📚 Transformers and the Turns Ratio Equation | 变压器与匝数比方程
Transformers are essential devices in the transmission and distribution of electrical energy. They operate on the principle of electromagnetic induction to change the size of an alternating voltage. In this article, we explore the structure, operation, and the key mathematical relationship known as the turns ratio equation, which is a core topic in the Edexcel IGCSE Physics specification (statement 6.5.5).
变压器是电能传输与分配中不可缺少的装置。它们利用电磁感应原理来改变交流电压的大小。本文将探讨变压器的结构、工作原理以及称为匝数比方程的关键数学关系，这是Edexcel IGCSE物理大纲（考点6.5.5）的核心内容。
1. What is a Transformer? | 什么是变压器？
A transformer is a static electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It can increase (step up) or decrease (step down) an alternating voltage without changing the frequency.
变压器是一种静止的电器装置，通过电磁感应在两个或多个电路之间传递电能。它可以升高（升压）或降低（降压）交流电压，而不改变其频率。
2. Basic Structure of a Transformer | 变压器的基本结构
A simple transformer consists of two coils of insulated wire wound around a laminated soft iron core. The coil connected to the input alternating voltage is called the primary coil, and the coil connected to the output circuit is the secondary coil. The soft iron core provides a closed magnetic path to link the magnetic flux between the two coils efficiently.
简单的变压器由两个缠绕在叠片软铁芯上的绝缘线圈组成。连接到输入交流电压的线圈称为初级线圈，连接到输出回路的线圈称为次级线圈。软铁芯提供闭合的磁路，以高效地耦合两个线圈之间的磁通量。
The primary coil receives electrical energy from the source.
初级线圈从电源接收电能。
The secondary coil delivers electrical energy to the load.
次级线圈向负载输出电能。
The laminated core reduces eddy current losses.
叠片铁芯可减少涡流损耗。
3. How a Transformer Works | 变压器如何工作
When an alternating current flows through the primary coil, it produces a changing magnetic field in the iron core. This changing magnetic field links with the secondary coil and, by electromagnetic induction, induces an alternating voltage across the secondary coil. The magnitude of the induced voltage depends on the rate of change of magnetic flux and the number of turns in the secondary coil.
当交流电流流过初级线圈时，会在铁芯中产生变化的磁场。这个变化的磁场与次级线圈交链，通过电磁感应在次级线圈两端感应出交流电压。感应电压的大小取决于磁通量的变化率以及次级线圈的匝数。
4. Step-up and Step-down Transformers | 升压与降压变压器
A step-up transformer has more turns on the secondary coil than on the primary coil (Ns > Np), which results in a higher secondary voltage. A step-down transformer has fewer turns on the secondary coil (Ns < Np), giving a lower output voltage. The type of transformer is determined solely by the turns ratio, not by the size of the coils.
升压变压器的次级线圈匝数多于初级线圈（Ns > Np），从而得到更高的次级电压。降压变压器的次级线圈匝数较少（Ns < Np），输出电压较低。变压器的类型仅由匝数比决定，与线圈的尺寸无关。
| Type | 类型 | Turns Ratio (Ns/Np) | 匝数比 | Voltage change | 电压变化 |
| Step-up | 升压 | > 1 | Vs > Vp |
| Step-down | 降压 | < 1 | Vs < Vp |
5. The Turns Ratio Equation | 匝数比方程
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 turns ratio equation:
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）之间的关系由匝数比方程给出：
Vp / Vs = Np / Ns
This equation shows that the voltage ratio is directly proportional to the turns ratio. If the number of secondary turns is doubled, the secondary voltage also doubles, provided the primary voltage remains constant.
该方程表明电压比与匝数比成正比。如果次级匝数加倍，在初级电压保持恒定的情况下，次级电压也会加倍。
6. Example Calculations | 计算实例
Worked example 1: A transformer has 500 turns on the primary coil and 1000 turns on the secondary coil. The primary voltage is 230 V. Calculate the secondary voltage.
计算示例1：某变压器初级线圈有500匝，次级线圈有1000匝。初级电压为230 V。请计算次级电压。
Using Vp / Vs = Np / Ns → 230 / Vs = 500 / 1000 → Vs = 230 × (1000 / 500) = 460 V. This is a step-up transformer.
使用 Vp / Vs = Np / Ns → 230 / Vs = 500 / 1000 → Vs = 230 × (1000 / 500) = 460 V。这是一个升压变压器。
Worked example 2: A step-down transformer has a primary coil of 2000 turns and delivers an output voltage of 12 V from a 240 V mains supply. Find Ns.
