📚 IB CCEA Physics: Resistance – Key Points | IB CCEA 物理：电阻 考点精讲
Resistance is a core concept in both IB and CCEA physics, linking voltage, current, material properties and circuit design. This article covers the essential definitions, laws, graphs and practical skills you need to score high marks on resistance questions, whether you are studying for Standard Level, Higher Level or the CCEA A-Level specification. Each topic is presented with paired English and Chinese explanations to build your subject vocabulary and deep understanding.
电阻是 IB 和 CCEA 物理共同的核心考点，将电压、电流、材料性质与电路设计紧密联系在一起。本文梳理了电阻的定义、定律、图像与实验技能，无论你准备的是标准级别、高级别还是 CCEA A-Level 考试，都能从中获得高分必备的知识。每个主题都配有中英双语讲解，帮你构建学科词汇和深层理解。
1. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance (R) is defined as the ratio of potential difference (V) across a component to the current (I) flowing through it. The defining equation is R = V / I, and the SI unit is the ohm (Ω).
电阻（R）定义为元件两端的电势差（V）与通过它的电流（I）之比。定义式为 R = V / I，国际单位是欧姆（Ω）。
Ohm’s law states that, for a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it, so its resistance remains constant. Components that follow this linear relationship are called ohmic conductors.
欧姆定律指出，在温度不变的条件下，通过金属导体的电流与其两端的电势差成正比，因此它的电阻保持恒定。满足这种线性关系的元件称为欧姆导体。
Not all materials obey Ohm’s law. Filament lamps, diodes and thermistors have non-linear I–V characteristics, and their resistance changes with voltage or current. These are known as non-ohmic devices.
并非所有材料都遵循欧姆定律。灯丝、二极管和热敏电阻都具有非线性的 I–V 特性，其电阻会随电压或电流的变化而改变。这类元件称为非欧姆器件。
R = V / I
2. Resistivity and Conductivity | 电阻率与电导率
The resistance of a uniform wire depends on its length L, cross-sectional area A and the material’s resistivity ρ. The relationship is given by ρ = RA / L, so resistance increases with length and decreases with larger area. Resistivity has the unit ohm metre (Ω·m).
一根均匀导线的电阻取决于它的长度 L、横截面积 A 和材料的电阻率 ρ。关系式为 ρ = RA / L，因此电阻随长度增加而增大，随截面积增大而减小。电阻率的单位是欧姆·米（Ω·m）。
Conductivity σ is the reciprocal of resistivity: σ = 1 / ρ. Good conductors like copper and silver have very low resistivities, while insulators such as glass and rubber have extremely high resistivities. Semiconductors lie in between and their resistivity can be altered by doping or temperature changes.
电导率 σ 是电阻率的倒数：σ = 1 / ρ。铜和银等良导体的电阻率非常低，而玻璃和橡胶等绝缘体的电阻率极高。半导体的电阻率介于两者之间，并且可以通过掺杂或温度变化来调节。
ρ = RA / L
3. Temperature Coefficient of Resistance | 电阻温度系数
For most metallic conductors, resistance increases with temperature. This can be modelled using the temperature coefficient α: R = R₀[1 + α (T − T₀)], where R₀ is the resistance at a reference temperature T₀ (often 0 °C or 20 °C). α is positive for pure metals.
对大多数金属导体而言，电阻随温度升高而增大。这可以用温度系数 α 来建模：R = R₀[1 + α (T − T₀)]，其中 R₀ 是在参考温度 T₀（通常为 0 °C 或 20 °C）下的电阻值。纯金属的 α 为正值。
Semiconductors and thermistors usually have a negative temperature coefficient, meaning their resistance decreases as they get hotter. This property makes negative-temperature-coefficient (NTC) thermistors useful for temperature sensing and circuit protection.
