📚 IGCSE Physics: Circuit Analysis – Key Points | IGCSE 物理：电路分析 考点精讲
Circuit analysis is a cornerstone of IGCSE Physics, equipping you to predict how current, voltage and resistance behave in complete loops. Mastering these concepts not only helps you solve numerical problems but also builds the foundation for understanding everyday electrical devices and safe wiring. This article unpacks every key point you need for the exam, from Ohm’s law to potential dividers and circuit protection.
电路分析是 IGCSE 物理的核心内容，它能帮助你预测电流、电压和电阻在完整回路中的行为。掌握这些概念不仅能解决计算题，还能为你理解日常电器和安全布线打下基础。本文梳理了从欧姆定律到分压器、电路保护等所有必考要点。
1. Circuit Symbols and Diagrams | 电路符号与电路图
You must instantly recognise standard IGCSE circuit symbols. A cell provides a fixed voltage, a battery is two or more cells joined together, and a lamp converts electrical energy into light. A switch controls the flow of current, while a fixed resistor has a constant resistance. Variable resistors (rheostats) allow you to change the resistance manually. A diode lets current pass in one direction only, and a light‑emitting diode (LED) gives out light when forward‑biased. A fuse is drawn as a box with a wire link and protects the circuit from excessive current. A voltmeter measures potential difference and an ammeter measures current; their symbols include a circle with V or A and show distinct connection rules. An LDR (light‑dependent resistor) and a thermistor are special resistors whose values change with light and temperature respectively.
你必须能立刻识别 IGCSE 标准电路符号。电池（cell）提供恒定电压，电池组（battery）是两个或更多电池的组合，灯泡将电能转化为光。开关控制电流的通断，固定电阻器具有不变的电阻，变阻器（滑动变阻器）可以手动改变电阻。二极管只允许电流单向通过，发光二极管在正向偏置时会发光。保险丝通常画为一个带有导线连接的方框，用于保护电路免受过流损坏。电压表测量电势差，电流表测量电流，它们的符号是圆圈内加 V 或 A，且接线规则截然不同。光敏电阻 (LDR) 和热敏电阻是两种特殊的电阻，其电阻值分别随光照和温度变化。
- Learn the exact shape of each symbol; examiners often deduct marks for sloppy drawing.
- 务必记住每个符号的精确画法，考官常因画图不规范而扣分。
- A complete circuit must provide a closed conducting path from the positive terminal of the supply back to its negative terminal.
- 完整的电路必须提供从电源正极回到负极的闭合导电通路。
2. Current, Voltage and Resistance | 电流、电压与电阻
Electric current is the rate of flow of charge. In a metal wire, it is carried by moving electrons. The unit of current is the ampere (A). Conventional current flows from the positive to the negative terminal of a battery, opposite to the direction of electron flow. Potential difference (voltage) is the energy transferred per unit charge between two points. It is measured in volts (V): one volt means one joule of energy is given to each coulomb of charge that passes. Resistance is the opposition to current, measured in ohms (Ω). For a fixed temperature, the resistance of a metallic conductor is constant, giving a linear relationship between voltage and current.
电流是电荷流动的速率。在金属导线中，它由运动的电子承载。电流的单位是安培 (A)。约定电流的方向是从电池正极流向负极，与电子流动方向相反。电势差（电压）是两点间每单位电荷转移的能量，单位为伏特 (V)：1 伏特意味着每库仑电荷通过时获得 1 焦耳的能量。电阻是对电流的阻碍作用，单位为欧姆 (Ω)。在温度固定时，金属导体的电阻恒定，使电压和电流之间呈线性关系。
Good conductors have very low resistance, while insulators have extremely high resistance. The resistance of a wire depends on its length (longer wire → higher resistance), cross‑sectional area (thicker wire → lower resistance), material (resistivity) and temperature (for most metals, resistance increases with temperature).
良导体的电阻极低，绝缘体的电阻极高。导线的电阻取决于长度（越长电阻越大）、横截面积（越粗电阻越小）、材料（电阻率）和温度（大多数金属的电阻随温度升高而增大）。
3. Ohm’s Law and I-V Characteristics | 欧姆定律及 I-V 特性曲线
V = I × R
Ohm’s law states that, at constant temperature, the current through a conductor is directly proportional to the potential difference across it. A component obeying this law is called an ohmic conductor, and its I‑V graph is a straight line passing through the origin. A fixed metallic resistor at steady temperature is a classic ohmic component.
