📚 IB AQA Physics: Circuit Analysis Key Points | IB AQA 物理：电路分析考点精讲
Circuit analysis forms the backbone of electricity and magnetism topics in IB and AQA Physics. A solid grasp of fundamental laws, component behaviour, and energy transfers allows you to solve complex circuits with confidence. This article breaks down key exam points, from Ohm’s law to Kirchhoff’s rules, potential dividers, and internal resistance, linking theory to typical problem‑solving strategies.
电路分析是 IB 和 AQA 物理中电学与磁学的核心。牢固掌握基本定律、元件特性及能量转换，是自信解答复杂电路题的基础。本文梳理了从欧姆定律到基尔霍夫定律、分压电路以及内阻等关键考点，将理论与典型解题策略紧密结合起来。
1. Ohm’s Law and Resistance | 欧姆定律与电阻
Ohm’s law states that the current I through a conductor between two points is directly proportional to the potential difference V across the two points, provided the temperature remains constant. The constant of proportionality is the resistance R: V = IR. The SI unit of resistance is the ohm (Ω).
欧姆定律指出，在温度不变的条件下，通过导体两点的电流 I 与这两点间的电势差 V 成正比，比例常数即为电阻 R：V = IR。电阻的 SI 单位是欧姆 (Ω)。
Resistance depends on the material’s resistivity ρ, length L, and cross‑sectional area A: R = ρL/A. Resistivity is a property of the material and increases with temperature in most conductors.
电阻取决于材料的电阻率 ρ、长度 L 及横截面积 A：R = ρL/A。电阻率是材料的一种属性，在大多数导体中随温度升高而增大。
For an ohmic conductor, the I–V graph is a straight line passing through the origin; the resistance is constant and equals the inverse of the gradient. Non‑ohmic components, such as a filament lamp or diode, show curved characteristics.
对于欧姆导体，I–V 图像是一条过原点的直线，电阻恒定，等于斜率倒数。非欧姆元件，如白炽灯或二极管，则呈现曲线特性。
2. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the current is the same everywhere: I = I₁ = I₂ = … . The total resistance is the sum of individual resistances: Rₜₒₜ = R₁ + R₂ + … . The supply voltage divides among the components in proportion to their resistances.
在串联电路中，各处电流相等：I = I₁ = I₂ = …。总电阻等于各电阻之和：Rₜₒₜ = R₁ + R₂ + …。电源电压按电阻比例分配给各元件。
In a parallel circuit, the voltage across each branch is the same: V = V₁ = V₂ = … . The total current splits among the branches, and the sum of branch currents equals the main current: Iₜₒₜ = I₁ + I₂ + … . The reciprocal of the total resistance is the sum of the reciprocals of individual resistances: 1/Rₜₒₜ = 1/R₁ + 1/R₂ + … .
在并联电路中，各支路电压相等：V = V₁ = V₂ = …。总电流在各支路间分配，支路电流之和等于干路电流：Iₜₒₜ = I₁ + I₂ + …。总电阻的倒数等于各电阻倒数之和：1/Rₜₒₜ = 1/R₁ + 1/R₂ + …。
Combining series and parallel sections requires systematic reduction: first replace parallel groups with their equivalent resistance, then treat the entire circuit as a series combination.
对于串联与并联混合的电路，需要系统地化简：先将并联部分等效为一个电阻，再将整个电路按串联处理。
3. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a junction is zero, or equivalently, the total current entering a junction equals the total current leaving it. This reflects the conservation of electric charge.
基尔霍夫电流定律 (KCL) 表明，流入节点的电流代数和为零，或者说流入节点的总电流等于流出节点的总电流。这体现了电荷守恒。
Kirchhoff’s voltage law (KVL) states that the algebraic sum of potential differences around any closed loop in a circuit is zero. This follows from the conservation of energy: the total energy gained per unit charge from sources equals the total energy dissipated per unit charge in the passive components.
基尔霍夫电压定律 (KVL) 表明，沿电路任一闭合回路的电势差代数和为零。这源于能量守恒：单位电荷从电源获得的总能量，等于其在无源元件中消耗的总能量。
When applying KVL, assign a direction of travel around the loop. A voltage rise (e.g., moving from – to + of a battery) is taken as positive, and a voltage drop (across a resistor in the direction of current) is negative. The sum must equal zero.