半导体和热敏电阻通常具有负温度系数，也就是说温度升高时电阻反而下降。这一特性使得负温度系数（NTC）热敏电阻广泛用于温度传感和电路保护。
The change in resistance with temperature can be explained by increased lattice vibrations in metals, which scatter the conduction electrons more. In semiconductors, the dominant effect is the release of more charge carriers as the thermal energy increases.
温度引起电阻变化的原因可以从微观解释：金属中晶格振动加剧，增强了对传导电子的散射；而在半导体中，主要效应是热激发释放出更多的载流子。
R = R₀[1 + α (T − T₀)]
4. Series and Parallel Resistors | 串联与并联电阻
In a series circuit, the total resistance is the sum of individual resistances: R_total = R₁ + R₂ + R₃ + … . The current is the same through each resistor, but the total potential difference is divided among them in proportion to their resistances.
在串联电路中，总电阻等于各个电阻之和：R_total = R₁ + R₂ + R₃ + … 。通过每个电阻的电流相同，但总电压按照电阻的大小成比例地分配到各个电阻上。
In a parallel circuit, the reciprocal of the total resistance is the sum of the reciprocals of each branch resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + … . The potential difference across each branch is the same, and the total current splits between the branches.
在并联电路中，总电阻的倒数等于各支路电阻的倒数之和：1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + … 。每个支路两端的电压相同，总电流在各支路之间分配。
For two resistors in parallel, a simplified formula can be used: R_total = (R₁R₂) / (R₁ + R₂). This is particularly handy when combining only two resistors at a time.
当只有两个电阻并联时，可以使用简化公式：R_total = (R₁R₂) / (R₁ + R₂)。这种方法在每次合并两个电阻时非常方便。
| Property | Series | Parallel |
|---|---|---|
| Current | Same through all | Divided, I = I₁ + I₂ + … |
| Potential difference | Divided, V = V₁ + V₂ + … | Same across all branches |
| Total resistance | R_total = R₁ + R₂ + … | 1/R_total = 1/R₁ + 1/R₂ + … |
5. I–V Characteristics | I–V 特性曲线
An I–V graph plots current against voltage and reveals whether a component is ohmic or non-ohmic. The resistance at any point can be found as the reciprocal of the slope for an ohmic conductor, or as V / I for non-linear devices.
I–V 图像描绘了电流随电压的变化关系，能够揭示元件是欧姆器件还是非欧姆器件。对欧姆导体而言，任意一点的电阻等于斜率倒数的倒数；对非线性器件，则用 V / I 来计算。
A metallic conductor at constant temperature produces a straight line through the origin, showing constant resistance. A filament lamp shows a curve that bends towards the voltage axis as the metal heats up and its resistance increases. A semiconductor diode conducts very little current when reverse-biased, but current rises sharply once a forward threshold voltage (around 0.6–0.7 V for silicon) is exceeded.
恒温下的金属导体给出过原点的直线，表明电阻恒定。灯丝灯泡的图像是一条向电压轴弯曲的曲线，这是因为金属温度升高、电阻增大。半导体二极管在反向偏置时几乎不导电，一旦正向电压超过阈值（硅管约为 0.6–0.7 V），电流会急剧增大。
Examiners often ask you to describe the shape of these graphs and to explain the underlying physics, such as the effect of temperature on lattice vibrations or the behaviour of charge carriers across a p–n junction.
考试中经常要求你描述这些曲线的形状并解释背后的物理原理，比如温度对晶格振动的影响，或者载流子在 p–n 结两侧的行为。
6. Internal Resistance and EMF | 电源内阻与电动势
A real power source, such as a battery or cell, is not ideal. It has an internal resistance r, which causes the terminal potential difference to be less than the electromotive force (emf, symbol ε) when a current is drawn. The relationship is given by V = ε − Ir.
真实的电源（如电池）不是理想的。它具有内阻 r，当电路中有电流流动时，端电压会小于电动势（ε）。两者之间的关系由 V = ε − Ir 给出。
The emf ε is the total energy supplied per unit charge by the source when no current flows. It is measured in volts. The ‘lost volts’ inside the source equal Ir, and the useful external voltage is V = IR, where R is the external load resistance.
