📚 6.9.5 Transformers | 6.9.5 变压器
Transformers are indispensable devices in modern electrical systems, and the Edexcel IGCSE Science specification point 6.9.5 focuses specifically on understanding their structure, operating principle, and the mathematical relationship between voltage and turns ratio. A transformer is a passive electrical component that transfers electrical energy from one alternating current (AC) circuit to another, either increasing or decreasing the voltage while keeping the frequency unchanged. This article provides a thorough revision resource covering every aspect of transformers required by the specification, from electromagnetic induction to practical applications in the national grid, with fully bilingual explanations to support both English- and Chinese-medium learners.
变压器是现代电力系统中不可或缺的设备，Edexcel IGCSE 科学大纲知识点 6.9.5 专门要求学生理解变压器的结构、工作原理以及电压与匝数之间的数学关系。变压器是一种无源电气元件，它能在保持频率不变的情况下，将电能从一个交流电路传递到另一个交流电路，并升高或降低电压。本文提供一份完整的复习资源，涵盖大纲要求的所有变压器内容，从电磁感应到国家电网中的实际应用，并以中英双语对照讲解，帮助中英文学习者在备考中彻底掌握该主题。
1. Electromagnetic Induction – The Foundation | 电磁感应——变压器的基础
To understand how a transformer operates, you must first recall the principle of electromagnetic induction. When a conductor cuts through magnetic field lines, or when the magnetic field passing through a coil changes, a potential difference (voltage) is induced across the ends of the conductor or coil. This effect is maximised if the conductor is part of a complete circuit, allowing an induced current to flow. In a transformer, the changing magnetic field is produced by an alternating current flowing through the primary coil, and the induced voltage appears across the secondary coil.
要理解变压器的工作方式，必须先回顾电磁感应原理。当导体切割磁感线，或者穿过线圈的磁场发生变化时，导体的两端或线圈两端就会产生感应电动势（电压）。如果导体是闭合回路的一部分，感应出的电流就会流动，此时感应效果最明显。在变压器中，变化的磁场是由流过初级线圈的交流电产生的，而感应电压则出现在次级线圈两端。
The crucial point is that a steady direct current (DC) cannot produce a continuously changing magnetic field; therefore, transformers only work with AC. In IGCSE exams, you are expected to state clearly that a transformer requires an alternating current to induce a voltage in the secondary coil.
关键点在于，稳定的直流电（DC）无法产生持续变化的磁场；因此，变压器只能使用交流电。在 IGCSE 考试中，要求你明确指出变压器需要交流电才能在次级线圈中感应出电压。
2. Basic Structure of a Transformer | 变压器的基本结构
A typical transformer consists of three main parts: a primary coil, a secondary coil, and a soft iron core. The primary coil is connected to the input AC supply, while the secondary coil is connected to the output circuit. The two coils are not electrically connected; energy transfer occurs purely through the magnetic field. The soft iron core forms a closed loop that passes through both coils, concentrating and directing the magnetic flux so that almost all the field lines generated by the primary coil pass through the secondary coil.
一个典型的变压器由三个主要部分组成：初级线圈、次级线圈和软铁芯。初级线圈连接到输入的交流电源上，次级线圈连接到输出电路上。两个线圈之间没有电的直接连接；能量完全通过磁场传递。软铁芯构成一个闭合环路，穿过两个线圈，集中并引导磁通量，使得初级线圈产生的磁感线几乎全部穿过次级线圈。
The core is laminated – made of thin sheets of iron insulated from one another – to reduce eddy currents, which would otherwise cause energy loss and heating. In an IGCSE diagram, you need to be able to label the primary coil, the secondary coil, the laminated iron core, and indicate which coil has more turns for a step‑up or step‑down arrangement.
铁芯由相互绝缘的薄铁片叠成，目的是减少涡流，否则涡流会造成能量损失和发热。在 IGCSE 的示意图中，你需要能够标出初级线圈、次级线圈、叠片铁芯，并指出升压或降压时哪个线圈的匝数更多。
3. How a Transformer Works | 变压器的工作原理
When an alternating current passes through the primary coil, it produces a magnetic field that continuously changes in strength and direction. Because the soft iron core channels this magnetic field through the secondary coil, the changing magnetic flux induces an alternating voltage across the secondary coil. If the secondary circuit is complete, an alternating current flows. The frequency of the output voltage is exactly the same as the frequency of the input AC because the magnetic field alternates at the same rate.
