📚 Why use a.c. for electricity supply? | 为什么使用交流电供电？
Alternating current (a.c.) is the standard form of electricity supplied to homes, schools and industry. This article explains the physics behind that choice: a.c. can be generated easily, transformed to high voltage for efficient transmission, and stepped down safely for everyday use.
交流电 (a.c.) 是家庭、学校和工业供电的标准形式。本文解释这一选择背后的物理原理：交流电易于产生，可升压至高压以实现高效输电，并可降压至安全电压供日常使用。
1. What is alternating current? | 什么是交流电？
An alternating current repeatedly reverses its direction, while a direct current flows in one direction only. The voltage and current in a mains a.c. supply vary sinusoidally with time, so the average value over a full cycle is zero, but the heating effect is not zero.
交流电的电流方向周期性反转，而直流电只沿一个方向流动。市电交流电的电压和电流随时间按正弦规律变化，因此一个完整周期内的平均值为零，但其热效应并不为零。
A sinusoidal a.c. voltage can be written as V(t) = V₀ sin(2πft), where V₀ is the peak voltage and f is the frequency. In a resistor, the current follows the same sinusoidal form if the load is purely resistive.
正弦交流电压可写作 V(t) = V₀ sin(2πft)，其中 V₀ 是峰值电压，f 是频率。在电阻中，如果负载为纯电阻，电流也遵循相同的正弦形式。
2. Generating an alternating e.m.f. | 交流电动势的产生
A simple a.c. generator consists of a coil rotating in a uniform magnetic field. The induced e.m.f. is proportional to the rate of change of magnetic flux linkage, giving a sinusoidal output.
简单的交流发电机由在匀强磁场中旋转的线圈构成。感应电动势与磁通链的变化率成正比，因此输出为正弦波形。
e = BANω sin(ωt)
Here B is the magnetic flux density, A is the coil area, N is the number of turns, and ω is the angular speed. When the coil rotates at constant speed, the output frequency is f = ω/2π.
其中 B 是磁通密度，A 是线圈面积，N 是匝数，ω 是角速度。当线圈匀速旋转时，输出频率为 f = ω/2π。
An a.c. generator uses slip rings to maintain the alternating output. A d.c. generator, by contrast, uses a split-ring commutator to reverse the connections every half cycle and produce a one-directional current.
交流发电机使用滑环来保持交流输出。相比之下，直流发电机使用裂环换向器，每半个周期反转连接，从而产生单向电流。
3. Why transformers require a changing flux | 为什么变压器需要变化的磁通量
A transformer works by electromagnetic induction. A changing current in the primary coil produces a changing magnetic flux in the iron core; this changing flux links the secondary coil and induces an e.m.f. in it.
变压器依靠电磁感应工作。初级线圈中变化的电流在铁芯中产生变化的磁通量；这一变化的磁通量穿过次级线圈，并在其中感应出电动势。
If the primary is connected to a steady d.c., the current and flux become constant after the switch-on transient, so no e.m.f. is induced in the secondary. This is the central reason a.c. is used: only a.c. can keep the flux changing continuously.
如果初级接上稳定的直流电，在接通瞬间过后电流和磁通量都变为恒定，因此次级不会感应出电动势。这是使用交流电的核心原因：只有交流电才能使磁通量持续变化。
4. The transformer equation and power conservation | 变压器方程与功率守恒
For an ideal transformer, the ratio of secondary to primary voltage equals the ratio of the number of turns:
对于理想变压器，次级电压与初级电压之比等于匝数之比：
Vₛ / Vₚ = Nₛ / Nₚ
If Nₛ > Nₚ, the output voltage is stepped up; if Nₛ < Nₚ, it is stepped down. An ideal transformer transfers power without loss, so IₚVₚ = IₛVₛ. Raising the voltage therefore lowers the current in the same proportion.
若 Nₛ > Nₚ，输出电压升高；若 Nₛ < Nₚ，则输出电压降低。理想变压器无损耗地传输功率，因此 IₚVₚ = IₛVₛ。因此升高电压会以相同比例降低电流。
5. Reducing transmission line power loss | 降低输电线功率损耗
Transmission lines have resistance R. When a current I flows through them, the power wasted as heat is:
输电线路具有电阻 R。当电流 I 通过时，以热形式浪费的功率为：
P_loss = I²R
For a fixed transmitted power P = VI, using a higher voltage V allows a smaller current I. Since the loss depends on I², even a modest voltage increase greatly reduces the loss.
对于固定的输送功率 P = VI，使用更高的电压 V 可使电流 I 更小。由于损耗取决于 I²，即使电压适度升高，也能大大降低损耗。
| Transmission voltage | Relative current for same power | Relative I²R loss |
|---|---|---|
| 25 kV | 1 | 1 |
| 400 kV | 1/16 | 1/256 |
This is why national grids transmit electricity at very high voltages, often 132 kV to 400 kV or more. The step-up transformer at the power station makes this possible.
这就是为什么国家电网以非常高的电压输电，通常为 132 kV 至 400 kV 或更高。发电站的升压变压器使这成为可能。
6. Stepping down for safe distribution | 降压实现安全配电
High voltage is efficient for transmission but dangerous for consumers. Near residential and industrial areas, substation transformers step the voltage down in stages, typically to about 230 V in many countries.
高压输电效率高，但对用户而言危险。在住宅和工业区附近，变电站变压器逐级降低电压，许多国家通常降至约 230 V。
Lower distribution voltages reduce insulation requirements, make appliances easier to design, and reduce the risk of electric shock. This combination of high-voltage transmission and low-voltage distribution is only practical with a.c. transformers.
较低的配电电压降低了绝缘要求，使电器更易设计，并减少触电风险。这种高压输电与低压配电的结合只有借助交流变压器才切实可行。
7. RMS values and average power | 方均根值与平均功率
The voltage and current of an a.c. supply are usually quoted as root-mean-square (r.m.s.) values, not peak values. The r.m.s. value is the equivalent steady d.c. value that would produce the same heating effect in a resistor.
交流电源的电压和电流通常用方均根 (r.m.s.) 值表示，而非峰值。方均根值是在电阻中产生相同热效应的等效稳定直流值。
V_rms = V₀ / √2, I_rms = I₀ / √2
For a purely resistive load, the average power is P_avg = I_rms²R = V_rms I_rms. Mains electricity labelled ‘230 V a.c.’ means an r.m.s. voltage of 230 V, with a peak of about 325 V.
对于纯电阻负载，平均
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