📚 Current and Circuits: Fundamental Laws | 电流与电路的基本规律
Electric current is the organised flow of charge, and circuits are the pathways that direct this flow to perform useful work. This chapter sets out the core definitions and laws that form the backbone of IB Physics Topic 5 and Edexcel International A-level Electricity.
电流是电荷的有序流动，而电路则是引导这种流动以完成有用功的通路。本章阐述构成IB物理Topic 5与Edexcel国际A-level电学核心的定义与基本定律。
1. Electric Current | 电流
Electric current I is defined as the rate at which charge flows through a cross-sectional area of a conductor. It is measured in amperes (A), where one ampere equals one coulomb per second.
电流I定义为电荷通过导体横截面的速率，单位为安培（A），即1安培等于每秒通过1库仑电荷。
In metallic conductors, current is carried by free electrons moving in the opposite direction to the conventional current. Conventional current is defined as flowing from positive to negative terminal; electron flow is from negative to positive.
在金属导体中，电流由自由电子承载，电子运动方向与传统电流方向相反。传统电流定义为从正极流向负极，而电子流则从负极流向正极。
A steady current requires a closed loop and a source of energy, such as a battery or power supply, that maintains a potential difference across the circuit.
稳定电流需要一个闭合回路和能量源（如电池或电源），以在电路两端维持电势差。
2. Potential Difference and Electromotive Force | 电势差与电动势
The potential difference (p.d.) across a component is the energy transferred per unit charge as charge passes through that component. It is measured in volts (V), equal to joules per coulomb.
元件两端的电势差（p.d.）是电荷通过该元件时每单位电荷所转移的能量，单位为伏特（V），即焦耳每库仑。
The electromotive force (e.m.f.) of a source is the total energy supplied per unit charge by the source. While p.d. describes energy dissipated in external components, e.m.f. describes energy supplied to the whole circuit.
电源的电动势（e.m.f.）是电源向每单位电荷提供的总能。电势差描述外部元件中耗散的能量，而电动势描述电源向整个电路提供的能量。
For a real battery with internal resistance r, the terminal voltage is less than the e.m.f. when current is drawn:
对于内阻为r的真实电池，当输出电流时端电压小于电动势：
3. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance is the opposition of a component to the flow of current, defined as the ratio of potential difference across a component to the current through it. The SI unit is the ohm (Ω).
电阻是元件对电流流动的阻碍作用，定义为元件两端电势差与通过其电流之比，国际单位是欧姆（Ω）。
Ohm’s law states that for an ohmic conductor at constant temperature, the current is directly proportional to the potential difference. This proportionality fails for non-ohmic devices such as diodes, filament lamps, and thermistors.
欧姆定律指出：对于恒定温度下的欧姆导体，电流与电势差成正比。对于非欧姆器件（如二极管、白炽灯、热敏电阻），这种正比关系不成立。
Current-voltage graphs provide a useful diagnostic: a straight line through the origin indicates ohmic behaviour; a curve indicates a changing resistance due to temperature or other effects.
电流-电压图像是有效工具：过原点的直线代表欧姆行为；曲线则表明电阻随温度或其他因素变化。
4. Resistivity | 电阻率
Resistivity ρ is an intrinsic property of a material that quantifies how strongly it opposes current flow. It is independent of the shape and size of the specimen and depends only on the material and temperature.
电阻率ρ是材料固有的属性，用以量化其对电流的阻碍程度。它与样品的形状和尺寸无关，仅取决于材料和温度。
where L is the length of the conductor and A is its cross-sectional area. Doubling the length doubles resistance; doubling the cross-sectional area halves it.
其中L为导体长度，A为横截面积。长度加倍，电阻加倍；横截面积加倍，电阻减半。
For most metals, resistivity increases with temperature because lattice vibrations scatter conduction electrons more frequently. For semiconductors, resistivity typically decreases with temperature.
对大多数金属而言，电阻率随温度升高而增大，因为晶格振动加剧了对导电电子的散射。而半导体材料的电阻率通常随温度升高而降低。
5. Series Circuits | 串联电路
In a series circuit, components are connected end-to-end along a single path. The current is identical at every point in the circuit, and the total potential difference across the circuit equals the sum of the p.d.s across each component.
串联电路中，各元件沿单一通路首尾相连。电路中每一点的电流相同，电路两端的电势差等于各元件两端电势差之和。
The total resistance of resistors in series is the sum of individual resistances:
串联电阻的总电阻等于各电阻之和：
Voltage division follows directly: the component with the largest resistance takes the largest share of the total voltage.
