📚 417 Electric Circuits and Ohm’s Law | 417 电路与欧姆定律
Understanding electric circuits is essential for exploring how everyday devices work, from simple flashlights to complex smartphones. This topic introduces the fundamental concepts of electric current, potential difference, and resistance, and explains how these quantities relate to each other through Ohm’s Law. By studying series and parallel circuits, measuring techniques, and power calculations, you will gain the ability to predict and analyse circuit behaviour, a core skill in IGCSE Science.
理解电路对于探索从简单手电筒到复杂智能手机等日常设备的工作原理至关重要。本主题介绍了电流、电势差和电阻的基本概念，并解释了这些量如何通过欧姆定律相互关联。通过学习串联与并联电路、测量方法以及功率计算，你将能够预测和分析电路行为，这是IGCSE科学中的一项核心技能。
1. Electric Current and Charge | 电流与电荷
Electric current is the rate at which electric charge flows past a point in a circuit. It is measured in amperes, commonly called amps (A). One ampere means one coulomb of charge passing a point per second. Charge is carried by tiny particles: in metal wires, the charge carriers are free electrons.
电流是电荷流过电路中某点的速率，以安培（通常称为安，A）为单位。1安培表示每秒有1库仑的电荷通过某点。电荷由微小粒子携带：在金属导线中，电荷载体是自由电子。
In a closed circuit, electrons move away from the negative terminal of the cell or battery and travel towards the positive terminal. However, conventional current is defined as flowing from positive to negative, which is the opposite direction to electron flow. Always be careful which direction is being referred to in exam questions.
在闭合回路中，电子从电池或电源的负极移开，流向正极。然而，常规电流被定义为从正极流向负极，这与电子流动的方向相反。在考试题目中，一定要注意所指的方向是哪一种。
Q = I × t
where Q is charge in coulombs (C), I is current in amperes (A), and t is time in seconds (s). This equation allows you to calculate any one quantity if the other two are known.
其中 Q 代表电荷（单位库仑，C），I 代表电流（单位安培，A），t 代表时间（单位秒，s）。利用该公式，只要知道其中两个量，就能求出第三个量。
2. Potential Difference and Voltage | 电势差与电压
Potential difference (p.d.) is the energy transferred per unit charge between two points in a circuit. It is measured in volts (V). A voltmeter must be connected in parallel across the component to measure the potential difference. The terms ‘voltage’ and ‘potential difference’ are often used interchangeably.
电势差（p.d.）是电路中两点之间每单位电荷所转移的能量，单位是伏特（V）。测量电势差时，电压表必须并联在元件两端。’电压’和’电势差’这两个术语经常互换使用。
A cell or battery provides a source of potential difference that pushes charge around a complete circuit. The greater the p.d., the more energy is supplied to each coulomb of charge, enabling components such as lamps and motors to convert electrical energy into light, heat, or kinetic energy.
电池或电源提供电势差，推动电荷在闭合回路中流动。电势差越大，提供给每库仑电荷的能量就越多，从而使灯泡、电机等元件能够将电能转化为光能、热能或动能。
V = W / Q
where V is potential difference in volts, W is work done or energy transferred in joules (J), and Q is charge in coulombs. One volt is equivalent to one joule per coulomb.
其中 V 是电势差（伏特），W 是做功或能量转移（焦耳，J），Q 是电荷（库仑）。1伏特等于1焦耳每库仑。
3. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance is a measure of how difficult it is for current to flow through a component. It is measured in ohms (Ω). The higher the resistance, the smaller the current for a given potential difference. Resistors and many other components are designed to provide a specific resistance.
电阻是衡量电流通过某个元件的难易程度的量，单位是欧姆（Ω）。在给定电势差下，电阻越大，电流就越小。电阻器和许多其它元件被设计用来提供特定的电阻值。
Ohm’s Law states that the current through a conductor is directly proportional to the potential difference across it, provided the temperature remains constant. This relationship is fundamental and can be written as V = I × R.
欧姆定律指出：在温度保持不变的条件下，通过导体的电流与其两端的电势差成正比。这一基本关系可以写作 V = I × R。
V = I × R
where V is potential difference in volts, I is current in amperes, and R is resistance in ohms. Rearranging gives I = V / R or R = V / I.