应用 KVL 时，先设定回路绕行方向。通常将电势升（如从电池负极到正极）取正，将电势降（沿电流方向通过电阻）取负，代数和需为零。
4. Potential Dividers | 分压电路
A potential divider uses two or more resistors in series to produce a fraction of the input voltage. The output voltage Vₒᵤₜ across a resistor R₂ in a series chain R₁–R₂ connected across a supply Vₛ is given by Vₒᵤₜ = Vₛ × R₂/(R₁ + R₂).
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。在电源 Vₛ 下的串联链 R₁–R₂ 中，电阻 R₂ 两端的输出电压 Vₒᵤₜ 为 Vₒᵤₜ = Vₛ × R₂/(R₁ + R₂)。
If one of the resistors is a variable resistor or a sensor (e.g., thermistor, LDR), the output voltage changes with temperature or light intensity, forming the basis of many sensing circuits. In the IB exam, you may be asked to show how Vₒᵤₜ varies as the sensor resistance changes.
若其中一个电阻为可变电阻或传感器（如热敏电阻、光敏电阻），输出电压会随温度或光照强度变化，构成多种传感电路的基础。在 IB 考试中，可能需要说明 Vₒᵤₜ 如何随传感器电阻变化。
When using a potentiometer as a variable potential divider, the sliding contact allows continuous adjustment of the output from zero to the full supply voltage.
当使用电位器作为可变分压器时，滑动触点可使输出电压从零连续调至全电源电压。
5. Internal Resistance and EMF | 内阻与电动势
The electromotive force (emf) ε of a source is the energy supplied per unit charge when no current flows. When a current I flows, the terminal potential difference V is less than ε due to the internal resistance r: V = ε – Ir. Ir is the ‘lost volts’.
电源的电动势 ε 是指无电流时每单位电荷提供的能量。当电流 I 流过时，由于内阻 r 的存在，路端电压 V 低于 ε：V = ε – Ir。Ir 即为“损耗电压”。
The relationship V = ε – Ir is a linear equation. Plotting V on the y‑axis against I on the x‑axis yields a straight line with gradient –r and y‑intercept ε. This is a common IB practical analysis task.
关系式 V = ε – Ir 是线性方程。以 V 为纵轴、I 为横轴作图，可得到一条斜率为 –r、截距为 ε 的直线。这是 IB 实验分析中的常见任务。
When a battery delivers maximum power to an external load R, R equals r. The power delivered is then Pₘₐₓ = ε²/(4r). However, the efficiency is only 50% under this condition.
电池向外接负载 R 输出最大功率时，满足 R = r，此时输出功率为 Pₘₐₓ = ε²/(4r)，但此条件下效率仅为 50%。
6. Electrical Power and Energy | 电功率与电能
Power P is the rate at which energy is transferred. For any circuit element, P = IV. Using Ohm’s law, for a resistor it can also be expressed as P = I²R = V²/R. The unit of power is the watt (W).
电功率 P 是能量传递的速率。对任意电路元件，P = IV。对于电阻，结合欧姆定律还可写成 P = I²R = V²/R。功率的单位是瓦特 (W)。
Energy transferred W equals power multiplied by time: W = Pt. The SI unit is the joule (J). In electricity billing, the kilowatt‑hour (kW·h) is often used: 1 kW·h = 3.6 × 10⁶ J.
传递的电能 W 等于功率乘以时间：W = Pt。SI 单位是焦耳 (J)。电费计量常用千瓦时 (kW·h)：1 kW·h = 3.6 × 10⁶ J。
When analysing circuits, you can compare the brightness of identical lamps by calculating the power dissipated in each; a lamp with a larger P will glow brighter, assuming the same efficiency.
在电路分析中，可通过计算每盏灯泡消耗的功率来比较相同灯泡的亮度；假设效率相同，功率越大，灯泡越亮。
7. Resistivity and Conductivity | 电阻率与电导率
Resistivity ρ is an intrinsic property of a material, measured in ohm‑metres (Ω·m). The resistance of a uniform wire is R = ρL/A. Conductors like copper have low resistivity (~1.7 × 10⁻⁸ Ω·m), while insulators have extremely high resistivity.
电阻率 ρ 是材料的固有属性，单位为欧姆·米 (Ω·m)。均匀导线的电阻为 R = ρL/A。铜等导体电阻率很低（~1.7 × 10⁻⁸ Ω·m），而绝缘体电阻率极高。
Conductivity σ is the reciprocal of resistivity: σ = 1/ρ. Its unit is siemens per metre (S m⁻¹). Good conductors have high conductivity.
