Resistance: Key Exam Points for IB & OCR Physics | IB OCR 物理：电阻考点精讲

📚 Resistance: Key Exam Points for IB & OCR Physics | IB OCR 物理：电阻考点精讲

Electrical resistance is one of the most central concepts in both IB and OCR A‑Level Physics. Understanding it fully means grasping not only the definition and Ohm’s law, but also how resistance depends on material, temperature and geometry, how it behaves in series and parallel, and how it links to power, internal resistance and potential dividers. This article breaks down every key learning objective and typical exam trap, with paired English–Chinese explanations that mirror the bilingual depth expected at aleveler.com.

电阻是 IB 和 OCR A‑Level 物理中最核心的概念之一。要真正掌握它，不仅需要理解定义和欧姆定律，还要明白电阻如何依赖于材料、温度和几何形状，在串联和并联电路中的行为，以及它与功率、内阻和分压器之间的关系。本文拆解了每一个核心考点和常见考试陷阱，并用中英双语对照解释，为你提供透彻的复习。

1. Defining Electrical Resistance | 定义电阻

Resistance quantifies how strongly a component opposes the motion of charge. For any two‑terminal device, the resistance R is defined as the ratio of the potential difference V across it to the electric current I passing through it.

电阻量化了一个元件对电荷运动的阻碍程度。对于任何两端器件，电阻 R 定义为它两端的电势差 V 与通过它的电流 I 之比。

R = V / I

The SI unit of resistance is the ohm (Ω), where 1 Ω = 1 V A⁻¹. This definition holds regardless of whether the component obeys Ohm’s law – it is simply the instantaneous ratio of V to I.

电阻的国际单位是欧姆（Ω），1 Ω = 1 V A⁻¹。该定义无论元件是否遵循欧姆定律都成立——它仅仅是 V 与 I 的瞬时比值。

2. Ohm’s Law and Ohmic Conductors | 欧姆定律与欧姆导体

Ohm’s law states that, provided the physical conditions (especially temperature) remain constant, the current through a metallic conductor is directly proportional to the potential difference across it. In equation form, V = I R, where R is a constant resistance. Materials and components that follow this linear relationship are called ohmic conductors; a fixed resistor is a classic example.

欧姆定律指出，在物理条件（特别是温度）保持不变的条件下，通过金属导体的电流与其两端的电势差成正比。写成公式为 V = I R，其中 R 为恒定电阻。遵循这种线性关系的材料或元件称为欧姆导体；固定电阻器就是一个典型例子。

V = I R

In an I‑V graph, an ohmic conductor gives a straight line passing through the origin. The slope is 1/R (if I is plotted on the y‑axis) or R (if V is on the y‑axis), so it is crucial to check which quantity is on each axis before deducing resistance from a graph.

在 I‑V 图像中，欧姆导体的图线是一条过原点的直线。如果 I 在 y 轴则斜率是 1/R，如果 V 在 y 轴则斜率是 R，因此从图像推断电阻前必须先确认坐标轴表示的量。

3. 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 intrinsic property of the material called resistivity ρ. The relationship is expressed as R = ρ L / A. Resistivity has units Ω m and is temperature‑dependent.

一根均匀导线的电阻取决于它的长度 L、横截面积 A 以及材料自身的属性——电阻率 ρ。表达式为 R = ρ L / A。电阻率的单位是 Ω m，且与温度相关。

R = ρ L / A

Conductivity σ is the reciprocal of resistivity: σ = 1/ρ, measured in S m⁻¹ (siemens per metre). Good conductors like copper have very low resistivity (~1.7×10⁻⁸ Ω m), while insulators have extremely high resistivity. In exams, you may be asked to calculate ρ from measurements of R, L and A, or to explain how the resistance of a wire changes if its length is doubled or its radius is halved.

电导率 σ 是电阻率的倒数：σ = 1/ρ，单位为 S m⁻¹。良导体如铜的电阻率极低（约 1.7×10⁻⁸ Ω m），而绝缘体则极高。考试中可能会要求你根据 R、L 和 A 的测量值计算 ρ，或解释当导线长度加倍、半径减半时其电阻如何变化。

4. Temperature Dependence of Resistance | 电阻的温度依赖性

For most metallic conductors, resistance increases with rising temperature. This is because thermal vibrations of the lattice ions scatter conduction electrons more effectively, reducing the mean free time between collisions. The linear approximation for a moderate temperature range is R = R₀ (1 + α Δθ), where R₀ is the resistance at a reference temperature, α is the temperature coefficient of resistance (positive for metals), and Δθ is the temperature change.

对于大多数金属导体，电阻随温度升高而增大。这是因为晶格离子的热振动更有效地散射传导电子，缩短了碰撞之间的平均自由时间。在适中温度范围内，线性近似式为 R = R₀ (1 + α Δθ)，其中 R₀ 是参考温度下的电阻，α 是电阻温度系数（金属为正值），Δθ 是温度变化。

R = R₀ (1 + α Δθ)

In contrast, semiconductors (such as silicon and germanium) and insulators typically show a negative temperature coefficient: their resistance decreases as temperature rises because more charge carriers become available. Thermistors, widely used in sensor circuits, exploit this strong negative temperature dependence.

相反，半导体（如硅和锗）与绝缘体通常呈现负温度系数：电阻随温度升高而下降，因为更多的电荷载流子获得了足够的能量。热敏电阻广泛应用于传感器电路中，正是利用了这种强烈的负温度依赖性。

5. I-V Characteristics: Ohm’s Law in Practice | I-V 特性曲线：欧姆定律的实际应用

Plotting I‑V graphs for different components reveals whether they obey Ohm’s law and how their resistance changes with current. The most frequently examined examples are the fixed resistor, the filament lamp and the semiconductor diode.

绘制不同元件的 I‑V 图线可以揭示它们是否服从欧姆定律以及它们的电阻如何随电流变化。最常见到的考试例子是固定电阻、灯丝灯泡和半导体二极管。

Always remember that for a non‑ohmic component, the ratio V/I gives the static resistance at a point, while the slope dV/dI gives the dynamic resistance. Confusing these two is a classic exam mistake.

务必记住：对于非欧姆元件，比值 V/I 给出的是该点的静态电阻，而斜率 dV/dI 给出的是动态电阻。混淆

Published by TutorHao | IB Physics Revision Series | aleveler.com

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