📚 Electric Current, Potential Difference and Resistance | 电流、电势差与电阻
In A-Level Physics, the concepts of electric current, potential difference, and resistance form the foundation for understanding electrical circuits. Charge flow is quantified as current, the energy per unit charge is described by potential difference and electromotive force, and the opposition to current is characterised by resistance and resistivity. This article provides a comprehensive revision guide aligned with CIE requirements, covering definitions, key formulas, circuit laws, and practical I-V characteristics.
在 A-Level 物理中，电流、电势差和电阻是理解电路的基础。电荷的流动被量化为电流，单位电荷的能量用电势差和电动势描述，而对电流的阻碍作用则由电阻和电阻率表征。本文提供一份符合 CIE 考点的全面复习指南，涵盖定义、关键公式、电路定律以及实用的伏安特性。
1. Electric Current and Charge | 电流与电荷
-sectional area in a time interval Δt, the current I is given by I = ΔQ / Δt. The SI unit of current is the ampere (A), where 1 A = 1 C s⁻¹. Although charge carries a sign, current is treated as a scalar; the conventional direction of current is taken as the flow of positive charge, opposite to the drift of electrons in a metallic conductor.
电流定义为单位时间内通过导体横截面的电荷量。若在 Δt 时间内有净电荷 ΔQ 通过截面，则电流 I = ΔQ / Δt。电流的国际单位是安培（A），1 A = 1 C s⁻¹。电流是标量，但习惯上规定正电荷流动的方向为电流方向，在金属导体中这与电子漂移的方向相反。
I = ΔQ / Δt
In a series circuit, charge conservation demands that the current is the same at all points. To measure current, an ammeter is connected in series with the component; an ideal ammeter has zero resistance so that it does not alter the circuit it is measuring.
在串联电路中，电荷守恒要求各处电流相等。测量电流时，将安培计串联接入电路；理想安培计的电阻为零，确保不会改变被测电路的状态。
2. Charge Carriers and the Microscopic Current Equation | 载流子与微观电流方程
In a metallic conductor, the charge carriers are free electrons that move randomly with high thermal speeds but acquire a small average drift velocity vd ity of free electrons (number per unit volume), A is the cross-sectional area of the conductor, v is the average drift speed, and e is the elementary charge (1.60 × 10⁻¹⁹ C).
在金属导体中，载流子是自由电子。它们在没有电场时高速随机运动，但当施加电场后，电子会获得一个很小的平均漂移速度 vd。电流可用微观量表示为 I = n A v e，其中 n 是自由电子的数密度（单位体积内的电子数），A 是导体横截面积，v 是平均漂移速率，e 是元电荷（1.60 × 10⁻¹⁹ C）。
I = n A v e
Despite the very small drift velocity (typically of the order of 10⁻⁴ m s⁻¹), electrical signals are transmitted almost instantaneously because the electric field propagates along the conductor at a speed close to the speed of light. In semiconductors and electrolytes, both positive and negative charge carriers contribute to the total current.
虽然漂移速度极小（通常约为 10⁻⁴ m s⁻¹），但电信号几乎瞬间传输，这是因为电场沿导体以接近光速传播。在半导体和电解质中，正、负两种载流子都会对总电流做出贡献。
3. Potential Difference | 电势差
oint to the other. Mathematically, V = W / Q. The SI unit is the volt (V), where 1 V = 1 J C⁻¹. Potential difference is measured using a voltmeter connected in parallel with the component under test; an ideal voltmeter has infinite resistance so that it draws no current.
电路中两点之间的电势差（电位差）定义为将单位正电荷从一点移到另一点时所做的功。数学表达式为 V = W / Q。国际单位是伏特（V），1 V = 1 J C⁻¹。电势差使用伏特计并联在元件两端进行测量；理想伏特计的电阻为无穷大，因而不会分走电流。
V = W / Q
The potential difference drives the flow of charge, causing an energy transfer from the electric field to the components in the circuit. A positive value of V means that a positive test charge loses electrical potential energy as it moves through the component.
