📚 Electromagnets 1.1.2 – Current and Potential Difference | 电流与电势差概念解析
Understanding current and potential difference is essential to mastering electricity and electromagnetism. These concepts describe how charges move through a circuit and how energy is transferred, providing the foundation for devices such as electromagnets, motors, and generators.
理解电流和电势差是掌握电学与电磁学的关键。这些概念描述了电荷如何在电路中移动以及能量如何传递，为电磁铁、电动机和发电机等设备奠定了基础。
1. What is Electric Current? | 什么是电流？
Electric current is the rate of flow of electric charge. In a metallic conductor, the moving charges are electrons, which drift slowly through the lattice of positive ions.
电流是电荷流动的速率。在金属导体中，移动的电荷是电子，它们在正离子晶格中缓慢漂移。
The SI unit of current is the ampere (A), where one ampere is equivalent to one coulomb of charge passing a point in one second.
电流的国际单位是安培 (A)，1 安培等于每秒有 1 库仑的电荷通过某一点。
I = Q ÷ t
Here I is current (A), Q is electric charge (C), and t is time (s). This relationship shows that for a given time, a greater charge flow yields a larger current.
式中 I 为电流 (A)，Q 为电荷 (C)，t 为时间 (s)。该关系式表明，在相同时间内，电荷流量越大，电流越大。
2. Charge Carriers and Conventional Current | 电荷载流子与约定电流方向
Conventional current is defined as the flow of positive charge, moving from the positive terminal of a power supply to the negative terminal. This historical convention is still used when drawing circuit diagrams and analysing circuits.
约定电流被定义为正电荷的流动，从电源的正极流向负极。这一历史惯例至今仍用于绘制电路图和分析电路。
In metal wires, the actual charge carriers are free electrons. These electrons move from the negative terminal to the positive terminal — opposite to the direction of conventional current. In semiconductors and electrolytes, both positive and negative charge carriers may contribute to the current.
在金属导线中，实际的电荷载流子是自由电子。这些电子从负极移向正极——与约定电流的方向相反。在半导体和电解液中，正负电荷载流子都可能参与导电。
3. Measuring Current | 测量电流
An ammeter is used to measure current. It must be connected in series with the component being investigated so that the full current passes through the meter.
安培表用于测量电流，必须与被测元件串联连接，以便完整的电流流过仪表。
Ammeters are designed with very low internal resistance to ensure they do not significantly alter the circuit’s current. When placing an ammeter, the positive terminal of the meter should be connected towards the positive terminal of the power supply.
安培表具有极低的内阻，以确保不会明显改变电路中的电流。连接安培表时，仪表的正极应朝向电源的正极。
4. Potential Difference (p.d.) | 电势差（电压）
Potential difference, often called voltage, is the work done (energy transferred) per unit charge as charge moves between two points in a circuit.
电势差，常称为电压，是单位电荷在电路两点间移动时所做的功（传递的能量）。
V = W ÷ Q
Where V is potential difference (V), W is work done or energy transferred (J), and Q is charge (C). One volt equals one joule per coulomb (1 V = 1 J/C).
式中 V 为电势差 (V)，W 为做功或传递的能量 (J)，Q 为电荷 (C)。1 伏特等于 1 焦耳每库仑 (1 V = 1 J/C)。
A voltmeter measures potential difference and must be connected in parallel with the component across which the p.d. is to be measured. Voltmeters have a very high internal resistance to minimise current drawn from the circuit.
电压表测量电势差，必须与待测元件并联连接。电压表具有非常高的内阻，以尽量减少从电路中分流出的电流。
5. Energy Transfer and Potential Difference | 能量转移与电势差
When a charge moves through a potential difference, electrical potential energy is converted into other forms. For example, in a resistor, electrical energy is dissipated as heat; in a lamp, it becomes light and heat; in a motor, it transforms into kinetic energy.
当电荷通过电势差时，电势能转化为其他形式的能量。例如，在电阻中，电能以热量形式耗散；在灯泡中，转化为光和热；在电动机中，转化为动能。
The power P (energy transferred per second) can be calculated using the product of current and potential difference:
功率 P（每秒传递的能量）可利用电流与电势差的乘积计算：
P = I × V
This equation is fundamental to understanding how much energy a component uses or generates every second.