电动势 ε 是电源在没有电流输出时每单位电荷提供的总能量，单位是伏特。电源内部损失的电压为 Ir，有用的外部电压为 V = IR，其中 R 是外部负载电阻。
You can find the internal resistance and emf from a graph of terminal p.d. (V) against current (I). The y-intercept gives ε, and the negative gradient gives r. Practical investigations often use a variable resistor to vary the current and measure V.
可以通过端电压 V 随电流 I 变化的图像来求出内阻和电动势。图像在纵轴上的截距就是 ε，斜率的绝对值就是内阻 r。实验中常用可变电阻来改变电流并测量 V。
ε = I (R + r)
7. Electrical Power | 电功率
Electrical power P is the rate of energy transfer. It can be expressed in three useful forms: P = IV, P = I²R, and P = V² / R. The formula you choose depends on which quantities are known or constant.
电功率 P 是能量转化的速率，有三种常用的表达形式：P = IV、P = I²R 和 P = V² / R。选择哪个公式取决于哪些量已知或保持不变。
For a purely resistive load, all the electrical energy is converted into internal energy, so the power dissipated as heat is P = I²R. This is why high-resistance wires or components with large currents get hot – the heat generated is proportional to the square of the current.
对于纯电阻负载，所有的电能都转化为内能，因此以热量形式耗散的功率为 P = I²R。这就是高电阻导线或流过较大电流的元件发热的原因——产生的热量与电流的平方成正比。
When combining resistors in series or parallel, remember that the total power dissipated by the network equals the sum of the individual powers only if you use consistent calculations. For a given supply voltage, lowering the total resistance increases the power drawn from the source.
在串并联组合电路中，要注意只有计算一致时网络的总耗散功率才等于各元件功率之和。对于给定的电源电压，降低总电阻会增大从电源汲取的功率。
P = I V = I²R = V² / R
8. Potential Divider | 分压器
A potential divider is a simple circuit that uses two or more resistors in series to provide a fraction of the input voltage. The output voltage across resistor R₂ is given by V₂ = Vₛ × R₂ / (R₁ + R₂), where Vₛ is the source voltage.
分压器是一种简单的电路，利用两个或多个串联电阻来提供输入电压的一部分。电阻 R₂ 两端的输出电压为 V₂ = Vₛ × R₂ / (R₁ + R₂)，其中 Vₛ 是电源电压。
A variable potential divider, or potentiometer, uses a sliding contact on a resistive track. It can be used as a rheostat to control current or as a true potential divider to supply a variable output voltage. These are common in volume controls, dimmers and sensor circuits.
可变分压器（电位器）在电阻轨道上使用滑动触头。它既可用作变阻器来控制电流，也可用作真正的分压器来提供可调的输出电压，广泛用于音量控制、调光器和传感器电路中。
When a load resistor is connected across the output of a potential divider, the output voltage decreases unless the load resistance is much larger than R₂. This loading effect is an important practical consideration.
当在分压器输出端并接一个负载电阻时，输出电压会下降，除非负载电阻远大于 R₂。这种负载效应是一个重要的实际考虑因素。
V₂ = Vₛ × R₂ / (R₁ + R₂)
9. Superconductivity | 超导性
Certain materials, when cooled below a critical temperature T_c, lose all electrical resistance and become superconductors. Once a current is set up in a superconducting loop, it persists indefinitely without any energy loss.
某些材料在冷却到临界温度 T_c 以下时，会完全失去电阻，成为超导体。一旦在超导环路中建立起电流，它就可以永不衰减地流动，没有任何能量损失。
Superconductors exhibit the Meissner effect – they expel magnetic fields from their interior, allowing magnetic levitation. High-temperature superconductors can operate above the boiling point of liquid nitrogen (77 K), making them more practical for applications like MRI machines, maglev trains and power transmission.
