📚 Circuit Analysis in IGCSE WJEC Physics | IGCSE WJEC 物理：电路分析 考点精讲
Mastering circuit analysis is a cornerstone of the IGCSE WJEC Physics syllabus. This topic covers everything from fundamental quantities like current, voltage and resistance, to more advanced ideas such as potential dividers and internal resistance. By following a structured approach, you will learn to predict how circuits behave, calculate unknown values, and design simple experiments to verify physical laws. The key is not just memorising formulas, but understanding how energy is transferred around a complete loop.
掌握电路分析是 IGCSE WJEC 物理大纲的基石。本主题涵盖电流、电压和电阻等基本量，以及分压器和内阻等更深入的概念。通过结构化的学习，你将学会预测电路行为、计算未知量并设计简单实验验证物理定律。关键不仅仅是记忆公式，而是理解能量如何在完整的回路中转移。
1. Current, Voltage and Resistance Fundamentals | 电流、电压和电阻基础
Electric current is the rate of flow of electric charge. In a metallic conductor, it is carried by delocalised electrons moving from the negative terminal to the positive terminal of a cell. Conventional current, however, flows from positive to negative. The unit of current is the ampere (A), and it is measured using an ammeter connected in series.
电流是电荷流动的速率。在金属导体中，电流由脱离原子的电子从电池负极流向正极所形成。然而，传统电流方向是从正极流向负极。电流的单位是安培 (A)，使用串联在电路中的安培表测量。
Voltage (potential difference) is the energy transferred per unit charge as charge passes through a component. It is measured in volts (V) using a voltmeter connected in parallel. Resistance is a measure of how much a component opposes the flow of current. It is defined by the ratio of voltage to current: R = V / I. The unit of resistance is the ohm (Ω).
电压（电势差）是单位电荷通过元件时转移的能量。单位为伏特 (V)，使用并联的伏特表测量。电阻是衡量元件对电流阻碍作用的物理量，由电压与电流的比值定义：R = V / I。电阻的单位是欧姆 (Ω)。
2. Ohm’s Law and I–V Characteristics | 欧姆定律及电流-电压特性
Ohm’s law states that, provided the temperature remains constant, the current through a conductor is directly proportional to the potential difference across it. This linear relationship gives a constant resistance. Resistors that obey Ohm’s law are called ohmic conductors; a filament lamp is non-ohmic because its resistance increases as it gets hotter.
欧姆定律指出，在温度不变的条件下，通过导体的电流与其两端的电势差成正比。这种线性关系表现为恒定电阻。遵循欧姆定律的电阻器称为欧姆导体；白炽灯丝是非欧姆导体，因为它的电阻会随温度升高而增大。
The I–V graph for an ohmic conductor is a straight line passing through the origin. For a filament lamp, the graph curves, showing higher resistance at larger currents. For a diode, current flows easily in one direction (forward bias) but is almost zero in the reverse direction, producing a characteristic ‘knee’ shape.
欧姆导体的 I–V 图像是一条过原点的直线。白炽灯丝的图像弯曲，表明电流较大时电阻较高。对于二极管，电流在一个方向（正向偏置）容易通过，但在反向时几乎为零，形成特有的拐点形状。
3. Series Circuits: Shared Current and Divided Voltage | 串联电路：电流相同，电压分压
In a series circuit, components are connected end-to-end, providing a single path for current. The current is the same at all points: I₁ = I₂ = I₃. The total voltage supplied by the battery is shared across the components, so Vₜₒₜₐₗ = V₁ + V₂ + V₃. The total resistance is the sum of individual resistances: Rₜₒₜₐₗ = R₁ + R₂ + R₃.
在串联电路中，元件首尾相接，为电流提供唯一路径。各处电流相同：I₁ = I₂ = I₃。电池提供的总电压分配给各个元件，因此 Vₜₒₜₐₗ = V₁ + V₂ + V₃。总电阻等于各电阻之和：Rₜₒₜₐₗ = R₁ + R₂ + R₃。
Adding more resistors in series increases the total resistance, reducing the current. If one component fails (e.g. a bulb blows), the circuit is broken and the current stops everywhere. Series connections are simple but have the disadvantage of dependency—all components must work for the circuit to function.
