📚 B.5 Current and circuits | 电流与电路
Electric currents are at the heart of every electronic device, from the simplest torch to the most sophisticated computer. In IB Physics Topic B.5, we explore how charge moves through conductors, the energy transformations that occur, and the rules that govern both simple and complex circuits. Understanding current, potential difference, resistance, and circuit laws provides the foundation for analysing electrical systems and solving practical problems.
电流是每个电子设备的核心，从最简单的手电筒到最复杂的计算机。在 IB 物理 B.5 课题中，我们将探究电荷如何在导体中运动、发生的能量转换，以及支配简单和复杂电路的规则。理解电流、电势差、电阻和电路定律为分析电气系统和解决实际问题奠定了基础。
1. Electric Current and Charge Carriers | 电流与载流子
¹. In metallic conductors, the charge carriers are free electrons, while in electrolytes, both positive and negative ions contribute to the current.
电流（I）定义为电荷流动的速率。若净电荷 ΔQ 在时间 Δt 内通过导体的横截面，则电流为 I = ΔQ / Δt。电流的国际单位是安培（A），1 A = 1 C s⁻¹。在金属导体中，载流子是自由电子，而在电解质中，正负离子都对电流有贡献。
ers, A is the cross-sectional area, v is the drift speed, and q is the charge on each carrier. For electrons, q = e = 1.60 × 10⁻¹⁹ C and the direction of conventional current is opposite to the electron flow.
在金属导线中，传导电子以高速随机运动，但当施加电场时，它们会获得一个与电场方向相反的小的平均漂移速度 v。电流可以用微观表达式 I = n A v q 表示，其中 n 是载流子的数密度，A 是横截面积，v 是漂移速度，q 是每个载流子的电荷量。对于电子，q = e = 1.60 × 10⁻¹⁹ C，并且约定电流的方向与电子流动方向相反。
2. Potential Difference and Electromotive Force | 电势差与电动势
¹. When a component such as a resistor or lamp is connected across a p.d., electrical energy is transferred to other forms, such as heat and light.
两点之间的电势差（p.d.）是将一个小的正检验电荷从一点移到另一点时每单位电荷所做的功。它以伏特（V）为单位，1 V = 1 J C⁻¹。当电阻器或灯泡等元件连接在电势差上时，电能会转化为其他形式，如热能和光能。
Electromotive force (emf, symbol ε) is the energy supplied by a source per unit charge passing through it. A battery with an emf of 9 V provides 9 J of energy to each coulomb of charge that flows. Despite its name, emf is not a force but a measure of energy per unit charge. The terminal p.d. of a real cell is less than its emf when current is drawn because of internal resistance.
电动势（emf，符号 ε）是电源对通过它的每单位电荷所提供的能量。一个电动势为 9 V 的电池对每库仑流过的电荷提供 9 J 的能量。尽管名称如此，电动势不是一种力，而是每单位电荷的能量度量。当有电流时，真实电池的端电压因内阻而低于其电动势。
3. Resistance and Ohm's Law | 电阻与欧姆定律
e p.d. across the component and I is the current through it. The unit of resistance is the ohm (Ω). A component obeys Ohm's law if the ratio V / I remains constant at constant temperature, meaning the I–V graph is a straight line through the origin.
电阻（R）是对元件中电流流动阻碍程度的量度。它由 R = V / I 定义，其中 V 是元件两端的电势差，I 是通过它的电流。电阻的单位是欧姆（Ω）。如果一个元件的 V / I 比值在恒定温度下保持不变，即 I-V 图是一条通过原点的直线，则该元件遵循欧姆定律。
Ohmic conductors, such as a metal wire at constant temperature, have a linear I–V characteristic. Non-ohmic components, such as a filament lamp or a semiconductor diode, have a non-linear relationship. In a filament lamp, resistance increases with current because the temperature rises, causing more frequent collisions between electrons and lattice ions. In a diode, current only flows substantially when the p.d. exceeds a threshold in the forward direction.
欧姆导体，例如恒温下的金属导线，具有线性的 I-V 特性。非欧姆元件，如灯丝灯泡或半导体二极管，具有非线性关系。在灯丝灯泡中，电阻随电流增加而增加，因为温度升高导致电子与晶格离子之间的碰撞更加频繁。在二极管中，仅当电势差在正向超过阈值时，才会有显著的电流流动。
4. Resistivity and Conductivity | 电阻率与电导率
of the material, L is the length, and A is the cross-sectional area. Resistivity has units of ohm-metres (Ω m) and is a property that quantifies how strongly a material opposes current. Good conductors like copper have very low resistivity, while insulators have extremely high resistivity.