该方程对于理解元件每秒钟消耗或产生多少能量至关重要。
6. Electromotive Force (emf) | 电动势
Electromotive force (emf) is the total energy supplied per unit charge by a source such as a battery or generator. Despite the word ‘force’, emf is not a force but a potential difference measured in volts.
电动势（emf）是电源（如电池或发电机）向每单位电荷提供的总能量。尽管名称中有“力”字，但电动势不是力，而是以伏特为单位的电势差。
The emf of a source represents the maximum potential difference it can provide, measured when no current is drawn. When a current flows, the terminal p.d. becomes slightly lower due to the internal resistance of the source.
电源的电动势表示它所能提供的最大电势差，在不接负载、无电流时测得。当有电流流过时，由于电源内阻的影响，路端电压会略低于电动势。
The energy supplied per coulomb is split between the external circuit and the energy wasted inside the source as heat: emf = terminal p.d. + lost volts (where lost volts = I × r, with r being internal resistance).
每库仑提供的能量一部分供应给外电路，一部分在电源内部以热量的形式损失：电动势 = 路端电压 + 内电压损失（内电压损失 = I × r，r 为内阻）。
7. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance (R) is a measure of the opposition to current flow in a component. It is defined as the ratio of potential difference across the component to the current flowing through it:
电阻 (R) 衡量元件对电流流动的阻碍程度，定义为元件两端的电势差与流过电流的比值：
R = V ÷ I
The unit of resistance is the ohm (Ω), where 1 Ω = 1 V/A.
电阻的单位是欧姆 (Ω)，1 Ω = 1 V/A。
Ohm’s Law states that, for a metallic conductor kept at constant temperature, the current through it is directly proportional to the potential difference across it. Components that obey this law are called ohmic conductors.
欧姆定律指出，对于温度恒定的金属导体，通过它的电流与导体两端的电势差成正比。遵循该定律的元件称为欧姆导体。
When temperature changes, resistance may vary. Many useful devices, such as thermistors and light-dependent resistors, deliberately change resistance in response to environmental conditions.
温度变化时，电阻也可能变化。许多有用的器件（如热敏电阻和光敏电阻）正是有意地根据环境条件改变电阻。
8. Current-Voltage Characteristics | 电流-电压特性
The current–voltage (I–V) graph of a component reveals much about its behaviour. For an ohmic conductor at constant temperature, the I–V graph is a straight line passing through the origin, showing a constant resistance.
元件的电流-电压（I–V）特性图揭示了它的行为。对于恒温下的欧姆导体，I–V 图是一条通过原点的直线，表明电阻恒定。
A filament lamp gives a curved I–V graph because its resistance increases as the wire heats up. For a diode, current flows easily in one direction (forward bias) but is almost zero in the reverse direction, producing a non-linear characteristic.
白炽灯产生弯曲的 I–V 曲线，因为灯丝温度升高导致电阻增大。对于二极管，正向偏压时电流容易通过，反向偏压时电流几乎为零，呈现非线性特性。
The gradient of an I–V graph can give information about resistance: a steeper slope at a given point indicates a lower resistance, while a shallower slope indicates higher resistance. For non-ohmic components, the resistance at any point is still defined as V/I.
I–V 图的斜率可提供电阻信息：某点斜率越陡表明电阻越小，斜率越平缓表明电阻越大。对于非欧姆元件，任一点的电阻仍定义为 V/I。
9. Series and Parallel Circuits | 串联与并联电路
Understanding how current and potential difference behave in different circuit arrangements is crucial for designing electromagnets and other electrical systems.
理解电流和电势差在不同电路连接方式中的行为，对于设计电磁铁和其他电气系统至关重要。
Series circuits: The current is the same everywhere. The total potential difference from the source is divided across components in proportion to their resistances. The total resistance is the sum of individual resistances: Rtotal = R1 + R2 + R3 + …
串联电路：各处电流相同。电源总电势差按电阻比例分配到各元件上。总电阻为各电阻之和：R总 = R1 + R2 + R3 + …
Parallel circuits: The potential difference across each branch is the same. The total current from the source is the sum of the currents in the separate branches. The combined resistance is less than the smallest individual resistance and is given by:
并联电路：每条支路两端的电势差相同。电源提供的总电流等于各支路电流之和。并联总电阻小于最小的单个电阻，计算公式为：
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
For two resistors in parallel, a convenient rearranged form is Rtotal = (R1 × R2) / (R1 + R2).