串联更多电阻会增加总电阻，从而减小电流。如果一个元件损坏（如灯泡烧坏），电路断路，各处电流停止。串联连接简单，但缺点是相互依赖——所有元件必须正常工作电路才能运行。
4. Parallel Circuits: Shared Current and Constant Voltage | 并联电路：电流分流，电压相同
In a parallel circuit, components are connected on separate branches between the same two nodes. The voltage across each branch is equal to the supply voltage: V₁ = V₂ = V₃. The total current drawn from the source is the sum of the currents in each branch: Iₜₒₜₐₗ = I₁ + I₂ + I₃.
在并联电路中，元件连接在相同两个节点之间的不同分支上。各支路电压等于电源电压：V₁ = V₂ = V₃。从电源流出的总电流等于各支路电流之和：Iₜₒₜₐₗ = I₁ + I₂ + I₃。
The total (effective) resistance for resistors in parallel is found using the reciprocal formula: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃. The total resistance is always less than the smallest individual resistance. Parallel circuits are fault-tolerant: if one branch fails, current can still flow in the other branches.
并联电阻的总（等效）电阻用倒数公式计算：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃。总电阻总是小于最小的单个电阻。并联电路具有容错能力：如果一条支路断开，其他支路仍有电流通过。
5. Ammeters, Voltmeters and Correct Circuit Connection | 安培表、伏特表及正确接线
An ammeter must be placed in series with the component through which you wish to measure current. It has a very low resistance so that it does not significantly affect the circuit. A voltmeter is always connected in parallel across the component under test; it has a very high resistance to draw negligible current.
安培表必须与被测电流的元件串联。其内阻非常小，不会明显影响电路。伏特表总是并联在待测元件两端；其内阻非常高，吸取的电流可忽略不计。
When constructing circuits, correct polarities must be observed for digital meters or moving-coil meters. A fuse is often placed in series with the ammeter to protect it from excessive current. Students should practise drawing and interpreting circuit diagrams using standard symbols for cells, switches, fixed and variable resistors, lamps, diodes and meters.
搭建电路时，需注意数字电表或动圈式电表的正确极性。通常在安培表上串联保险丝，以防过流损坏。学生应练习使用标准符号绘制和解读电路图，包括电池、开关、定值电阻和可变电阻、灯泡、二极管及电表。
6. Experimental Determination of Resistance | 电阻的实验测定
The resistance of an unknown resistor can be found by measuring the current through it and the voltage across it, then applying R = V / I. The circuit consists of a power supply, an ammeter in series, the resistor under test, and a voltmeter in parallel. A variable resistor (rheostat) may be included to adjust the current and obtain multiple pairs of readings.
未知电阻的阻值可通过测量通过它的电流和两端电压，再应用 R = V / I 得到。电路包括电源、串联的安培表、待测电阻以及并联的伏特表。可加入可变电阻（滑线变阻器）来调节电流，获取多组读数。
Plotting a graph of V against I for an ohmic resistor yields a straight line whose gradient equals the resistance. If the line is not straight, the component is non-ohmic. Repetition and calculation of a mean value improve reliability. Common precautions include avoiding overheating and checking for zero error on meters.
对于欧姆电阻，绘制 V-I 图像得到一条直线，其斜率等于电阻。若非直线，则元件为非欧姆导体。重复实验并计算平均值可提高可靠性。常见的注意事项包括避免过热和检查电表零位误差。
7. The Potential Divider: Controlling Voltage | 分压电路：控制电压
A potential divider is a circuit that uses two (or more) resistors in series to provide a fraction of the input voltage. The output voltage Vₒᵤₜ across one resistor R₂ is given by: Vₒᵤₜ = Vᵢₙ × (R₂ / (R₁ + R₂)). This is extremely useful for sensors, volume controls and adjusting the brightness of a lamp.
分压电路是一种利用两个（或多个）串联电阻来提供输入电压一部分的电路。跨接在电阻 R₂ 上的输出电压 Vₒᵤₜ 为：Vₒᵤₜ = Vᵢₙ × (R₂ / (R₁ + R₂))。这在传感器、音量控制和调节灯泡亮度方面非常有用。
If one resistor is replaced by a light-dependent resistor (LDR) or thermistor, the output voltage changes with light intensity or temperature. When the LDR resistance falls in bright light, Vₒᵤₜ across a fixed series resistor rises. This principle underpins automatic street lights and temperature alarms.
如果用一个光敏电阻 (LDR) 或热敏电阻替换其中一个电阻，输出电压会随光照强度或温度变化。当 LDR 在强光下电阻下降时，与之串联的固定电阻上的 Vₒᵤₜ 会升高。这一原理是自动路灯和温度报警器的基础。
8. Electrical Power and Energy Transfer | 电功率与能量转换
Power is the rate at which energy is transferred. For an electrical component, power P can be calculated using three equivalent equations: P = I × V, P = I² × R and P = V² / R. The unit of power is the watt (W), where 1 W = 1 J/s.