均匀导体的电阻取决于其材料和几何形状：R = ρ L / A，其中 ρ 是材料的电阻率，L 是长度，A 是横截面积。电阻率的单位是欧姆·米（Ω m），它是一个量化材料对电流阻碍程度强弱的属性。像铜这样的良导体电阻率非常低，而绝缘体电阻率极高。
discussing materials such as semiconductors. The resistivity of a metal increases with temperature because the increased lattice vibrations scatter electrons more effectively. For a given p.d., doubling the length of a wire doubles its resistance, while doubling its cross-sectional area halves the resistance.
电导率 σ 是电阻率的倒数：σ = 1 / ρ。在讨论半导体等材料时很有用。金属的电阻率随温度升高而增加，因为增强的晶格振动更有效地散射电子。对于给定的电势差，将导线长度加倍会使电阻加倍，而横截面积加倍则使电阻减半。
5. Electric Power and Energy Dissipation | 电功率与能量耗散
s W = V Q. Power, the rate of energy transfer, is P = W / t = V I. Combining this with Ohm' to calculate the power dissipated as heat in a resistor or the power supplied by a source.
当电荷 Q 通过电势差 V 时，所做的电功为 W = V Q。功率，即能量转换的速率，为 P = W / t = V I。将其与欧姆定律结合，可得到其他形式：P = I² R 和 P = V² / R。这些方程使我们能够计算电阻器中以热形式耗散的功率或电源提供的功率。
W heater operating for 3 hours consumes 6 kW h of energy. When designing circuits, the power rating of components must be respected to avoid overheating and damage.
千瓦时（kW h）是电能表常用的能量单位。1 kW h = 3.6 × 10⁶ J。例如，一个 2 kW 的加热器运行 3 小时消耗 6 kW h 的能量。在设计电路时，必须遵守元件的额定功率，以避免过热和损坏。
6. Series Circuits | 串联电路
In a series circuit, components are connected end-to-end, providing a single path for current. The current I is the same at every point. The total potential difference supplied by the source is equal to the sum of the p.d.s across the individual components: Vtotal = V₁ + V₂ + V₃ + ... The total resistance is the sum of the individual resistances: Rtotal = R₁ + R₂ + R₃ + ...
在串联电路中，元件首尾相连，为电流提供单一通路。电流 I 在每一点都相同。电源提供的总电势差等于各元件两端电势差之和：Vtotal = V₁ + V₂ + V₃ + ...。总电阻等于各电阻之和：Rtotal = R₁ + R₂ + R₃ + ...。
divider rule states that the voltage across one resistor in a series chain is Vᵢ = (Rᵢ / Rtotal) × Vtotal. This is extremely useful for sensor circuits and for obtaining a desired fraction of a supply voltage. If one component in a series circuit fails, the entire circuit is broken and current stops.
分压规则指出，串联链中一个电阻器两端的电压为 Vᵢ = (Rᵢ / Rtotal) × Vtotal。这对于传感器电路以及获得所需比例电源电压非常有用。如果串联电路中的一个元件损坏，整个电路就会断开，电流停止。
7. Parallel Circuits | 并联电路
In a parallel circuit, components are connected across the same two points, providing multiple paths for current. The p.d. across each branch is the same and equals the source voltage. The total current supplied by the source is the sum of the currents in each branch: Itotal = I₁ + I₂ + I₃ + ... The total resistance is given by 1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...
在并联电路中，元件连接在相同的两点之间，为电流提供多条通路。各支路两端的电势差相同，等于电源电压。电源提供的总电流是各支路电流之和：Itotal = I₁ + I₂ + I₃ + ...。总电阻由 1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + ... 给出。
Adding a resistor in parallel always decreases the total resistance because it provides an additional path for current. The current divider rule allows calculation of branch currents without first finding the total resistance. Parallel circuits are common in household wiring because each appliance operates independently at the full supply voltage.
并联添加电阻器总是会降低总电阻，因为它为电流提供了额外的通路。分流规则允许不先求总电阻就能计算支路电流。并联电路在家庭布线中很常见，因为每个电器都能在完全电源电压下独立工作。
8. Combination Circuits and Kirchhoff's Laws | 组合电路与基尔霍夫定律
Many practical circuits are neither purely series nor purely parallel but a combination of both. To analyse such circuits, we simplify stepwise: find equivalent resistances for series and parallel sections, redraw the circuit, and work backwards to determine currents and voltages. A systematic approach requires the application of Kirchhoff's two laws.
许多实际电路既不是纯串联也不是纯并联，而是两者的组合。为分析此类电路，我们逐步简化：求出串联和并联部分的等效电阻，重画电路，然后倒推求出电流和电压。系统性的分析方法需要应用基尔霍夫两条定律。
Kirchhoff's current law (KCL) states that the algebraic sum of currents entering a junction is zero: Σ Iin = Σ Iout. It is based on the conservation of charge. Kirchhoff' nservation of energy. By writing loop equations, we can solve for unknown currents even in multi-loop networks.