电导率 σ 是电阻率的倒数：σ = 1/ρ，单位为西门子每米 (S m⁻¹)。良导体具有高电导率。
Resistivity depends on temperature; for a metal, ρ ≈ ρ₀[1 + α(T – T₀)], where α is the temperature coefficient of resistivity. For a typical metal, α is positive, meaning resistance increases with temperature.
电阻率随温度变化；对金属，近似有 ρ ≈ ρ₀[1 + α(T – T₀)]，其中 α 为电阻温度系数。典型金属的 α 为正，即电阻随温度升高而增大。
8. I–V Characteristics | 电流–电压特性曲线
The I–V characteristic of a component shows how current changes with applied voltage. It is essential for identifying whether a component is ohmic or non‑ohmic and for determining its resistance at a specific operating point.
元件的 I–V 特性曲线展示了电流随外加电压的变化关系。这对于判断元件是否为欧姆元件以及确定其特定工作点的电阻至关重要。
Key I–V shapes to remember for IB/AQA: a metallic conductor at constant temperature gives a straight line through the origin. A filament lamp curves with decreasing gradient as V increases because heating raises resistance. A semiconductor diode conducts only in forward bias, with a very steep rise once the threshold voltage (~0.6 V for silicon) is exceeded.
IB/AQA 需记住的关键 I–V 形状：恒温金属导体为过原点的直线；白炽灯的曲线随 V 增大斜率递减，因为升温使电阻增加；半导体二极管仅在正向偏置时导通，超过阈值电压（硅约 0.6 V）后电流陡升。
To find resistance from an I–V graph, take the reciprocal of the gradient at a point (R = V/I) for an ohmic component, or use the slope of the tangent if the characteristic is curved.
从 I–V 图像求电阻时，对于欧姆元件，可计算该点的 V/I（即斜率的倒数）；若为曲线，则使用该点切线的斜率。
9. Applying Kirchhoff’s Laws in Multi‑Loop Circuits | 基尔霍夫定律在多回路电路中的应用
In multi‑loop circuits, start by labelling all currents, assigning directions arbitrarily. Write KCL equations at as many junctions as needed, then use KVL for independent loops. Solve the simultaneous equations to find unknown currents or voltages.
处理多回路电路时，先标出所有电流并任意设定方向。在必要数量的节点上写出 KCL 方程，然后对独立回路应用 KVL，联立方程求解未知电流或电压。
A common IB exam scenario involves two batteries in parallel with resistors, or a Wheatstone bridge circuit. In a balanced Wheatstone bridge, the ratio R₁/R₂ = R₃/R₄, and the galvanometer current is zero, which can be derived using KVL and KCL.
IB 考试常见的题型包括两电池并联带电阻，或惠斯通电桥电路。当惠斯通电桥平衡时，满足 R₁/R₂ = R₃/R₄，检流计电流为零，这可通过 KVL 和 KCL 推导得出。
When the bridge is unbalanced, you need to solve a network of equations; often it is efficient to use loop analysis, assigning loop currents to reduce the number of unknowns.
当电桥不平衡时，需解网络方程组；采用回路分析法并设定回路电流，可以有效减少未知量数目。
10. Real-World Considerations and Exam Tips | 实际情境与答题技巧
In practical circuits, wires have small but non‑zero resistance, and connections may introduce contact resistance. In exam questions, always check whether internal resistance of meters should be considered. An ideal voltmeter has infinite resistance; an ideal ammeter has zero resistance.
实际电路中，导线具有微小但不可忽略的电阻，连接处可能有接触电阻。在考题中，务必确认是否需要考虑电表内阻：理想电压表内阻无限大，理想电流表内阻为零。
Always express final answers with the correct SI units and to an appropriate number of significant figures. Clearly state any assumptions, such as ‘neglecting internal resistance’ or ‘assuming the temperature remains constant’.
最终答案务必使用正确的 SI 单位，并保留适当有效数字。清晰说明所做的假设，例如“忽略内阻”或“假设温度恒定”。
When a question asks to ‘show that’ a relationship holds, begin from fundamental principles (e.g. conservation of charge or energy) and build the proof step by step, quoting the laws you apply.
当题目要求“证明”某一关系时，应从基本原理（如电荷或能量守恒）出发，逐步推导，并引用所使用的定律。
Practice interpreting circuit diagrams and redrawing them in a simpler equivalent form; this skill is invaluable for both multiple‑choice and structured questions on circuit analysis.
多练习解读电路图并将其重画为更简洁的等效形式；这一技巧对电路分析的选择题和结构化题目都极为有用。
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