欧姆定律指出，在温度恒定时，通过导体的电流与导体两端的电势差成正比。遵从该定律的元件称为欧姆导体，其 I‑V 特性图是一条通过原点的直线。恒温下的固定金属电阻器是典型的欧姆元件。
Several components are non‑ohmic. A filament lamp has an I‑V curve that bends at higher currents because its temperature rises, increasing resistance. The graph is symmetric about the origin. A diode has a very different characteristic: it conducts easily in forward bias (above about 0.7 V for a silicon diode) with a steep rise in current, but in reverse bias the current remains near zero until breakdown. An LED behaves similarly but emits light when conducting. A thermistor’s resistance falls as temperature rises, and an LDR’s resistance falls as light intensity increases, giving curved I‑V graphs that depend on external conditions.
许多元件是非欧姆的。白炽灯的 I‑V 曲线在高电流区域弯曲，因为灯丝温度升高导致电阻增大；曲线关于原点对称。二极管的特性截然不同：正向偏置时（硅二极管约 0.7 V 以上）很容易导通，电流急剧上升；反向偏置时电流几乎为零，直到击穿。发光二极管具有类似特性，但在导通时会发光。热敏电阻的阻值随温度升高而下降，光敏电阻的阻值随光照增强而下降，它们的 I‑V 曲线受外部条件影响而弯曲。
4. 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 every point: Itotal = I₁ = I₂ = I₃. The total potential difference supplied by the battery is shared across the components: Vsupply = V₁ + V₂ + V₃. The total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + R₃. Adding more resistors in series increases the total resistance, which reduces the current for a fixed supply voltage.
在串联电路中，元件首尾相连形成单一环路。电路中各点的电流处处相等：I 总 = I₁ = I₂ = I₃。电池提供的总电势差由各元件分担：V 电源 = V₁ + V₂ + V₃。总电阻等于各个电阻之和：R 总 = R₁ + R₂ + R₃。串联更多电阻会使总电阻增大，从而在电源电压不变时减小电流。
If one component breaks or is disconnected, the entire circuit becomes an open circuit and all current stops. Series connections are used when you want to share voltage—for example, in a potential divider or when connecting several low‑voltage lamps to match a higher supply voltage.
如果某个元件损坏或断开，整个电路变为断路，所有电流停止。串联连接常用于需要分配电压的场合，例如分压器，或者将多个低压灯泡串联以匹配较高电源电压。
5. Parallel Circuits | 并联电路
In a parallel circuit, components are connected on separate branches between the same two points of the supply. The voltage across each branch is the same as the supply voltage: V₁ = V₂ = Vsupply. Current splits at junctions and recombines: Itotal = I₁ + I₂ + I₃. The total resistance is lower than the smallest individual branch resistance because more paths are available for the current. For two resistors in parallel, the equivalent resistance is given by:
在并联电路中，各元件分别连接在电源相同两点之间的不同支路上。每条支路两端的电压均与电源电压相等：V₁ = V₂ = V 电源。电流在节点分叉后重新汇合：I 总 = I₁ + I₂ + I₃。由于电流有多条通路，总电阻小于各支路中的最小电阻。对于两个并联电阻，等效电阻由下式给出：
1/Rtotal = 1/R₁ + 1/R₂ or Rtotal = (R₁ × R₂) / (R₁ + R₂)
A key feature of parallel circuits is that each component operates independently: switching off one branch does not stop current in the other branches. This is why household wiring uses parallel connections—so that turning off a lamp does not cut power to the refrigerator.
并联电路的一个重要特性是各个元件独立工作：断开一条支路不会中断其他支路的电流。这正是家用电路采用并联连接的原因——关掉一盏灯不会切断冰箱的供电。
6. Equivalent Resistance Calculations | 等效电阻计算
For series resistors, simply add their values. For parallel resistors, you can use the reciprocal formula or the product‑over‑sum shortcut for exactly two resistors. Combined series‑parallel circuits require careful step‑by‑step reduction: first combine clear series or parallel groups, redraw the simplified circuit and repeat until you obtain the total resistance between the terminals of the supply.