当交流电通过初级线圈时，会产生一个不断改变大小和方向的磁场。由于软铁芯将这个磁场引导穿过次级线圈，变化的磁通量便在次级线圈两端感应出一个交变电压。如果次级电路是闭合的，就会有交流电流流动。输出电压的频率与输入交流电的频率完全相同，因为磁场以相同的速率交变。
It is important to note that in an ideal transformer, the power input to the primary coil equals the power output from the secondary coil (neglecting tiny energy losses). This principle of energy conservation leads directly to the relationship linking voltage, current, and the number of turns in each coil.
值得注意的是，在理想变压器中，输入初级线圈的功率等于次级线圈输出的功率（忽略微小的能量损耗）。这个能量守恒原理直接引出了电压、电流与各线圈匝数之间的关系。
4. Step‑up and Step‑down Transformers | 升压变压器与降压变压器
A transformer that increases the voltage from primary to secondary is called a step‑up transformer. In such a device, the secondary coil has more turns than the primary coil (Nₛ > Nₚ). Conversely, a transformer that decreases the voltage is called a step‑down transformer, where the secondary coil has fewer turns than the primary coil (Nₛ < Nₚ).
将初级电压升高的变压器称为升压变压器。在这种装置中，次级线圈的匝数多于初级线圈（Nₛ > Nₚ）。反过来，将电压降低的变压器称为降压变压器，此时次级线圈的匝数少于初级线圈（Nₛ < Nₚ）。
An easy way to remember this is: ‘STEP UP = MORE TURNS ON SECONDARY; STEP DOWN = FEWER TURNS ON SECONDARY.’ In the national grid, step‑up transformers are used at power stations to raise the voltage for efficient long‑distance transmission, while step‑down transformers are used near homes to reduce the voltage to safe levels.
一个简单的记忆方法是：“升压 = 次级匝数更多；降压 = 次级匝数更少。”在国家电网中，发电站使用升压变压器将电压升高以实现高效远距离输电，而住宅附近则使用降压变压器将电压降到安全水平。
| Transformer type 变压器类型 | Turns ratio 匝数比 | Voltage change 电压变化 | Example application 应用实例 |
|---|---|---|---|
| Step‑up 升压 | Nₛ > Nₚ | Vₛ > Vₚ | Power station output |
| Step‑down 降压 | Nₛ < Nₚ | Vₛ < Vₚ | Phone charger, local substation |
5. The Transformer Equation | 变压器公式
The relationship between the voltages and the number of turns on the primary and secondary coils is given by the transformer equation:
Vₚ / Vₛ = Nₚ / Nₛ
where Vₚ is the primary voltage, Vₛ is the secondary voltage, Nₚ is the number of turns on the primary coil, and Nₛ is the number of turns on the secondary coil. This equation assumes an ideal transformer with no energy losses. It tells us that the ratio of the voltages is exactly equal to the ratio of the turns.
初级线圈和次级线圈的电压与匝数之间的关系由变压器公式给出：Vₚ / Vₛ = Nₚ / Nₛ，其中 Vₚ 是初级电压，Vₛ 是次级电压，Nₚ 是初级线圈的匝数，Nₛ 是次级线圈的匝数。该公式假定为无能量损耗的理想变压器。它表明电压之比恰好等于匝数之比。
For example, if the primary coil has 200 turns and the secondary coil has 1000 turns, and the primary is connected to a 50 V AC supply, the secondary voltage Vₛ can be found by rearranging the equation: Vₛ = Vₚ × (Nₛ / Nₚ) = 50 × (1000 / 200) = 250 V. IGCSE questions frequently ask you to either calculate an unknown voltage or an unknown number of turns, so practising equation rearrangement is essential.