基尔霍夫电流定律（KCL）指出，流入一个节点的电流代数和为零：Σ Iin = Σ Iout。它基于电荷守恒。基尔霍夫电压定律（KVL）指出，沿任一闭合回路的电动势和电势差的代数和为零：Σ ε = Σ I R。它源于能量守恒。通过列写回路方程，我们甚至可以在多回路网络中求解未知电流。
9. Internal Resistance and Terminal Potential Difference | 内阻与端电压
A real electrical source, such as a battery, has internal resistance (r) that causes energy dissipation inside the source when current flows. The terminal potential difference (Vt) is the voltage actually available at the terminals. It is given by Vt = ε - I r, where ε is the emf and I is the current delivered. When no current flows, Vt = ε.
真实的电源，例如电池，具有内阻（r），当电流流动时会在电源内部引起能量耗散。端电压（Vt）是接线端实际可用的电压。它由 Vt = ε - I r 给出，其中 ε 是电动势，I 是输出的电流。当没有电流流动时，Vt = ε。
A graph of terminal p.d. against current yields a straight line with a y-intercept equal to the emf and a gradient equal to –r. The power delivered to the external load is maximised when the load resistance equals the internal resistance, a result known as maximum power transfer. However, under this condition, the efficiency is only 50%.
端电压随电流变化的图线是一条直线，其 y 轴截距等于电动势，斜率等于 –r。当负载电阻等于内阻时，输送到外部负载的功率最大，这一结果称为最大功率传输。不过，在此条件下效率仅为 50%。
10. Electrical Measurements: Ammeters and Voltmeters | 电学测量：电流表与电压表
An ammeter measures current and must be connected in series with the component of interest. It should have a very low resistance so that it does not appreciably reduce the current in the circuit. An ideal ammeter has zero resistance. A voltmeter measures potential difference and is connected in parallel with the component. It must have a very high resistance to draw negligible current.
电流表测量电流，必须与待测元件串联。它应具有非常低的电阻，以免显著减小电路中的电流。理想电流表电阻为零。电压表测量电势差，与元件并联。它必须具有非常高的电阻，以吸取可忽略的电流。
To extend the range of a moving-coil ammeter, a low-resistance shunt is placed in parallel with the meter movement. To convert a galvanometer into a voltmeter, a high resistance multiplier is connected in series. Understanding these modifications reinforces the principles of series and parallel circuits.
为了扩大量程，动圈式电流表并联一个低电阻分流器。要将检流计改装成电压表，则串联一个高电阻倍率器。理解这些改装可以深化对串联和并联电路原理的认识。
11. Potential Dividers | 分压器
A potential divider consists of two or more resistors in series across a fixed supply voltage. The output voltage Vout is taken across one of the resistors and can be varied by changing the resistance values. For two resistors R₁ and R₂ in series, Vout = [R₂ / (R₁ + R₂)] × Vin. This circuit is widely used to provide a variable voltage source from a fixed one.
分压器由两个或多个电阻串联在一个固定电源电压上组成。输出电压 Vout 取自其中一个电阻两端，并可通过改变电阻值来调节。对于两个串联电阻 R₁ 和 R₂，Vout = [R₂ / (R₁ + R₂)] × Vin。该电路广泛用于从固定电压源获得可变电压。
A potentiometer is a three-terminal device that acts as an adjustable potential divider. When a sensor such as a thermistor or light-dependent resistor (LDR) replaces one of the fixed resistors, the output voltage becomes sensitive to temperature or light level. This principle is the basis of many automatic control systems.
电位器是一种三端器件，起到可调分压器的作用。当一个传感器，如热敏电阻或光敏电阻（LDR），替代其中一个固定电阻时，输出电压便对温度或光照水平敏感。这一原理是许多自动控制系统的基础。
12. Safety and Circuit Protection | 安全与电路保护
Excessive currents can cause overheating, insulation failure, and fires. Fuses and circuit breakers are protective devices that disconnect the circuit when the current exceeds a safe rated value. A fuse contains a thin wire that melts and breaks the circuit; it must be connected in series with the live wire. The fuse rating should be slightly higher than the normal operating current of the appliance.
过大的电流会导致过热、绝缘失效和火灾。保险丝和断路器是当电流超过安全额定值时会断开电路的保护装置。保险丝内含一根细金属丝，它会熔断并断开电路；它必须与火线串联连接。保险丝的额定电流应略高于设备的正常工作电流。
Double insulation, earthing, and residual current devices (RCDs) provide additional protection, especially in mains-powered circuits. Earthing connects the metal case of an appliance to the ground, ensuring that any fault current flows safely to earth rather than through a user. These safety measures rely on fundamental circuit principles and are essential knowledge for IB Physics.
双重绝缘、接地和漏电保护器（RCD）提供了额外的保护，尤其是在市电供电电路中。接地将设备的金属外壳与大地相连，确保任何故障电流安全流入大地，而不是通过使用者。这些安全措施依赖于基本的电路原理，是 IB 物理必备的知识。
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