分压规律直接由此得出：电阻最大的元件分得最大电压。
6. Parallel Circuits | 并联电路
In a parallel circuit, components are connected across the same two points, providing multiple paths for current. Each component experiences the same potential difference.
并联电路中，各元件联接在相同两点之间，为电流提供多条路径。每个元件两端承受相同的电势差。
The total current is the sum of currents through each parallel branch:
总电流等于各并联支路电流之和：
For resistors in parallel, the reciprocal of total resistance equals the sum of reciprocals:
并联电阻的总电阻倒数等于各电阻倒数之和：
Adding more parallel branches reduces total resistance, a key principle in household wiring where additional appliances should not reduce voltage across existing ones.
增加并联支路会降低总电阻，这是家庭电路的重要原则——新增电器不应降低已有电器两端的电压。
7. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s first law (junction rule) states that the sum of currents entering a junction equals the sum of currents leaving it. This is a statement of charge conservation.
基尔霍夫第一定律（节点定律）：流入节点的电流之和等于流出节点的电流之和。这是电荷守恒的体现。
The second law (loop rule) states that the algebraic sum of e.m.f.s around any closed loop equals the algebraic sum of the products of current and resistance in each branch. This follows from energy conservation.
第二定律（回路定律）：沿任何闭合回路，电动势的代数和等于各支路电流与电阻乘积的代数和。这源于能量守恒。
These laws underpin the analysis of complex circuits that cannot be simplified by series-parallel reduction alone. They require careful attention to sign conventions for current direction and e.m.f. polarity.
这些定律是分析无法仅通过串并联简化处理的复杂电路的基础。应用时必须仔细关注电流方向与电动势极性的符号约定。
8. Electrical Power and Energy | 电功率与电能
The power delivered to or dissipated by a component is the rate at which electrical energy is transformed into other forms. Combining the definitions of current and p.d. gives:
元件接收或耗散的功率是电能转化为其他形式的速率。结合电流与电势差的定义可得：
Each form is useful in different contexts: P = VI applies generally; P = I²R is convenient for series circuits where current is common; P = V²/R suits parallel circuits where voltage is common.
每种形式在不同场景各有用途：P = VI普遍适用；P = I²R适合电流相同的串联电路；P = V²/R适合电压相同的并联电路。
Electrical energy is calculated by E = Pt = VIt. In practical terms, this underlies electricity billing, where energy is measured in kilowatt-hours.
电能的计算式为E = Pt = VIt。在实际应用中，这是电费计量的基础，能量以千瓦时为单位。
9. Internal Resistance and Terminal Voltage | 内阻与端电压
Every real source of e.m.f. possesses internal resistance r. When current flows, energy is lost within the source itself, reducing the terminal voltage available to the external circuit.
任何真实电源都具有内阻r。当电流通过时，部分能量在电源内部损耗，降低了提供给外电路的端电压。
The terminal voltage therefore decreases linearly as current increases. The lost volts Ir represent energy dissipated inside the source as heat.
因此端电压随电流增大呈线性下降。损耗电压Ir代表电源内部以热形式耗散的能量。
In an experimental context, plotting terminal voltage against current produces a straight line whose y-intercept equals e.m.f. and whose slope equals −r. This method is central to IB required practicals.
在实验情境中，作端电压-电流图得到一条直线，纵截距等于电动势，斜率等于−r。这是IB必做实验的核心内容。
10. Potential Divider Circuits | 分压电路
The potential divider is a simple and powerful circuit configuration using two or more resistors in series to obtain a fraction of the input voltage. The output voltage across one resistor is:
分压器是简单而强大的电路结构，利用两个或多个串联电阻获取输入电压的一部分。某个电阻上的输出电压为：
By replacing one fixed resistor with a variable component (thermistor, LDR), the divider converts changes in physical conditions into measurable voltage changes. This enables sensing applications in temperature and light detection circuits.
将一个固定电阻替换为可变元件（热敏电阻、光敏电阻）后，分压器将物理条件的变化转换为可测量的电压变化。这使其能够应用于温度和光照探测电路。
Loaded dividers, where an external resistance draws current from the output, are more complex: the effective resistance of the load in parallel with the lower resistor must be considered.
当分压器接入负载时（即外电路从输出端抽取电流），分析更为复杂：必须考虑负载电阻与下部电阻并联后的等效电阻。
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