其中 V 是电势差（伏特），I 是电流（安培），R 是电阻（欧姆）。通过变形可得 I = V / R 或 R = V / I。
4. Verifying Ohm’s Law Experimentally | 通过实验验证欧姆定律
To verify Ohm’s Law, set up a circuit with a resistor, a variable power supply, an ammeter in series, and a voltmeter in parallel across the resistor. Vary the potential difference and record the corresponding current values. Plot a graph of current against voltage; for an ohmic conductor, you will obtain a straight line passing through the origin.
要验证欧姆定律，可以搭建一个包含电阻、可调电源、与电阻串联的电流表以及与电阻并联的电压表的电路。改变电势差，记录相应的电流值。画出电流对电压的图形；对于欧姆导体，你将得到一条通过原点的直线。
The constant gradient of the line indicates that resistance does not change. If the resistor gets hot during the experiment, the graph may start to curve, revealing that resistance increases with temperature. Always take readings quickly to minimise heating effects.
直线的恒定斜率表明电阻不变。如果实验中电阻变热，图形可能会开始弯曲，这表明电阻随温度升高而增大。应快速读取数据以减小发热带来的影响。
5. Ohmic and Non-Ohmic Conductors | 欧姆导体与非欧姆导体
Ohmic conductors obey Ohm’s Law, meaning their current–voltage (I–V) graph is a straight line through the origin. Fixed resistors and metal wires at constant temperature are typical examples. Their resistance remains constant regardless of the voltage applied.
欧姆导体遵循欧姆定律，意味着它们的电流-电压（I-V）图形是一条通过原点的直线。固定电阻器和处于恒温下的金属导线是典型例子。无论施加多大电压，它们的电阻都保持不变。
Non-ohmic conductors have a changing resistance. Filament lamps show a curved I–V graph because their filament heats up and resistance increases. Diodes allow current to flow in one direction only, so their graph shows almost zero current in reverse bias and a steep rise in forward bias above the threshold voltage.
非欧姆导体的电阻是变化的。白炽灯的 I-V 图形是弯曲的，因为灯丝发热使电阻增大。二极管只允许电流单向导通，因此其图形在反向偏置时电流几乎为零，在正向偏置超过阈值电压后电流急剧上升。
6. Series Circuits | 串联电路
In a series circuit, components are connected end-to-end in a single loop. The current is the same at all points because there is only one path for charge to flow. The total potential difference from the battery is shared across the components, so V_total = V₁ + V₂ + V₃.
在串联电路中，元件首尾相连形成单一回路。由于只有一条电荷流通的路径，电路各处电流都相等。电池提供的总电势差在各个元件上分配，因此 V_total = V₁ + V₂ + V₃。
The total resistance in series is the sum of the individual resistances. Adding more resistors increases the total resistance and reduces the current flowing from the source.
串联电路的总电阻等于各个电阻之和。增加更多电阻会使总电阻增大，从而减小从电源流出的电流。
R_total = R₁ + R₂ + R₃
7. Parallel Circuits | 并联电路
In a parallel circuit, components are connected on separate branches. The potential difference across each branch is the same and equal to the battery voltage. However, the total current leaving the battery splits at the junctions, so I_total = I₁ + I₂ + I₃.
在并联电路中，元件连接在各自的分支上。每条分支两端的电势差都相同，并等于电池电压。但离开电池的总电流在分支点分流，因此 I_total = I₁ + I₂ + I₃。
Adding extra branches in parallel decreases the total resistance of the circuit, because more paths are available for charge. The total resistance is calculated using the reciprocal formula. For two resistors in parallel, the combined resistance R_total is given by:
并联增加额外分支会降低电路总电阻，因为为电荷提供了更多的通路。总电阻可使用倒数公式计算。对于两个并联电阻，其总电阻 R_total 由下式给出：
1 / R_total = 1 / R₁ + 1 / R₂
or equivalently R_total = (R₁ × R₂) / (R₁ + R₂). The total resistance is always less than the smallest individual resistance in the parallel network.
