HKDSE Physics – Electric Circuit

HKDSE Physics Elective
Chapter 2: Electric Circuit | 電路

Billy Sir’s Smart Notes: Master Ohm’s Law, Circuit Networks, and Practical Batteries.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握歐姆定律、電路網絡及實際電池分析。

1. Basic Circuit Concepts | 基本電路概念

Concept (概念)	Definition (定義)	Formula & Unit (公式與單位)
Current (I) 電流	Rate of flow of electric charge. (電荷流動的速率)	$$ I = \frac{Q}{t} $$ Unit: Ampere (A)
Potential Difference (V) 電勢差 / 電壓	Work done per unit charge to move it between two points. (將單位電荷在兩點間移動所作的功)	$$ V = \frac{W}{Q} $$ Unit: Volt (V)
Electromotive Force (e.m.f., $ \varepsilon $) 電動勢	Electrical energy supplied by a source per unit charge. (電源提供給單位電荷的電能)	$$ \varepsilon = \frac{W}{Q} $$ Unit: Volt (V)

2. Resistance & Ohm’s Law | 電阻與歐姆定律

Ohm’s Law states that the current through a conductor is directly proportional to the potential difference across it, provided its temperature remains constant. 歐姆定律指出，在溫度不變的情況下，通過導體的電流與其兩端的電勢差成正比。

📐 Ohm’s Law Formula | 歐姆定律公式

$$ V = IR $$

Where $ V $ is voltage (V), $ I $ is current (A), and $ R $ is resistance ($ \Omega $).

3. Series and Parallel Circuits | 串聯與並聯電路

Property (特性)	Series Circuit (串聯電路)	Parallel Circuit (並聯電路)
Current (I) 電流	Same everywhere: $ I = I_1 = I_2 = … $	Sum of branches: $ I = I_1 + I_2 + … $
Voltage (V) 電壓	Sum of components: $ V = V_1 + V_2 + … $	Same across branches: $ V = V_1 = V_2 = … $
Equivalent Resistance (R) 等效電阻	$$ R_{eq} = R_1 + R_2 + … $$	$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + … $$

4. Measurement & Components | 測量與元件

⚡ Meters | 測量儀器

Ammeter (安培計): Measures current. Must be connected in series. An ideal ammeter has zero resistance. (測量電流，必須串聯，理想安培計電阻為零)
Voltmeter (伏特計): Measures voltage. Must be connected in parallel. An ideal voltmeter has infinite resistance. (測量電壓，必須並聯，理想伏特計電阻無限大)

🎛️ Rheostat | 變阻器

A variable resistor used to control current or voltage in a circuit. (用於控制電路中電流或電壓的可變電阻器)

5. Potential Divider & Short Circuit | 分壓器與短路

⚖️ Potential Divider | 分壓器

A circuit that produces an output voltage that is a fraction of its input voltage. (產生輸入電壓一部分作為輸出電壓的電路)

V_{out} = V_{in} \times \frac{R_1}{R_1 + R_2}

⚠️ Short Circuit | 短路

Occurs when a low-resistance path is connected across a component or power supply. Current bypasses the normal load, leading to a massive surge in current which can cause overheating or fire. (當低電阻路徑連接在元件或電源兩端時發生。電流繞過正常負載，導致電流激增，可能引起過熱或火災。)

6. Ideal vs Practical Battery | 理想與實際電池

A practical battery is not perfect; it has an internal resistance ($ r $) that uses up some of the energy when current flows. (實際電池並不完美；它具有內阻($ r $)，當電流流動時會消耗部分能量。)

🔋 Internal Resistance Formula | 內阻公式

\varepsilon = V + Ir

Or, if connected to an external resistance $ R $:

\varepsilon = I(R + r)

$ \varepsilon $: Electromotive force (e.m.f.) (電動勢)
$ V $: Terminal voltage (useful voltage available to the circuit) (端電壓)
$ Ir $: Voltage drop across internal resistance (內阻造成的電壓降)

7. Electrical Power Calculation | 電功率計算

Electrical power is the rate at which electrical energy is transferred by an electric circuit. 電功率是電路轉移電能的速率。

⚡ Power Formulas | 功率公式

The general formula for electrical power (Unit: Watt, W):

$$ P = VI $$

By substituting Ohm’s Law ($ V = IR $), we get two more useful forms: (代入歐姆定律，可得另外兩條常用公式：)

P = I^2R \quad \text{and} \quad P = \frac{V^2}{R}

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