计算示例2：一台降压变压器的初级线圈为2000匝，将240 V市电降压为12 V输出。求Ns。
240 / 12 = 2000 / Ns → 20 = 2000 / Ns → Ns = 2000 / 20 = 100 turns.
240 / 12 = 2000 / Ns → 20 = 2000 / Ns → Ns = 2000 / 20 = 100 匝。
7. The Relationship Between Voltage and Turns | 电压与匝数的关系
The induced voltage in a coil is directly proportional to its number of turns, provided the rate of change of magnetic flux is the same for both coils. Because the primary and secondary share the same iron core, the changing flux linkage is practically identical. Therefore, a coil with more turns experiences a larger induced voltage.
只要两线圈的磁通量变化率相同，线圈中感应出的电压就与其匝数成正比。由于初级和次级共用同一个铁芯，变化的磁链几乎完全相同。因此，匝数更多的线圈会感应出更大的电压。
8. Ideal Transformer Assumptions | 理想变压器假设
In an ideal transformer, we assume no energy losses. This means the power input to the primary equals the power output from the secondary: Vp Ip = Vs Is. Additionally, the core is perfectly magnetisable with no hysteresis or eddy currents, and the coils have zero resistance. Real transformers approach these ideals but experience small losses.
在理想变压器中，我们假设没有能量损耗。这意味着初级输入功率等于次级输出功率：Vp Ip = Vs Is。此外，铁芯完全可磁化，不存在磁滞或涡流，线圈电阻为零。实际变压器接近这些理想状态，但存在少量损耗。
9. Power Conservation in Transformers | 变压器中的功率守恒
From the power equation for an ideal transformer, Vp Ip = Vs Is, we can deduce that if a transformer steps up the voltage, the secondary current must step down in proportion, and vice versa. This is why high-voltage transmission lines use low currents to reduce resistive heating losses over long distances.
由理想变压器的功率公式 Vp Ip = Vs Is，我们可以推知，若变压器升压，次级电流必然按比例降低，反之亦然。这就是远距离高压输电线采用低电流以减少电阻发热损耗的原因。
10. Practical Applications | 实际应用
Transformers are used in the national grid: step-up transformers raise the voltage from power stations to hundreds of kilovolts for efficient transmission, and step-down transformers reduce the voltage to safe levels for domestic use (e.g., 230 V). They are also found in mobile phone chargers, laptop adaptors, and many household appliances to convert mains voltage to lower direct current (DC) voltages after rectification.
变压器用于国家电网：升压变压器将发电厂的电压升至几十万伏以实现高效输送，降压变压器则将电压降至家庭安全用电水平（如230 V）。手机充电器、笔记本电源适配器以及许多家用电器中也有变压器，用于将市电降压再整流为低压直流电。
Power station generators produce electricity at around 25 kV.
发电厂发电机产生的电压约为25 kV。
Step-up transformers increase this to 400 kV for transmission.
升压变压器将其提高至400 kV用于传输。
Local substations step down the voltage to 11 kV, then to 230 V.
地方变电站将电压降至11 kV，再降至230 V。
11. Common Exam Mistakes | 常见考试错误
Many students forget that the turns ratio equation applies only to the voltages, not directly to the currents unless using the power conservation relation. Another common mistake is applying the equation to DC supplies, which will not work because a changing magnetic flux is essential. Also, always ensure the ratio Np/Ns is placed on the correct side of the equation relative to Vp/Vs.
许多学生忘记了匝数比方程仅适用于电压，不能直接用于电流，除非通过功率守恒关系转换。另一个常见错误是将该方程用于直流电源，这是行不通的，因为必须要变化的磁通。同时，务必确保Np/Ns与Vp/Vs在等式中的对应位置正确。
Also, careless substitution of turns numbers can invert the result. Always identify which coil has more turns before calculating. In a step-up transformer, Vs > Vp and Ns > Np; the ratio Np/Ns must be less than 1.
此外，粗心代入匝数数值可能导致结果颠倒。计算前务必判断哪个线圈的匝数更多。在升压变压器中，Vs > Vp，Ns > Np；Np/Ns 必定小于1。
12. Summary | 总结
The turns ratio equation Vp/Vs = Np/Ns is a fundamental tool for predicting secondary voltage in an ideal transformer. It arises from electromagnetic induction and the identical flux change in the primary and secondary coils. Mastery of this equation, together with an understanding of step-up and step-down behaviour and power conservation, is essential for success in the Edexcel IGCSE Physics examination.
匝数比方程 Vp/Vs = Np/Ns 是预测理想变压器次级电压的基本工具。它来源于电磁感应以及初级和次级线圈中相同的磁通变化。掌握该方程，并结合对升压/降压原理以及功率守恒的理解，对于在Edexcel IGCSE物理考试中取得成功至关重要。
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