📚 Transformers in Edexcel IGCSE Science – Key Concepts & Calculations | Edexcel IGCSE 科学中的变压器 – 关键概念与计算
Transformers are essential components in the transmission and distribution of electricity. They allow us to change the voltage of an alternating current (AC) supply without altering the frequency, making it possible to send electrical power efficiently over long distances and then use it safely in homes. This article explains how transformers work, the key equations you need to know for Edexcel IGCSE Science, and the most common mistakes to avoid.
变压器是电力输送与分配中不可或缺的元件。它们能改变交流电的电压而不改变其频率，从而使电能可以高效地远距离传送，再安全地用在家庭中。本文为你讲解变压器的工作原理、Edexcel IGCSE 科学中必须掌握的关键公式，以及最容易出错的常见问题。
1. What Is a Transformer? | 什么是变压器？
A transformer is a device that changes the potential difference (voltage) of an alternating current. It consists of two coils of insulated wire wound around a soft iron core. The coil connected to the input voltage is called the primary coil, and the coil that delivers the output voltage is the secondary coil. Transformers only work with AC; a steady direct current (DC) cannot produce the changing magnetic field required.
变压器是一种改变交流电电压的装置。它由两组绕在软铁芯上的绝缘线圈构成。连接输入电压的线圈叫初级线圈，输出端接的线圈叫次级线圈。变压器只能用于交流电；恒定的直流电无法产生所需要的变化磁场。
2. Basic Structure of a Transformer | 变压器的基本结构
The primary coil and secondary coil are electrically isolated from each other; there is no direct electrical connection between them. They are both wound on a laminated soft iron core, which provides an efficient path for the magnetic flux. The laminations reduce eddy currents and energy losses. The number of turns on the primary coil (Nₚ) and the secondary coil (Nₛ) determine whether the transformer steps the voltage up or down.
初级线圈与次级线圈彼此电气隔离，两者之间没有直接的电路连接。它们都绕在叠片式软铁芯上，铁芯为磁通提供低磁阻路径。叠片结构能减少涡流导致的能量损耗。初级线圈的匝数（Nₚ）和次级线圈的匝数（Nₛ）决定了变压器升压还是降压。
3. How a Transformer Works: Electromagnetic Induction | 变压器的工作原理：电磁感应
When an alternating current flows through the primary coil, it produces a changing magnetic field in the iron core. This changing magnetic field continuously cuts through the secondary coil, inducing an alternating potential difference (voltage) across it by electromagnetic induction. If the secondary circuit is complete, an alternating current flows. The frequency of the output voltage is the same as that of the input voltage because the magnetic field changes at the same rate.
当交流电通过初级线圈时，会在铁芯中产生变化的磁场。这个变化的磁场持续地穿过次级线圈，通过电磁感应在次级线圈两端感应出交变的电压。若次级回路闭合，便会产生交流电。输出电压的频率与输入电压相同，因为磁场变化的速率一致。
4. The Turns Ratio Equation | 匝数比公式
The relationship between the primary voltage (Vₚ), secondary voltage (Vₛ), primary turns (Nₚ) and secondary turns (Nₛ) for an ideal transformer is given by the following simple ratio:
对于理想变压器，初级电压（Vₚ）、次级电压（Vₛ）、初级匝数（Nₚ）和次级匝数（Nₛ）满足以下简单的比例关系：
Vₚ / Vₛ = Nₚ / Nₛ
This equation states that the voltage ratio is exactly equal to the turns ratio. If the secondary coil has more turns than the primary (Nₛ > Nₚ), the output voltage is greater than the input voltage – a step‑up transformer. Conversely, if Nₛ < Nₚ, it is a step‑down transformer.
该公式表明电压比等于匝数比。如果次级匝数大于初级匝数（Nₛ > Nₚ），输出电压就高于输入电压，便是升压变压器。反之，若 Nₛ < Nₚ，则为降压变压器。
5. Relationship Between Voltage and Turns | 电压与匝数的关系
voltage will be 12 V × 5 = 60 V. This assumes an ideal transformer with no energy losses.
由于线圈感应出的电压与其匝数成正比，变压器可以将电压乘以 Nₛ/Nₚ。例如，若初级有 100 匝，次级有 500 匝，那么 Nₛ/Nₚ = 5。如果初级电压为 12 V，次级电压就是 12 V × 5 = 60 V。这是假设理想变压器无能量损耗的情况。
6. Current and the Turns Ratio | 电流与匝数比
bining this with Vₚ/Vₛ = Nₚ/Nₛ gives the following relationship between current and turns:
在理想变压器中，输入功率等于输出功率：Pₚ = Pₛ。由于电功率 P = I × V，可写出 Iₚ × Vₚ = Iₛ × Vₛ。将其与 Vₚ/Vₛ = Nₚ/Nₛ 结合，便得到电流与匝数的关系：
Iₚ / Iₛ = Nₛ / Nₚ
This tells us that if a transformer steps up the voltage, the secondary current is smaller than the primary current. Conversely, a step‑down transformer has a larger secondary current. The current ratio is the inverse of the turns ratio.
