📚 Electric Current, Potential Difference and Resistance | 电流、电位差与电阻
In CIE A Level Physics, the topic “Electric current, potential difference and resistance” underpins almost every circuit problem. This article explains the definitions, units, equations and experimental behaviours you need, with each concept paired in English and Chinese.
在 CIE A Level 物理中，电流、电位差与电阻是几乎每道电路题的基础。本文讲解你需要掌握的定義、单位、公式与实验行为，每个概念均以中英对照呈现。
1. Charge and Current | 电荷与电流
Electric current is defined as the rate of flow of electric charge. If a net charge ΔQ passes through a conductor in time Δt, the current I is given by:
I = ΔQ / Δt
电流定义为单位时间内通过导体截面的净电荷量。若净电荷 ΔQ 在时间 Δt 内通过导体，则电流 I 由上式给出。
The SI unit of current is the ampere (A), where 1 A = 1 C s⁻¹. Charge is measured in coulombs (C). The elementary charge is e = 1.60 × 10⁻¹⁹ C, so one coulomb is equivalent to about 6.25 × 10¹⁸ elementary charges.
电流的 SI 单位是安培 (A)，1 A = 1 C s⁻¹。电荷单位为库仑 (C)。基本电荷 e = 1.60 × 10⁻¹⁹ C，所以 1 库仑约等于 6.25 × 10¹⁸ 个基本电荷。
2. Conventional Current and Electron Flow | 常规电流方向与电子流动
Conventional current is taken to be the direction in which positive charge would move. In metallic conductors, the charge carriers are free electrons, so the actual electron flow is opposite to the conventional current direction.
常规电流方向规定为正电荷运动的方向。在金属导体中，载流子是自由电子，因此实际电子流动方向与常规电流方向相反。
This convention is historical but remains standard in circuit diagrams and analysis. When you mark current arrows on a circuit, they always represent conventional current, not electron movement.
这一约定源于历史，但在电路图和分析中仍为标准。当你在电路上标电流箭头时，它们始终表示常规电流方向，而不是电子运动方向。
3. Potential Difference and EMF | 电位差与电动势
Potential difference (p.d.) between two points is the energy transferred per unit charge moving between those points. If work W is done when charge Q moves, then:
V = W / Q
两点之间的电位差 (p.d.) 是单位电荷在这两点之间移动时转移的能量。若电荷 Q 移动时做功 W，则 V = W / Q。
The unit of potential difference is the volt (V), equal to one joule per coulomb. On a circuit diagram, the p.d. across a component tells you how much energy each coulomb gives to that component.
电位差的单位是伏特 (V)，等于 1 焦耳每库仑。在电路图中，元件两端的电位差表示每库仑电荷向该元件转移了多少能量。
The electromotive force (emf) of a source is the total energy converted into electrical energy per unit charge delivered around a complete circuit. It is measured in volts, but it is not a force; it represents the energy supplied by the cell or generator.
电源的电动势 (emf) 是单位电荷绕完整电路一周时由电源转化为电能的能量。它用伏特测量，但不是力；它表示电池或发电机所提供的能量。
4. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance is defined as the ratio of potential difference across a component to the current through it:
R = V / I
电阻定义为元件两端电位差与通过电流之比：R = V / I。
The SI unit of resistance is the ohm (Ω), where 1 Ω = 1 V A⁻¹. A component has a resistance of one ohm if a p.d. of one volt drives a current of one ampere through it.
电阻的 SI 单位是欧姆 (Ω)，1 Ω = 1 V A⁻¹。若 1 伏特电位差使 1 安培电流通过某元件，则该元件的电阻为 1 欧姆。
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. A conductor that obeys this law is called an ohmic conductor, and its resistance remains constant.
欧姆定律指出，对温度恒定的金属导体，通过它的电流与其两端电位差成正比。遵守该定律的导体称为欧姆导体，其电阻保持不变。
5. I-V Characteristics | 电流-电压特性
For an ohmic conductor, the I-V graph is a straight line through the origin, showing constant resistance. The gradient of the I-V graph gives 1/R, while the gradient of a V-I graph gives R.
对欧姆导体，I-V 特性曲线是一条过原点的直线，表明电阻恒定。I-V 图线的斜率给出 1/R，而 V-I 图线的斜率给出 R。
For a filament lamp, the graph curves because the wire heats up and its resistance increases with temperature. Since the temperature is not constant, the lamp does not obey Ohm’s law over a wide voltage range.
对白炽灯丝，曲线弯曲，因为灯丝温度升高、电阻增大。由于温度不恒定，灯丝在较大电压范围内不遵守欧姆定律。
For a semiconductor diode, current is very small in reverse bias and rises rapidly after the forward threshold voltage, which is about 0.6 V for silicon. The diode is non-ohmic because its resistance depends on the direction and size of the applied p.d.
对半导体二极管，反向偏置时电流很小，正向超过阈值电压后（硅约 0.6 V）电流迅速上升。二极管是非欧姆元件，因为其电阻取决于外加电位差的方向和大小。
6. Resistivity | 电阻率
The resistance of a wire depends on its length L, cross-sectional area A, and the material. Resistivity ρ is defined by ρ = RA / L, so:
R = ρL / A
导线的电阻取决于其长度 L、截面积 A 和材料。电阻率 ρ 由 ρ = RA / L 定义，因此 R = ρL / A。
The unit of resistivity is the ohm metre (Ω m). Resistivity is a material property independent of dimensions for a given temperature, so copper has a lower resistivity than nichrome, for example.
电阻率的单位是欧姆米 (Ω m)。在给定温度下，电阻率是材料性质，与尺寸无关。例如铜的电阻率比镍铬合金低。
In CIE practicals, resistivity can be determined by measuring R for different lengths of a wire and plotting R against L. The gradient of the R-L graph is ρ / A, allowing ρ to be calculated.
在 CIE 实验中，可通过测量不同长度导线的 R，并绘制 R-L 图来测定电阻率。R-L 图线的斜率为 ρ / A，从而可计算出 ρ。
7. Drift Velocity | 漂移速度
In a metal, free electrons move randomly at high speeds but drift slowly in one direction under an electric field. The current is related to the mean drift velocity v by:
I = nAvq
在金属中，自由电子高速随机运动，但在电场作用下缓慢地沿一个方向漂移。电流与平均漂移速度 v 的关系为 I = nAvq。
Here n is the number density of charge carriers, A is the cross-sectional area, and q is the charge of each carrier, usually the elementary charge e for electrons.
其中 n 是载流子数密度，A 是截面积，q 是每个载流子的电荷，对电子通常等于基本电荷 e。
Since n and q are fixed for a metal wire, a smaller cross-sectional area leads to a larger drift velocity for the same current. In typical copper wires, drift velocities are only a fraction of a millimetre per second.
由于金属导线中 n 和 q 固定，当电流相同时，截面积越小，漂移速度越大。在典型铜导线中，漂移速度只有每秒零点几毫米。
8. Series and Parallel Circuits | 串联与并联电路
In series, components carry the same current, and the total p.d. is the sum of individual p.d.s. The total resistance is:
Rₛ = R₁ + R₂ + R₃ + …
串联时，各元件电流相同，总电位差等于各电位差之和。总电阻为：Rₛ = R₁ + R₂ + R₃ + …。
In parallel, components have the same p.d., and the total current is the sum of branch currents. The total resistance is given by:
1/Rₚ = 1/R₁ + 1/R₂ + …
并联时，各元件两端电位差相同
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