对于串联电阻，直接相加即可。对于并联电阻，可使用倒数公式，或对两个电阻使用“积和商”简化公式。串并联混合电路需要逐步化简：先合并明显的串联或并联部分，重绘简化电路，重复此过程，直至得到电源两端之间的总电阻。
Always check that your calculated total resistance makes sense. In series, the total must be larger than any individual resistor; in parallel, it must be smaller than the smallest branch resistance. Common exam errors involve putting resistors in series when the diagram shows them in parallel, or forgetting that an ammeter’s tiny internal resistance is negligible when calculating.
永远要检查计算出的总电阻是否合理。串联总电阻一定大于任何一个单独的电阻，并联总电阻一定小于最小的支路电阻。常见的考试错误包括将图中明明是并联的电阻误当作串联处理，或在计算时忽略了电流表极小的内阻。
7. The Potential Divider | 分压器
A potential divider uses two or more resistors in series to produce a fraction of the input voltage. If a total voltage Vin is applied across two series resistors R₁ and R₂, the output voltage taken across R₂ is:
分压器利用两个或多个串联电阻来获得输入电压的一部分。若将总电压 V in 加在两个串联电阻 R₁ 和 R₂ 两端，则取 R₂ 两端的输出电压为：
Vout = (R₂ / (R₁ + R₂)) × Vin
This relationship holds only when negligible current is drawn from the output terminals—otherwise the effective value of R₂ changes. A variable potential divider can be made with a rheostat or a potentiometer wired as a three‑terminal device. By sliding the wiper, you continuously vary the output voltage from 0 V to Vin. Practically, an LDR or thermistor replacing one of the fixed resistors turns the circuit into a sensor. For instance, an LDR in series with a fixed resistor can make an automatic night light: as darkness increases, LDR resistance rises, so the voltage across it increases and can trigger a transistor switch.
该关系仅在输出端几乎不吸取电流时成立，否则 R₂ 的有效值会改变。利用三端接线的滑动变阻器或电位器可以构成可变分压器。移动滑片时，输出电压可连续地从 0 V 调节到 V in。在实际应用中，若用光敏电阻或热敏电阻替代其中一个固定电阻，电路就变成传感器。例如，LDR 与固定电阻串联可做成自动夜灯：光线越暗，LDR 阻值越大，其两端电压随之升高，进而触发晶体管开关。
8. Electrical Power and Energy | 电功率与电能
P = I × V P = I² × R P = V² / R
Electrical power is the rate at which electrical energy is transferred to other forms. The unit is the watt (W), where 1 W = 1 J/s. The formula P = I × V is the most fundamental; the other two are derived by substituting V = I × R into it. The energy transfers are often as heat in a resistor, light in a lamp, or kinetic energy in a motor.
电功率是电能转化为其他形式能量的速率，单位为瓦特 (W)，1 W = 1 J/s。公式 P = I × V 最为基本，另外两个公式通过代入 V = I × R 推导得出。功率转化通常表现为电阻中的热能、灯泡中的光能或电动机中的动能。
Energy consumed by an appliance is power multiplied by time: E = P × t. When time is measured in seconds, energy is in joules. In practical electricity billing, kilowatt‑hours (kW h) are used, where 1 kW h = 3.6 × 10⁶ J. Always convert time to hours and power to kilowatts when using this unit.
用电器消耗的电能等于功率乘以时间：E = P × t。若时间以秒计，能量单位为焦耳。在实际电费账单中，常使用千瓦时 (kW h)，1 kW h = 3.6 × 10⁶ J。使用该单位时须将时间转换为小时、功率转换为千瓦。
Fuses and circuit breakers are rated by current, but their selection depends on power as well. For a given appliance power and supply voltage, you can calculate the normal operating current and choose a fuse with a slightly higher rating.
保险丝和断路器是按电流额定值选用的，但其选择也涉及功率。根据电器功率和电源电压，可计算出正常工作电流，然后选用额定值稍高的保险丝。
9. Using Ammeters and Voltmeters | 电流表与电压表的使用
An ammeter measures current and must be connected in series so that the same current flows through it. Its internal resistance is extremely low to avoid affecting the circuit. A voltmeter measures potential difference and is always connected in parallel across the component of interest. Its internal resistance is extremely high to draw negligible current.
电流表测量电流，必须串联在电路中，使被测电流流过它。电流表内阻极低，以免影响电路。电压表测量电势差，总是并联在待测元件两端。电压表内阻极高，几乎不吸取电流。
Connecting an ammeter in parallel would create a very low‑resistance path between two points—effectively a short circuit—and may damage the meter or blow a fuse. Connecting a voltmeter in series would insert an enormous resistance, almost stopping the current and giving a false reading near the supply voltage. Always double‑check your connection before turning on the circuit.