电势差驱动电荷流动，导致电场能量转移给电路中的元件。正的 V 值表示正电荷经过该元件时电势能减少。
4. Electromotive Force (EMF) | 电动势
e source. It is the energy converted from chemical, mechanical, or other forms into electrical energy per unit charge: E = W / Q. Although also measured in volts, e.m.f. is distinct from the terminal potential difference because some of the energy may be dissipated within the internal resistance of the source.
电源（如电池或发电机）的电动势（e.m.f.）是每单位电荷通过电源时获得的总能量，即化学能、机械能或其他形式能量转化为电能的值：E = W / Q。虽然电动势也用伏特计量，但它不同于路端电压，因为部分能量可能在电源内阻上消耗。
E = Wsource / Q
The terminal p.d. V across a real source is always less than its e.m.f. when current is being drawn, due to the voltage drop across internal resistance, as will be discussed further in a later section.
当有电流输出时，实际电源两端的路端电压 V 总是低于其电动势 E，因为内阻上存在电压降，这一点将在后面的小节中详述。
5. Resistance | 电阻
nce V across the component to the current I flowing through it: R = V / I. The SI unit of resistance is the ohm (Ω), where 1 Ω = 1 V A⁻¹. Resistance is a property that depends on the material, its dimensions (length and cross-sectional area), and its temperature.
电阻表示元件对电流流动的阻碍程度，定义为元件两端的电势差 V 与通过它的电流 I 之比：R = V / I。电阻的国际单位是欧姆（Ω），1 Ω = 1 V A⁻¹。电阻的大小取决于材料、尺寸（长度和横截面积）以及温度。
R = V / I
In some components, the ratio V / I remains constant over a wide range of applied p.d.; in others, it changes significantly with current, temperature, or direction of applied voltage. Understanding this behaviour is central to circuit analysis.
在某些元件中，V / I 的比值在很宽的电压范围内保持恒定；在另一些元件中，该比值随电流、温度或施加电压的方向发生显著变化。理解这一行为是电路分析的核心。
6. Ohm's Law | 欧姆定律
Ohm' ctor kept at constant temperature, the current through it is directly proportional to the potential difference across it, provided physical conditions remain unchanged. Symbolically, V ∝ stant. Materials and components that follow this linear relationship are described as ohmic conductors.
欧姆定律指出，在温度恒定的条件下，对于金属导体，只要物理条件保持不变，通过它的电流与两端电势差成正比，即 V ∝ I，从而电阻 R = V / I 为常数。遵循这种线性关系的材料和元件称为欧姆导体。
V ∝ I or V = I R
Common ohmic components include fixed metal resistors at constant temperature. The I-V graph of an ohmic conductor is a straight line passing through the origin, with the gradient equal to 1/R for a current vs. voltage plot. Many practical components, however, do not obey Ohm's law and are termed non-ohmic.
常见的欧姆元件包括恒温下的固定金属电阻器。欧姆导体的 I-V 图为一条过原点的直线，若绘制电流-电压关系，其斜率等于 1/R。然而，许多实际元件不遵守欧姆定律，被称为非欧姆元件。
7. Resistivity and Conductivity | 电阻率与电导率
terial. Resistivity is an intrinsic property that does not depend on the shape or size of the sample; its SI unit is the ohm-metre (Ω m). The reciprocal of resistivity is conductivity σ (sigma), so σ = 1 / ρ, with units of siemens per metre (S m⁻¹).
对于长度为 L、横截面积为 A 的均匀导体，其电阻由公式 R = ρ L / A 给出，其中 ρ 为材料的电阻率。电阻率是物质的本征特性，不依赖于样品的形状或尺寸，其国际单位是欧姆·米（Ω m）。电阻率的倒数是电导率 σ，即 σ = 1 / ρ，单位为西门子每米 (S m⁻¹)。
R = ρ L / A and σ = 1 / ρ
Materials with low resistivity, such as copper and silver, are good electrical conductors, while those with high resistivity, such as glass and rubber, are insulators. Semiconductors have intermediate resistivity values that can be controlled by doping, temperature, or light exposure.