对于两个电阻并联，便利的变换形式为 R总 = (R1 × R2) / (R1 + R2)。
10. Practical Application: Electromagnets | 实际应用：电磁铁
An electromagnet is created by wrapping a coil of insulated wire around a soft iron core. When a current passes through the coil, a magnetic field is induced. The core becomes magnetised and greatly strengthens the field.
电磁铁是通过将绝缘导线线圈绕在软铁芯上制成的。当电流通过线圈时，就会产生磁场。铁芯被磁化，并大大增强了磁场。
The strength of the magnetic field depends on the magnitude of the current (I) and the number of turns per unit length of the coil (n). Greater current and more turns produce a stronger electromagnet.
磁场强度取决于电流大小（I）和线圈单位长度的匝数（n）。电流越大、匝数越多，电磁铁就越强。
Potential difference drives the current; therefore, by adjusting the p.d. across the coil (using a variable resistor or changing the source), one can control the current and hence the magnetic field strength precisely.
电势差驱动电流；因此，通过调节线圈两端的电势差（使用变阻器或改变电源），即可精确控制电流，进而控制磁场强度。
Electromagnets are found in countless devices: electric bells, relays, loudspeakers, scrap metal lifting cranes, and magnetic resonance imaging (MRI) scanners. Their ability to be switched on and off by controlling current makes them exceptionally versatile.
电磁铁存在于无数设备中：电铃、继电器、扬声器、废金属提升起重机和磁共振成像（MRI）扫描仪。通过控制电流即可通断磁场，使得电磁铁用途极其广泛。
11. Electrical Safety and Measurement Precautions | 电气安全与测量注意事项
When working with electric circuits, always ensure that fuses or circuit breakers of appropriate ratings are installed to protect against excessive currents that could cause overheating or fire.
使用电路时，务必确保安装额定电流适当的保险丝或断路器，以防止过大的电流导致过热或火灾。
Never connect an ammeter directly across a power supply; its very low resistance would draw a dangerously large current. Likewise, when measuring voltage, ensure the voltmeter is set to a suitable range to avoid damaging the instrument.
切勿将安培表直接并联在电源两端；其极低的内阻会导致危险的大电流。同样，测量电压时，确保电压表设置在合适的量程，以免损坏仪器。
Check that all connections are secure and that insulation is intact before energising a circuit. When building electromagnets, be aware that high currents can generate significant heat — use properly rated wires and limit the time of operation if necessary.
通电前应检查所有连接是否牢固、绝缘是否完好。制作电磁铁时，谨记大电流会产生大量热量——应使用额定电流合适的导线，必要时限制工作时间。
12. Key Concepts Summary | 核心概念总结
Electric current (I) measures the rate of charge flow; potential difference (V) measures the energy transferred per coulomb. Resistance (R) quantifies opposition to current, and Ohm’s Law (V = IR) governs ohmic materials at constant temperature.
电流 (I) 衡量电荷流动的速率；电势差 (V) 衡量每库仑电荷所传递的能量。电阻 (R) 量化对电流的阻碍，欧姆定律 (V = IR) 适用于恒温下的欧姆材料。
In series circuits, current is constant and p.d. divides; in parallel circuits, p.d. is constant and current divides. The emf of a source is the energy supplied per unit charge, equal to the terminal p.d. plus internal lost volts.
在串联电路中，电流恒定而电势差分压；在并联电路中，电势差恒定而电流分流。电源的电动势是每单位电荷提供的能量，等于路端电压加内电压损失。
These principles are directly applied in electromagnets, where a current-carrying coil produces a controllable magnetic field. Mastering current and potential difference provides the toolkit to analyse, design, and safely operate electric circuits in physics and engineering.
这些原理直接应用于电磁铁，其中载流线圈产生可控的磁场。掌握电流和电势差的概念，为分析、设计和安全操作物理及工程中的电路提供了必备的工具包。
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