若将电流表并联到两点之间，会形成极低电阻通路，实质上造成短路，可能损坏电表或烧断熔丝。若将电压表串联在电路中，则会引入极大电阻，几乎切断电流，读数仅接近电源电压，完全失实。通电前务必仔细检查接线。
10. Diodes and Their Function | 二极管及其功能
A diode is a semiconductor device that permits current to flow in one direction only. In forward bias (anode connected to the positive terminal), it presents low resistance; in reverse bias (cathode negative), it has extremely high resistance. A typical silicon diode begins to conduct significantly when the forward voltage exceeds about 0.7 V. If the reverse voltage exceeds the breakdown limit, the diode can be destroyed.
二极管是一种半导体器件，只允许电流单向通过。正向偏置（阳极接正极）时，它呈现低电阻；反向偏置（阳极接负极）时，电阻极高。典型的硅二极管在正向电压超过约 0.7 V 时才开始显著导通。若反向电压超过击穿极限，二极管可能被烧毁。
Diodes are used to convert alternating current (AC) to direct current (DC) in rectifier circuits and to protect sensitive components from reverse connection. An LED emits light of a specific colour when it conducts. The longer lead of an LED is the anode, and a series resistor is essential to limit the forward current, preventing damage.
二极管常用于整流电路中将交流 (AC) 转换为直流 (DC)，也可保护敏感元件免受反接之害。发光二极管在导通时发出特定颜色的光。LED 较长的引线为阳极，必须串联限流电阻以防止损坏。
11. Circuit Protection – Fuses and Circuit Breakers | 电路保护——保险丝和断路器
A fuse is a thin wire that melts and breaks the circuit if the current exceeds its rated value. It is always placed in the live wire, so that when it blows, the appliance is fully isolated from the mains. Common fuse ratings are 3 A, 5 A and 13 A. The rating should be slightly above the normal operating current of the appliance.
保险丝是一根细导线，当电流超过额定值时熔断，切断电路。它总是接在火线上，这样一旦熔断，电器就与市电完全断开。常见的保险丝额定值有 3 A、5 A 和 13 A。额定值应略高于电器的正常工作电流。
A circuit breaker performs the same function but can be reset electrically or mechanically. It trips when the current becomes dangerously high, often due to an overload or a short circuit. Both fuses and circuit breakers prevent overheating of wires, reducing the risk of fire. Double insulation and earthing are additional safety measures used in appliances, but these are not the focus of basic circuit analysis.
断路器功能类似，但可通过电或机械方式复位。当电流由于过载或短路而变得危险时，它会跳闸。保险丝和断路器都能防止导线过热，降低火灾风险。双层绝缘和接地是用电器的额外安全措施，但不属于基础电路分析的核心考点。
12. Short Circuits and Open Circuits | 短路与断路
A short circuit occurs when a low‑resistance path is accidentally provided between two points of different potential, bypassing the intended load. This can happen if a bare live wire touches a neutral or earth wire. Because resistance is very low, the current rises dramatically, generating huge amounts of heat in the wires and potentially causing a fire. Fuses or circuit breakers are designed to detect this overcurrent and disconnect the circuit quickly.
短路发生在不同电位的两点之间意外出现低电阻通路，绕过了正常负载。例如裸露的火线接触到零线或地线就会造成短路。由于电阻极低，电流急剧增大，导线中产生大量热量，可能引发火灾。保险丝或断路器正是为此而设计，能检测到过电流并迅速切断电路。
An open circuit means the conductive path is broken. No current flows, and the full supply voltage appears across the break. In a series circuit, an open switch or burned‑out bulb stops all current. In a parallel circuit, only the branch with the break goes off; other branches continue to function normally. Diagnosing open circuits with a voltmeter is a common practical skill: measuring full supply voltage across a component suggests it is open or disconnected.
断路是指导电通路被中断。无电流流动，断路处两端会出现全部电源电压。在串联电路中，断开的开关或烧坏的灯泡会使所有电流停止。在并联电路中，只有发生断路的那条支路停止工作，其他支路正常运行。用电压表诊断断路是一项常见实验技能：若测得某元件两端为全电源电压，则暗示它已断开或未接通。
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