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HKDSE Physics – Alternating Current

HKDSE Physics Elective
Chapter 6: Alternating Current | 交流電

Billy Sir’s Smart Notes: Master AC vs DC, RMS Values, Transformers, and Power Transmission.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握交流電、方均根值、變壓器及電力傳輸。

1. AC vs DC | 交流電與直流電

Type (類型) Characteristics (特徵) Examples (例子)
Direct Current (DC)
直流電		 Current flows in only one direction. The voltage is usually constant over time. (電流只沿單一方向流動，電壓通常隨時間保持恆定。) Batteries, Solar Cells (電池、太陽能板)
Alternating Current (AC)
交流電		 Current periodically reverses its direction. In HK, the mains supply is sinusoidal AC at 50 Hz. (電流週期性地改變方向。香港的市電為 50 Hz 的正弦交流電。) Mains electricity, AC Generators (市電、交流發電機)

2. R.M.S. Voltage and Current | 方均根電壓與電流

The root-mean-square (r.m.s.) value of an AC is the value of the steady DC that would produce the same heating effect (power) in a given resistor. 交流電的方均根值，等於在同一電阻器中產生相同熱效應（功率）的穩定直流電數值。

📈 Formulas for Sinusoidal AC | 正弦交流電公式

$$ I_{rms} = \frac{I_0}{\sqrt{2}} \quad \text{and} \quad V_{rms} = \frac{V_0}{\sqrt{2}} $$
  • \( I_0, V_0 \): Peak current and peak voltage (峰值電流與峰值電壓)
  • Average Power (平均功率):
$$ P = V_{rms} I_{rms} = I_{rms}^2 R = \frac{V_{rms}^2}{R} $$

3. Transformers | 變壓器

A transformer is a device that changes the voltage of an alternating current using electromagnetic induction. It only works with AC, not DC! 變壓器是利用電磁感應改變交流電壓的裝置。它只適用於交流電，不適用於直流電！

🔄 Transformer Equations | 變壓器公式

The ratio of voltages is equal to the ratio of the number of turns in the coils: (電壓比等於線圈匝數比：)

$$ \frac{V_P}{V_S} = \frac{N_P}{N_S} $$

For an ideal transformer (100% efficiency), power input equals power output: (對於理想變壓器，輸入功率等於輸出功率：)

$$ V_P I_P = V_S I_S $$
  • Step-up Transformer (升壓變壓器): \( N_S > N_P \), so \( V_S > V_P \) (Voltage increases).
  • Step-down Transformer (降壓變壓器): \( N_S < N_P \), so \( V_S < V_P \) (Voltage decreases).

⚠️ Transformer Efficiency | 變壓器效率

In reality, efficiency is less than 100% due to energy losses: (在現實中，由於能量損耗，效率低於 100%：)

  • Joule Heating in Coils (銅損): Heat lost due to the resistance of the copper wires (\( I^2 R \)). (銅線電阻產生的焦耳熱)
  • Eddy Currents in Core (渦流損耗): Changing magnetic fields induce swirling currents in the iron core, causing heating. Reduced by using a laminated core. (鐵芯中感應出的渦電流產生熱能。可透過使用層壓鐵芯減少)
  • Hysteresis Loss (磁滯損耗): Energy required to repeatedly magnetize and demagnetize the iron core. (反覆磁化和去磁鐵芯所需的能量)
  • Magnetic Flux Leakage (漏磁): Not all magnetic flux produced by the primary coil links with the secondary coil. (初級線圈產生的磁通量未能完全穿過次級線圈)

4. Long Distance Power Transmission | 長距離電力傳輸

Electricity is transmitted over long distances at very high voltages (e.g., 400 kV) to minimize power loss in the transmission cables. 電力在長距離傳輸時會使用極高電壓（例如 400 kV），以盡量減少傳輸電纜中的功率損耗。

⚡ Why High Voltage? | 為何使用高壓？

  1. For a given transmitted power \( P = VI \), increasing the transmission voltage \( V \) significantly reduces the current \( I \). (對於給定的傳輸功率，提高傳輸電壓會大幅降低電流。)
  2. The power lost as heat in the cables is given by Joule heating: (電纜中以熱能形式流失的功率由焦耳熱決定：)
$$ P_{loss} = I^2 R $$

Since the current \( I \) is much smaller, the power loss \( I^2 R \) is drastically reduced. (由於電流變得極小，功率損耗也隨之大幅減少。)

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