这表明，若变压器升压，则次级电流小于初级电流；降压变压器则次级电流更大。电流比恰好是匝数比的倒数。
7. Power in an Ideal Transformer | 理想变压器的功率
ormers have small losses, but the ideal model is still excellent for most IGCSE calculations. The power equation is often written as:
在理想变压器中，能量没有损失，输入给初级线圈的功率全部传递到次级。因此，我们可以放心使用 Pₚ = Pₛ。实际变压器存在少许损耗，但在绝大多数 IGCSE 计算中，理想模型依然非常适用。功率方程常写作：
Vₚ × Iₚ = Vₛ × Iₛ
8. Step‑Up vs Step‑Down Transformers | 升压变压器与降压变压器
| Type 类型 | Turns Ratio 匝数比 | Voltage 电压 | Current 电流 | Application 应用 |
|---|---|---|---|---|
| Step‑up 升压 | Nₛ > Nₚ | Vₛ > Vₚ | Iₛ < Iₚ | Power station output 电站输出 |
| Step‑down 降压 | Nₛ < Nₚ | Vₛ < Vₚ | Iₛ > Iₚ | Domestic supply 家庭供电 |
9. Transformer Efficiency and Energy Losses | 变压器的效率与能量损失
Real transformers are not 100% efficient. Some energy is lost as heat in the coils due to resistance (copper losses), and eddy currents induced in the iron core also cause heating. To minimise these, the core is made of thin laminated sheets, and soft iron is used because it is easily magnetised and demagnetised. Despite these losses, large power transformers can have efficiencies exceeding 99%.
实际变压器并不能达到 100% 的效率。线圈因存在电阻会发热（铜损），铁芯中感生的涡流也会导致发热。为减少这些损耗，铁芯采用薄片叠压结构，并使用软铁，因为它易磁化也易去磁。即使存在这些损耗，大型电力变压器的效率仍可超过 99%。
10. Transformers in the National Grid | 国家电网中的变压器
In the National Grid, step‑ d because the power lost in the cables is proportional to I², the heating losses in the transmission lines become much smaller. Near towns and homes, step‑n transformers then reduce the voltage to a safe level, typically 230 V in many countries.
在国家电网中，升压变压器将发电站产出的电压升高至数十万伏（通常为 400 kV）。这样，在输送相同功率时电流大幅减小（P = I × V），由于电缆中的功率损耗正比于 I²，传输线路的发热损耗便大大降低。在城镇和用户附近，降压变压器将电压降至安全水平，很多国家为 230 V。
11. Worked Calculation Examples | 计算示例
Example 1 – Step‑up: A transformer has a primary coil with 200 turns connected to a 230 V supply. The secondary coil has 1000 turns. Calculate the secondary voltage.
示例 1 – 升压：一台变压器的初级线圈有 200 匝，接在 230 V 电源上。次级线圈有 1000 匝。请计算次级电压。
Using Vₚ/Vₛ = Nₚ/Nₛ → 230 / Vₛ = 200 / 1000 → Vₛ = 230 × (1000/200) = 230 × 5 = 1150 V.
Example 2 – Current: The same transformer supplies a current of 0.50 A in the secondary. Find the primary current (assume ideal operation).
示例 2 – 电流：同一台变压器在次级输出 0.50 A 的电流。求初级电流（按理想情况计算）。
ly, using power: P = VₛIₛ = 1150 V × 0.50 A = 575 W, so Iₚ = P/Vₚ = 575 W / 230 V = 2.5 A.
12. Common Mistakes and Exam Tips | 常见错误与考试提示
Mistake 1: Applying the turns ratio formula to DC. Transformers require a changing magnetic field, so they only work with AC. Always check the question statement.
错误 1：把匝数比公式用于直流电。变压器依赖变化的磁场，因此仅适用于交流电。务必看清题目条件。
Mistake 2: condary. The ratio Vₚ/Vₛ = Nₚ/Nₛ always places the primary value on the left of the ratio.
错误 2：混淆初级和次级的物理量。记住，连接电源的是初级，输出端是次级。公式 Vₚ/Vₛ = Nₚ/Nₛ 总是把初级放在分子位置。
Mistake 3: Forgetting that current changes inversely with voltage. A step‑up transformer gives a lower secondary current, which is crucial for reducing transmission losses.
错误 3：忘记电流与电压成反比。升压变压器会使次级电流变小，这对于降低输电损耗至关重要。
Exam tip: Show all substitutions clearly, write the formula first, and state whether the transformer is ideal. If the question mentions heat losses, you may need to comment on efficiency.
考试技巧：清晰地写出代入步骤和公式，先写字母表达式，再代入数值。若题目提到发热损耗，可能需要你评论效率。
A solid understanding of transformers will help you tackle not only direct calculation questions but also explain why the National Grid uses high voltages. By mastering the turns ratio equation and the power relationship, you can confidently handle any transformer problem in Edexcel IGCSE Science.
透彻理解变压器不仅能帮你应对直接计算题，还能解释为什么国家电网使用高电压。掌握匝数比公式和功率关系后，你就能自信地解决 Edexcel IGCSE 科学中任何关于变压器的问题。
Published by TutorHao | Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图