或等效为 R_total = (R₁ × R₂) / (R₁ + R₂)。并联网络的总电阻总是小于其中最小的单个电阻。
8. Measuring Current and Voltage | 测量电流与电压
Ammeters are used to measure current and must be connected in series with the component. You must break the circuit and insert the ammeter so that the same current passes through it. An ideal ammeter has zero resistance so that it does not affect the circuit.
电流表用于测量电流，必须与元件串联。你需要断开电路并接入电流表，使相同的电流流经它。理想的电流表电阻为零，因此不会影响电路。
Voltmeters are always connected in parallel with the component under test. They have a very high resistance, which means very little current flows through them, minimising any disturbance to the circuit. Both meters should be handled carefully, ensuring the correct polarity is observed when using analogue instruments.
电压表则总是并联在待测元件两端。它们的内阻非常高，这意味着只有极小的电流流过，从而将对电路的干扰降至最低。两种仪表都应小心使用，使用模拟仪表时务必注意正确的极性连接。
9. Factors Affecting Resistance | 影响电阻的因素
The resistance of a wire depends on its length, cross-sectional area, the material it is made from, and its temperature. Resistance increases with length because the electrons have to travel further and experience more collisions with metal ions. A thicker wire has lower resistance because there is a larger area for the electrons to flow through.
导线的电阻取决于其长度、横截面积、材料种类及温度。电阻随长度增加而增大，因为电子需要移动更远的距离，并与金属离子发生更多碰撞。更粗的导线电阻更低，因为有更大的横截面积供电子流动。
Different materials have different resistivities; for instance, copper has a low resistivity while nichrome has a much higher resistivity, making it suitable for heating elements. As temperature rises, metal ions vibrate more vigorously, causing more frequent electron scattering, so the resistance of a metal increases with temperature.
不同材料具有不同的电阻率；例如，铜的电阻率很低，而镍铬合金的电阻率要高得多，这使它适用于加热元件。温度升高时，金属离子振动加剧，导致电子散射更加频繁，因此金属的电阻随温度升高而增大。
10. Electrical Power and Energy | 电功率与电能
Electrical power is the rate at which energy is transferred or converted in a circuit. It is measured in watts (W). For any component, power can be calculated using the product of current and potential difference.
电功率是电路中能量转移或转换的速率，单位是瓦特（W）。对于任何元件，功率都可以用电流与电势差的乘积来计算。
P = I × V
Combining this with Ohm’s Law gives two other useful forms: P = I² × R and P = V² / R. The total energy transferred depends on both the power and the time for which the circuit operates.
将此式与欧姆定律结合可以得到另外两个常用形式：P = I² × R 以及 P = V² / R。转移的总能量取决于功率和电路工作时间。
E = P × t
where E is energy in joules, P is power in watts, and t is time in seconds. In domestic electricity, energy is often measured in kilowatt-hours (kWh).
其中 E 是能量（焦耳），P 是功率（瓦特），t 是时间（秒）。在家庭用电中，能量常以千瓦时（kWh）为单位计量。
11. Safety in Circuits | 电路安全
High currents can cause wires to overheat, which may lead to insulation melting and fires. Fuses and circuit breakers are safety devices that disconnect the circuit when the current exceeds a safe level. A fuse contains a thin wire that melts and breaks the circuit if the current becomes too large.
过大的电流会使导线过热，可能导致绝缘层熔化并引发火灾。保险丝和断路器是安全装置，当电流超过安全水平时会切断电路。保险丝内部有一根细金属丝，一旦电流过大，金属丝就会熔断从而断开电路。
Earthing and double insulation protect users from electric shock. Short circuits occur when a low-resistance path bypasses the normal circuit parts, causing a dangerously high current. Always avoid overloading sockets and check the rating of fuses to match the appliance’s power.
接地与双重绝缘可保护用户免受电击。短路发生时，低电阻路径绕过正常电路元件，导致危险的高电流。始终避免插座过载，并检查保险丝的额定值是否与电器的功率匹配。
Resistors and other components also have power ratings; exceeding them can damage the component. Safety in practical work also demands turning off power before making changes to a circuit and keeping liquids away from electrical equipment.
电阻器和其他元件也有额定功率；超过其额定功率会损坏元件。实验中的安全操作还要求在对电路进行改动前关闭电源，并使液体远离电气设备。
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