电阻率低的材料（如铜和银）是良好的电导体，而电阻率高的材料（如玻璃和橡胶）是绝缘体。半导体的电阻率介于两者之间，且可通过掺杂、温度或光照加以控制。
8. I-V Characteristics of Components | 元件的伏安特性
The current–voltage (I-V) characteristic of a component is a graph showing how the current varies as the applied potential difference is changed. For an ohmic resistor, the characteristic is a straight line through the origin. In contrast, a metallic filament lamp shows a curve that becomes shallower as the p.d. increases, because the filament heats up, increasing its resistance.
元件的电流–电压（I-V）特性曲线展示了电流如何随外加电势差变化。对于欧姆电阻器，特性曲线是过原点的直线。相反，金属灯丝灯泡的曲线随着电压增大而逐渐变得平缓，因为灯丝温度升高，电阻增大。
Filament lamp: resistance increases with temperature.
A semiconductor diode exhibits a characteristic that is highly directional. In forward bias, once the applied p.d. exceeds a small threshold (about 0.7 V for silicon diodes), the current rises steeply. In reverse bias, almost no current flows until breakdown occurs at a very high reverse voltage. A thermistor shows a decrease in resistance with increasing temperature, leading to a steepening I-V curve.
半导体二极管的特性具有很强的方向性。在正向偏置下，一旦外加电压超过一个较小的阈值（硅管约为 0.7 V），电流便急剧上升。在反向偏置下，几乎无电流通过，直至达到很高的反向击穿电压。热敏电阻的阻值随温度升高而降低，其 I-V 曲线随之变陡。
9. Electrical Power and Energy Dissipation | 电功率与能量耗散
e potential difference across the component and the current through it: P = V I. Using Ohm' ained: P = I² R and P = V² / R. The SI unit of power is the watt (W), where 1 W = 1 J s⁻¹.
电路中元件耗散的电功率 P 是能量转移的速率，由元件两端的电势差与流过电流的乘积给出：P = V I。结合欧姆定律，可得到等效表达式：P = I² R 和 P = V² / R。功率的国际单位是瓦特（W），1 W = 1 J s⁻¹。
P = V I = I² R = V² / R
y (heat), a process known as Joule heating. The choice of the power formula depends on which quantities are known; for constant-resistance devices, using P = V² / R is convenient, while for a known current, P = I² R is preferred.
在时间 t 内转换的电能为 E = V I t。在电阻性元件中，电能全部转化为内能（热量），这一过程称为焦耳热效应。选择哪个功率公式取决于已知量：对于恒定电阻器件，使用 P = V² / R 较方便；若已知电流，则优先使用 P = I² R。
10. Internal Resistance and Terminal Potential Difference | 内阻与路端电压
e terminal potential difference V across the source is given by V = E − I r. The term I r represents the lost volts inside the source. This explains why the terminal p.d. of a battery decreases when a larger current is drawn.
实际电源可等效为一个电动势为 E 的理想电池与一个内阻 r 串联。当电路中有电流 I 流过时，电源两端的路端电压 V 为 V = E − I r。其中 I r 表示电源内部损失的电压。这解释了为何电池输出的电流越大，其路端电压越低。
V = E − I r
ansfer occurs when the load resistance equals the internal resistance of the source, a condition known as impedance matching. However, at this condition, the efficiency is only 50% because half the power is dissipated in the internal resistance.
输送给外部负载的功率为 P = I V = I E − I² r。当负载电阻等于电源内阻时，负载获得最大功率，这一条件称为匹配。但此时效率仅为 50%，因为一半功率耗散在内阻上。
11. Kirchhoff's Laws | 基尔霍夫定律
Kirchhoff's two laws provide a systematic method for analysing complex circuits. Kirchhoff's current law (KCL) states that at any junction, the algebraic sum of currents entering the junction equals the sum of currents leaving it. This is a direct consequence of conservation of charge. Symbolically, Σ Iin = Σ Iout.
基尔霍夫两条定律为分析复杂电路提供了系统方法。基尔霍夫电流定律（KCL）指出，对于电路中任一节点，流入该节点的电流之和等于流出该节点的电流之和，这是电荷守恒的直接结果，可表示为 Σ Iin = Σ Iout。
Kirchhoff's voltage law (KVL) states that around any closed loop
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