connected in parallel to measure voltage.
要测量元件的电阻，可以测量通过它的电流和它两端的电压，然后用 R = V ÷ I 计算。电流表串联在电路中测量电流，电压表并联在元件两端测量电压。
Alternatively, an ohmmeter can measure resistance directly when the component is removed from the circuit. The unit on the meter display is ohms (Ω).
另外，欧姆表可以在元件从电路中断开后直接测量电阻。表盘上的单位是欧姆 (Ω)。
When measuring resistance, make sure the component is not connected to a power source. A direct ohmmeter reading is only reliable for an isolated component.
测量电阻时，确保元件没有连接到电源。对于独立的元件，欧姆表的直接读数才可靠。
9. Series and Parallel Resistance | 串联与并联电阻
In a series circuit, the total resistance is the sum of the individual resistances. Adding more resistors in series increases the total resistance, so the current decreases for the same voltage.
在串联电路中，总电阻等于各个电阻之和。串联更多电阻会增加总电阻，因此在相同电压下电流会减小。
Total resistance = R₁ + R₂ + R₃
In a parallel circuit, the
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