例如，若初级线圈有 200 匝，次级线圈有 1000 匝，初级接在 50 V 交流电源上，则次级电压 Vₛ 可通过公式变形求得：Vₛ = Vₚ × (Nₛ / Nₚ) = 50 × (1000 / 200) = 250 V。IGCSE 考题常要求你计算未知电压或未知匝数，因此熟练变换公式至关重要。
6. Energy Conservation and the Current Equation | 能量守恒与电流公式
In an ideal transformer, energy cannot be created or destroyed, so the electrical power input to the primary coil equals the electrical power output from the secondary coil. Electrical power is the product of voltage and current (P = I × V). Therefore:
Iₚ × Vₚ = Iₛ × Vₛ
where Iₚ is the primary current and Iₛ is the secondary current. From this, we can deduce that in a step‑up transformer (Vₛ > Vₚ), the secondary current Iₛ must be smaller than the primary current Iₚ to keep the product constant. Conversely, in a step‑down transformer, the secondary current becomes larger than the primary current.
在理想变压器中，能量既不会凭空产生也不会消失，因此输入初级线圈的电功率等于次级线圈输出的电功率。电功率是电压与电流的乘积（P = I × V）。因此：Iₚ × Vₚ = Iₛ × Vₛ，其中 Iₚ 为初级电流，Iₛ 为次级电流。由此可推断，在升压变压器中（Vₛ > Vₚ），次级电流 Iₛ 必须小于初级电流 Iₚ，以保持乘积不变。反之，在降压变压器中，次级电流会大于初级电流。
Combining the transformer equation and the power equation gives the full relationship:
Vₚ / Vₛ = Nₚ / Nₛ = Iₛ / Iₚ
This shows that voltage is directly proportional to the number of turns, while current is inversely proportional to the number of turns. IGCSE candidates should be able to use any combination of these relationships to solve numerical problems involving transformers.
将变压器公式与功率公式结合，得到完整关系式：Vₚ / Vₛ = Nₚ / Nₛ = Iₛ / Iₚ。这表明电压与匝数成正比，而电流与匝数成反比。IGCSE 考生应能灵活运用这些关系的任意组合来解决变压器相关的计算题。
7. Transformer Efficiency and Energy Losses | 变压器效率与能量损耗
Whilst an ideal transformer has 100% efficiency, real transformers inevitably dissipate some energy as heat. The main sources of energy loss include: eddy currents in the iron core, which are reduced by using a laminated core; hysteresis losses due to the repeated magnetisation and demagnetisation of the core material, minimised by choosing soft iron; and resistive heating in the copper windings (copper losses), which can be reduced by using thicker wire. These losses mean that the output power is slightly less than the input power, and efficiency is defined as (output power / input power) × 100%.
尽管理想变压器效率为 100%，但真实变压器不可避免地会以热量形式耗散一部分能量。能量损耗的主要来源包括：铁芯中的涡流（可通过采用叠片铁芯来减少）；铁芯材料反复磁化和退磁产生的磁滞损耗（可通过选用软铁来降低）；以及铜绕组中的电阻发热（铜损），这可以通过使用更粗的导线来减少。这些损耗使得输出功率略小于输入功率，效率的定义为（输出功率 / 输入功率）× 100%。
IGCSE specification 6.9.5 requires you to describe ways to improve transformer efficiency. These include: designing a laminated core to disrupt eddy current paths, using soft magnetic materials with low hysteresis loss, winding coils with low‑resistance copper wire, and ensuring a tightly closed core to maximise flux linkage. Exam questions often ask ‘why is the core laminated?’ – the answer is ‘to reduce eddy currents, which would otherwise heat the core and waste energy.’
IGCSE 大纲 6.9.5 要求你描述提高变压器效率的方法。这些方法包括：设计叠片铁芯以阻断涡流路径；使用磁滞损耗低的软磁性材料；用低电阻铜线绕制线圈；以及确保铁芯紧密闭合以最大化磁链。考题常问“铁芯为什么要叠片？”——答案是“为了减少涡流，否则涡流会使铁芯发热并浪费能量。”
8. The National Grid and Transformer Applications | 国家电网与变压器的应用
Transformers are a critical component of the national grid. At the power station, a step‑up transformer increases the generated voltage (typically around 25 kV) to 400 kV or more. Transmitting electricity at very high voltages reduces the current for a given power level, which drastically lowers resistive energy losses in the transmission cables (since power lost = I²R). Near towns and homes, local substations use step‑down transformers to gradually reduce the voltage to safer levels, eventually to 230 V for domestic use.