超导体展现出迈斯纳效应——将磁场完全排斥在自身外部，从而实现磁悬浮。高温超导体可以在液氮沸点（77 K）以上工作，这使得它们在 MRI 设备、磁悬浮列车和电力传输等应用领域更具实用性。
The BCS theory explains conventional superconductivity through the formation of Cooper pairs – electrons that move through the lattice without scattering. Superconductivity is a fascinating example of quantum mechanics at a macroscopic scale.
BCS 理论通过形成库珀对来解释常规超导——这些电子在晶格中运动而不发生散射。超导性是量子力学在宏观尺度上的一个迷人实例。
10. Practical Measurements and Uncertainties | 实验测量与误差
The most common method for measuring resistance is the voltmeter-ammeter method. You measure the potential difference and current simultaneously and apply R = V / I. To avoid systematic errors, you should take readings for both increasing and decreasing voltages and average the resistance.
测量电阻最常用的方法是伏安法。你同时测量电压和电流，然后应用 R = V / I。为避免系统误差，应当分别记录电压升高和降低时的读数并计算电阻的平均值。
A more precise technique is the Wheatstone bridge, which compares an unknown resistance with known standard resistors. The bridge is balanced when the galvanometer reads zero, and the unknown R is given by Rₓ = (R₁/R₂) × R₃.
更精确的方法是惠斯通电桥，它将未知电阻与已知的标准电阻进行比较。当检流计示数为零时电桥平衡，此时未知电阻 Rₓ 由 Rₓ = (R₁/R₂) × R₃ 给出。
When analysing results, you must combine uncertainties appropriately. For a resistance calculated from V / I, the percentage uncertainty in R is the sum of the percentage uncertainties in V and I. Use repeated readings to reduce random error and discuss any systematic offsets.
分析结果时，必须恰当合成不确定度。对于由 V / I 算出的电阻，R 的百分不确定度等于 V 和 I 百分不确定度之和。应通过重复读数减少偶然误差并讨论任何系统偏差。
Rₓ = (R₁/R₂) × R₃
11. Exam Tips and Common Pitfalls | 考试技巧与常见陷阱
Always use the correct unit: resistance in ohms (Ω), resistivity in ohm metres (Ω·m). A common mistake is to confuse R = V / I with the gradient of an I–V graph – the gradient gives I / V, not V / I, unless the axes are swapped.
务必使用正确的单位：电阻是欧姆（Ω），电阻率是欧姆·米（Ω·m）。常见的错误是把 R = V / I 与 I–V 图像的斜率混淆——图像的斜率给出的是 I / V，而不是 V / I，除非坐标轴交换了。
When writing about temperature dependence, specify whether you are discussing a metal (positive coefficient) or a semiconductor (negative coefficient). Graphs must be labelled clearly, and for non-linear elements you should calculate R at a point, not from the whole curve.
在讨论温度依赖性时，要明确指出你讨论的是金属（正温度系数）还是半导体（负温度系数）。图像必须清晰标注；对于非线性元件，你应当计算某一点的电阻，而不是整条曲线的电阻。
In series circuits, current is constant; in parallel circuits, voltage is constant. Many exam questions test the ability to combine these rules. Practice deriving the total resistance for mixed networks step by step rather than memorising results.
在串联电路中，电流是恒定的；在并联电路中，电压是恒定的。很多试题都考查综合运用这些规则的能力。应逐步推导混联电路的总电阻，而不是死记硬背结果。
Finally, always check your internal resistance calculations: the gradient of a V–I graph may be negative, but internal resistance r is a positive magnitude. A clear understanding of ‘lost volts’ can save you marks in both qualitative and quantitative sections.
最后，一定要检查你的内阻计算：V–I 图像的斜率可能是负值，但内阻 r 是一个正值。透彻理解“内电压降”能帮你在定性和定量题中都拿到分数。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply