A-Level Physics: Resistance and Ohm's Law | A-Level 物理：电阻与欧姆定律

📚 A-Level Physics: Resistance and Ohm’s Law | A-Level 物理：电阻与欧姆定律

Resistance and Ohm’s Law form the foundation of circuit analysis in A-Level Physics. Understanding how materials oppose electric current and how voltage, current, and resistance interrelate is essential for solving both theoretical and practical problems in the CIE syllabus.

电阻与欧姆定律是 A-Level 物理电路分析的基石。理解材料如何阻碍电流，以及电压、电流和电阻三者之间的关系，对于解决 CIE 考纲中的理论与实验问题至关重要。

1. Current, Voltage and Resistance | 电流、电压与电阻

Electric current is the rate of flow of charge, measured in amperes (A). Voltage, or potential difference, is the energy transferred per unit charge between two points, measured in volts (V). Resistance is the opposition to the flow of charge, measured in ohms (Ω).

电流是电荷流动的速率，单位为安培（A）。电压（或电势差）是单位电荷在两点之间转移的能量，单位为伏特（V）。电阻是对电荷流动的阻碍，单位为欧姆（Ω）。

Current: I = ΔQ / Δt, where ΔQ is charge passing a point in time Δt.
Voltage: V = W / Q, where W is energy transferred and Q is charge.
Resistance: R = V / I, the ratio of voltage to current.

电流：I = ΔQ / Δt，其中 ΔQ 是在时间 Δt 内通过某一点的电荷量。
电压：V = W / Q，其中 W 是转移的能量，Q 是电荷量。
电阻：R = V / I，即电压与电流之比。

2. Ohm’s Law | 欧姆定律

Ohm’s Law states that the current through an ohmic conductor is directly proportional to the potential difference across it, provided that physical conditions such as temperature remain constant. Mathematically, V = IR.

欧姆定律指出：对于欧姆导体，在温度等物理条件保持恒定的情况下，通过导体的电流与导体两端的电势差成正比。数学表达式为 V = IR。

V = I × R

For an ohmic conductor, the I–V graph is a straight line through the origin with constant gradient. Non-ohmic devices, such as filament lamps and diodes, do not follow this linear relationship.

对于欧姆导体，其 I-V 图是一条过原点的直线，斜率恒定。非欧姆器件（如白炽灯、二极管）不符合这种线性关系。

3. Resistivity | 电阻率

Resistivity is an intrinsic property of a material. It is defined by the equation:

电阻率是材料自身的固有属性，其定义式为：

ρ = R × A / L

where R is resistance, A is cross-sectional area, and L is the length of the conductor. The unit of resistivity is ohm-metre (Ω·m).

其中 R 是电阻，A 是横截面积，L 是导体长度。电阻率的单位是欧姆·米（Ω·m）。

For a wire, increasing its length increases resistance, while increasing its cross-sectional area decreases resistance. This relationship is used when calculating wire resistance in circuit design.

对于导线而言，增加长度会增大电阻，而增加横截面积则会减小电阻。在电路设计中，常用此关系计算导线的电阻。

4. Resistance and Temperature | 电阻与温度

For metallic conductors, resistance increases with temperature because lattice vibrations scatter conduction electrons more frequently. This means the I–V graph of a metal is a straight line only if temperature stays constant; at higher currents the line curves.

对于金属导体，电阻随温度升高而增大，因为晶格振动增大了对导电电子的散射频率。这意味着金属的 I-V 图只有在温度恒定时才为直线；电流较高时曲线会弯曲。

For a thermistor (NTC type), resistance decreases sharply as temperature rises. This property makes thermistors useful in temperature sensors and control circuits.

对于热敏电阻（负温度系数型），电阻随温度升高而急剧减小。这一特性使热敏电阻常用于温度传感器和控制电路。

5. Series and Parallel Resistors | 电阻的串联与并联

When resistors are connected in series, the same current flows through each resistor and the total resistance is the sum of individual resistances:

当电阻串联时，通过每个电阻的电流相同，总电阻等于各个电阻之和：

R_total = R₁ + R₂ + R₃ + …

When resistors are connected in parallel, the potential difference is the same across each resistor and the reciprocal of total resistance equals the sum of reciprocals:

当电阻并联时，每个电阻两端的电势差相同，总电阻的倒数等于各电阻倒数之和：

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …

In parallel circuits, the total resistance is always smaller than the smallest individual resistance. This is a common CIE exam question.

并联电路中的总电阻总是小于其中最小的那个电阻。这是 CIE 考试中的常见考点。

6. Electromotive Force (EMF) and Internal Resistance | 电动势与内阻

The electromotive force (e.m.f.) of a cell is the total energy supplied per unit charge, while the terminal potential difference is the energy delivered to the external circuit. The difference is due to the internal resistance r of the cell.

电池的电动势（e.m.f.）是单位电荷获得的全部能量，而路端电压是提供给外电路的能量。两者之差是由电池内阻 r 引起的。

E = V_terminal + I × r

Therefore, the terminal voltage is V = E – I r. When current increases, terminal voltage falls. This explains why a battery’s voltage drops under heavy load.

因此，路端电压为 V = E – I r。当电流增大时，路端电压下降。这解释了电池在大电流负载下电压会降低的原因。

7. I–V Characteristics | 伏安特性曲线

Different circuit components display different current–voltage relationships, which are summarised in their I–V graphs.

不同的电路元件具有不同的电流-电压关系，可用 I-V 图来归纳。

Component	I–V Shape	Explanation
Fixed resistor	Straight line through origin	Constant resistance
Filament lamp	Curved, gradient decreases at high V	Resistance increases with temperature
Diode	Near zero forward current until threshold, then steep rise; negligible reverse current	Conducts mainly in one direction
Thermistor	Curved, gradient increases with V	Resistance decreases as heating occurs

元件	I-V 图形	解释
定值电阻	过原点的直线	电阻恒定
白炽灯	曲线，高电压处斜率减小	温度升高导致电阻增大
二极管	正向电流在阈值前近似为零，超过后急剧上升；反向电流极小	主要单向导电
热敏电阻	曲线，斜率随电压增大而增大	受热后电阻减小

8. Potential Divider and Potentiometer | 分压器与电位差计

A potential divider uses two resistors in series to produce a desired output voltage. The output voltage across R₂ is given by:

分压器利用两个串联电阻产生所需的输出电压。R₂ 两端的输出电压为：

V_out = V_in × R₂ / (R₁ + R₂)

By replacing one resistor with a variable component such as a thermistor or light-dependent resistor (LDR), the divider can act as a sensor circuit. The potentiometer is a form of continuously variable potential divider used for measuring a voltage without drawing current.

若将其中一个电阻替换为可变元件（如热敏电阻或光敏电阻），分压器即可构成传感电路。电位差计是连续可变的分压器，用于在几乎不抽取电流的情况下测量电压。

9. Measurement of Resistance | 电阻的测量

Resistance can be measured using an ohmmeter, which applies a known voltage and measures current. More accurately, the voltmeter–ammeter method requires measuring both V and I, then calculating R = V/I.

使用欧姆表测量电阻时，欧姆表施加已知电压并测量电流。更精确的方法是伏安法，即同时测量电压 V 和电流 I，再计算 R = V/I。

Care must be taken with meter connections. If the voltmeter is placed across the resistor alone (amometer external), the ammeter also reads current through the voltmeter, causing a small error. If the ammeter is inside the voltmeter loop, the voltmeter reads the voltage across both the ammeter and the resistor.

必须注意电表的连接方式。若电压表单独跨接在电阻两端（电流表外接），电流表会额外读入电压表中的电流，造成微小误差；若电流表位于电压表回路内，则电压表读数是电流表和电阻两端的电压之和。

10. Superconductivity | 超导现象

Some materials, when cooled below a critical temperature, have exactly zero resistivity and can conduct current without any energy loss. These are called superconductors.

某些材料冷却到临界温度以下时，电阻率会变为严格的零，能够在无能量损耗的情况下传导电流，这种材料称为超导体。

Critical temperature T_c depends on the material.
Applications include strong electromagnets in MRI scanners and particle accelerators.
In an A-Level exam, you may be asked to explain the advantage of zero resistance in power transmission.

临界温度 T_c 取决于材料本身。
应用包括 MRI 扫描仪和粒子加速器中的强电磁体。
在 A-Level 考试中，你可能会被要求解释零电阻在电力传输中的优势。

11. Common Pitfalls and Exam Tips | 常见易错点与应试技巧

Students often confuse resistance with resistivity. Resistance is property of a particular object; resistivity is a property of the material. Another common mistake is using the gradient of an I–V graph as resistance; the resistance is actually V/I, which is the ratio, not the gradient of an I–V graph (the gradient gives 1/R if the graph is linear).

学生常混淆电阻与电阻率。电阻是特定物体的属性，电阻率是材料的属性。另一个常见错误是使用 I-V 图的斜率作为电阻；实际上电阻是 V/I，即电压与电流的比值，而不是 I-V 图的斜率（如果图线为线性，斜率给出的是 1/R）。

For series circuits, power dissipated is proportional to resistance (P = I²R) since current is same. For parallel circuits, power is proportional to conductance (P = V²/R) since voltage is same.

在串联电路中，由于电流相同，耗散功率与电阻成正比（P = I²R）；在并联电路中，由于电压相同，功率与电导成正比（P = V²/R）。

12. Summary | 总结

Resistance is a central concept in A-Level Physics. The key equations V = IR, ρ = RA/L, and the series/parallel formulas are essential weapons in your exam arsenal. Understanding the physical causes of resistance and the behaviour of non-ohmic devices will help you tackle both calculation and explanation questions confidently.

电阻是 A-Level 物理的核心概念。关键公式 V = IR、ρ = RA/L 以及串并联公式是考试中的必备工具。理解电阻产生的物理原因以及非欧姆器件的行为，将帮助你自信地应对计算题和解释题。

Regularly practice drawing I–V graphs and solving circuits containing internal resistance. Master these fundamentals, and you will build a strong foundation for more advanced topics such as capacitance and alternating current.

要经常练习绘制 I-V 图并求解包含内阻的电路。掌握这些基础知识，你将为进一步学习电容、交流电等进阶主题奠定坚实基础。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

A-Level Physics: Resistance and Ohm’s Law | A-Level 物理：电阻与欧姆定律