功率是能量转移的速率。对于电气元件，功率 P 可用三个等价公式计算：P = I × V、P = I² × R 和 P = V² / R。功率的单位是瓦特 (W)，1 W = 1 J/s。
The energy E transferred by a component is the product of power and time: E = P × t or E = I × V × t. Energy is measured in joules (J). In the home, the kilowatt-hour (kW h) is often used: energy (kW h) = power (kW) × time (h). Understanding energy transfer helps in selecting suitable fuse ratings and explaining why components get hot.
元件转换的能量 E 是功率与时间的乘积：E = P × t 或 E = I × V × t。能量的单位是焦耳 (J)。家庭中常用千瓦时 (kW h)：能量 (kW h) = 功率 (kW) × 时间 (h)。理解能量转换有助于选择合适的保险丝额定值，并解释元件为何会发热。
9. EMF, Terminal Voltage and Internal Resistance | 电动势、端电压和内阻
All real cells have internal resistance (r) due to the materials inside the cell. The electromotive force (EMF, symbol ε) is the energy supplied per unit charge by the cell when no current is flowing. When a current I flows, the terminal voltage V across the cell terminals is less than the EMF: V = ε − I × r.
所有真实电池由于内部材料而存在内阻 (r)。电动势（EMF，符号 ε）是电池在没有电流时每单位电荷提供的能量。当电流 I 通过时，电池两端的端电压 V 小于电动势：V = ε − I × r。
This explains why a battery appears to ‘lose’ voltage under load. The lost volts are equal to I × r. By measuring terminal voltage for different currents, a graph of V against I gives a straight line with gradient −r and y-intercept ε. This is a common practical investigation in IGCSE physics.
这解释了为什么电池在有负载时电压似乎“下降”。损耗的电压等于 I × r。通过测量不同电流下的端电压，绘制 V-I 图像可得到一条斜率为 −r、y 轴截距为 ε 的直线。这是 IGCSE 物理中常见的实验研究。
10. Energy Transfers and Circuit Safety | 电路中的能量转换与安全
In any circuit, energy is conserved: electrical energy is transformed into other forms. In a resistor, electrical energy is converted into thermal energy (heating effect). In a lamp, some energy becomes light, but much is still heat. In a loudspeaker, electrical energy becomes sound. Understanding power ratings allows us to choose components that can dissipate heat safely.
在任何电路中，能量是守恒的：电能转化为其他形式。在电阻器中，电能转化为热能（热效应）。在灯泡中，部分能量变成光，但大部分仍是热。在扬声器中，电能转化为声能。了解功率额定值可以帮助我们选择能安全散热而不过热的元件。
Fuses and circuit breakers protect circuits by melting or tripping when the current exceeds a safe limit. The fuse rating should be slightly higher than the normal operating current of the appliance. Earth wires and double insulation are also key safety features in mains circuits, which are part of the broader electricity topic.
保险丝和断路器通过在电流超过安全限值时熔断或跳闸来保护电路。保险丝的额定值应略高于电器的正常工作电流。接地线和双重绝缘也是市电电路的重要安全特性，这些属于更广泛的电学主题的一部分。
11. Systematic Circuit Analysis and Fault Finding | 系统化电路分析与排错
To analyse a complex combination circuit, first simplify parallel sections into their equivalent resistance, then treat the whole network as a series circuit. Determine the total current from the source using V = I × R, then work backwards to find branch currents and individual voltages. This layered approach ensures accuracy.
要分析复杂的混联电路，首先将并联部分简化为等效电阻，然后将整个网络视为串联电路。利用 V = I × R 确定电源总电流，再逆向推导支路电流和各个电压值。这种分层方法可保证准确性。
Common faults in circuits include short circuits (very low resistance bypassing a component), open circuits (break in the path causing zero current), and incorrect meter connections causing zero or negative readings. Practising with predicted outcomes, such as the effect of a blown bulb in a string of Christmas lights, builds deep understanding.
电路中的常见故障包括短路（极低电阻旁路元件）、断路（路径断开导致电流为零）以及电表接线错误导致读数为零或负值。练习预测结果，例如一串圣诞灯中一个灯泡烧坏的影响，可以加深理解。
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