变压器是国家电网的关键组成部分。在发电站，升压变压器将发出的电压（通常约 25 kV）升高到 400 kV 或以上。以极高电压传输电能可以在一定功率水平下降低电流，从而大幅减少传输电缆中的电阻能量损耗（因为损耗功率 = I²R）。在城镇和住宅附近，本地变电站使用降压变压器将电压逐级降到安全水平，最终降为家用的 230 V。
Smaller step‑down transformers are also built into countless household devices such as mobile phone chargers, laptop adapters, and LED lighting drivers. These convert the mains AC voltage to a much lower DC voltage suitable for the device’s electronics. Being able to link the abstract equation to these real‑world applications solidifies your understanding and prepares you for contextual exam questions.
较小的降压变压器还内置于无数家用设备中，如手机充电器、笔记本电脑适配器和 LED 照明驱动器。它们将市电交流电压转换为适合设备电子元件的低得多的直流电压。能够将抽象的公式与实际应用联系起来，可以加深你的理解，并为应对情境化考题做好准备。
9. Experimental Investigation of Transformers | 实验探究变压器
In the laboratory, a simple demonstration transformer can be built by winding two separate coils around a U‑shaped soft iron core with a yoke to close the magnetic circuit. By connecting the primary to a low‑voltage AC supply and measuring both primary and secondary voltages with multimeters, students can verify the transformer equation. Varying the number of turns and recording the voltage ratios allows you to confirm that Vₛ/Vₚ ≈ Nₛ/Nₚ within experimental error.
在实验室中，可以用一个 U 形软铁芯和一个闭合磁轭来绕制两个独立的线圈，搭建一个简易的演示变压器。将初级线圈接到低压交流电源上，用万用表测量初级和次级电压，学生就可以验证变压器公式。改变匝数并记录电压比，可以证实 Vₛ/Vₚ ≈ Nₛ/Nₚ 在实验误差范围内成立。
Safety note: always use a safe low‑voltage AC source (e.g. 2–6 V) and ensure that all connections are secure. The iron core may become warm if eddy currents are significant, providing a visual and tactile clue to energy dissipation.
安全提示：务必使用安全的低压交流电源（如 2–6 V），并确保所有连接牢固。如果涡流明显，铁芯可能会变热，为能量耗散提供直观的视觉和触觉线索。
10. Common Exam Pitfalls and Top Tips | 常见考试失分点与高分技巧
Many students lose marks by stating that a transformer works with direct current, or by confusing the current direction in step‑up and step‑down transformers. Remember: a transformer must use AC; if a DC supply were connected, there would be no changing magnetic field and hence no induced voltage in the secondary. Another frequent error is misapplying the formula: for step‑down, Vₛ is less than Vₚ, so Nₛ must be less than Nₚ – check your substitution carefully.
许多学生因为声称变压器能使用直流电而失分，或是混淆了升压和降压变压器中的电流方向。请记住：变压器必须使用交流电；如果接入直流电源，就不会有变化的磁场，因此次级线圈中不会感应出电压。另一个常见错误是套错公式：对于降压变压器，Vₛ 小于 Vₚ，所以 Nₛ 必须小于 Nₚ——请仔细检查代入的数值。
When explaining the purpose of step‑up transformers in the national grid, always link the concept to power loss: high voltage → low current → less I²R heating in cables. Use the phrase ‘to reduce energy lost as heat in the transmission lines’ to secure full marks. Finally, label all parts clearly on diagrams: core, primary coil, secondary coil, and state whether it is step‑up or step‑down with a brief justification.
在解释升压变压器在国家电网中的用途时，始终要将概念与功率损耗联系起来：高电压 → 低电流 → 电缆中 I²R 发热更少。使用“为了减少传输线路中因热而损失的能量”这一表述可获得满分。最后，在图上清晰地标出所有部件：铁芯、初级线圈、次级线圈，并说明它是升压还是降压变压器，同时给出简短的理由。
11. Summary and Quick Revision Checklist | 总结与快速复习清单
Transformers are devices that change the voltage of an AC supply by means of electromagnetic induction.
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