Edexcel物理 电路 欧姆定律 电阻 EMF 内阻 | Edexcel Physics: Circuits, Ohms Law, Resistance, EMF & Internal Resistance

Edexcel物理 电路 欧姆定律 电阻 EMF 内阻

Electricity is one of the most fundamental and rewarding topics in A-Level Edexcel Physics. It accounts for approximately 25% of Paper 1 and appears regularly in the practical endorsement assessments too. From the simple I = Q / t relationship to complex multi-loop circuit analysis using Kirchhoff's Laws, mastering electricity requires both conceptual understanding and disciplined calculation skills. 电学是Edexcel物理A-Level中最基础也最容易拿分的板块之一，大约占Paper 1的25%，并且在实验考核中频繁出现。从简单的I=Q/t关系式到复杂的多回路基尔霍夫分析，掌握电学需要概念的清晰和计算的严谨。

In this guide we will walk through every major sub-topic step by step, with worked examples, common pitfalls, and Edexcel-specific exam tips. Whether you are targeting a grade A or A*, this is your complete electricity study companion. 本指南将逐步覆盖每一个重要子专题，包含计算例题、常见错误和Edexcel考试技巧。无论你的目标是A还是A*，这都是一份完整的电学学习伴侣。

Edexcel A-Level Physics: Paper Structure

Paper 1 (1h 45min, 90 marks): Advanced Physics I ： Mechanics, Electric Circuits, Further Mechanics, EM Spectrum, Nature of Light. Electricity is bundled with Mechanics and Further Mechanics in this paper. 试卷1包含力学、电路、进阶力学等板块。

1. Current, Charge and Potential Difference: The Building Blocks

Electric current is the rate of flow of charge: I = Q / t, where Q is measured in coulombs (C) and t in seconds (s). One coulomb is the charge carried by approximately 6.25 × 1018 electrons. The direction of conventional current is opposite to electron flow ： this is a classic trick question in Edexcel multiple-choice. 电流是电荷的流动速率：I=Q/t，Q的单位是库仑。1库仑约等于6.25×1018个电子所带的电荷量。常规电流方向与电子流动方向相反，这是Edexcel选择题中的经典陷阱。

Potential difference (p.d.) between two points is the work done per unit charge: V = W / Q. One volt = one joule per coulomb. Think of p.d. as the "push" that drives current through a circuit, just like a water pump creates pressure to push water through pipes. 电势差是单位电荷所做的功：V=W/Q。1伏特=1焦耳每库仑。可以把电势差理解为驱动电流的"推力"，就像水泵产生压力推动水流一样。

I = Q / t

Current (A) = Charge (C) / time (s)
电流=电荷量/时间

V = W / Q

P.d. (V) = Work done (J) / Charge (C)
电势差=功/电荷量

R = V / I

Ohm's Law: Resistance = Voltage / Current
欧姆定律：电阻=电压/电流

2. Ohm's Law and I-V Characteristics

Ohm's Law states that the current through a conductor is directly proportional to the potential difference across it, provided the temperature remains constant. The constant of proportionality is resistance: V = IR. An ohmic conductor (e.g., a metal wire at constant temperature) produces a straight-line I-V graph through the origin. 欧姆定律指出，在温度不变的情况下，通过导体的电流与两端电势差成正比。比例常数就是电阻V=IR。欧姆导体在恒温下产生过原点的直线I-V图。

However, not all components follow Ohm's Law. The filament lamp shows a curved I-V characteristic because its resistance increases as it heats up (the metal ions vibrate more, making electron flow harder). The semiconductor diode conducts in only one direction, showing near-zero current in reverse bias. 并非所有元件都遵循欧姆定律。白炽灯的I-V曲线弯曲，因为加热后电阻增加。半导体二极管单向导通，反向偏置时电流几乎为零。

Ohmic Conductor

Straight line through origin. V proportional to I. 直线过原点。

Filament Lamp

Curve flattening at high I. Resistance increases with temperature. 曲线在高电流时变平。

Diode

Almost zero current for negative V. Knee voltage for forward bias (~0.6V for Si). 反向几乎无电流。

3. Resistance, Resistivity and Conductivity

Resistance depends on both the material and geometry of a conductor. The formula R = ρL / A ties them together: ρ (rho) is resistivity, an intrinsic material property measured in Ω·m. A longer wire has higher resistance; a thicker wire has lower resistance. Resistivity decreases with temperature for semiconductors (negative temperature coefficient) but increases for metals (positive coefficient). 电阻取决于材料的本身属性和几何形状。公式R=ρL/A将它们联系在一起：ρ是电阻率，是材料的固有属性，单位为Ω·m。更长的导线电阻更大，更粗的导线电阻更小。

Worked Example: A copper wire of length 2.0 m and diameter 0.50 mm has resistivity 1.7 × 10-8 Ω·m. Find its resistance.
Step 1: Cross-sectional area A = πr² = π × (0.25 × 10-3)² = 1.96 × 10-7 m²
Step 2: R = ρL / A = (1.7 × 10-8 × 2.0) / (1.96 × 10-7) = 0.17 Ω
Answer: 0.17 Ω. This typical copper wire resistance is very low, which is why copper is used for household wiring. 这就是为什么铜被用于家庭电路。

4. Series and Parallel Circuits: Kirchhoff's Laws

Kirchhoff's First Law (Current Law): The total current entering a junction equals the total current leaving it. This is conservation of charge: charge cannot be created or destroyed at a junction. In a series circuit, the same current flows through all components. In parallel, the current splits across branches. 基尔霍夫第一定律：进入节点的总电流等于离开的总电流。这是电荷守恒的体现。串联电路中各处电流相同，并联电路中电流分支。

Kirchhoff's Second Law (Voltage Law): The sum of the EMFs in any closed loop equals the sum of the p.d.'s across the components. In series, the supply voltage equals the sum of individual p.d.'s. In parallel, each branch receives the full supply voltage. 基尔霍夫第二定律：任意闭合回路中，电动势之和等于电势差之和。串联电路中总电压等于各分电压之和，并联各支路电压相等。

Worked Example: A 12V battery is connected to two resistors in series: R1 = 4Ω and R2 = 8Ω. Find the current and the p.d. across each resistor.
Step 1: Total resistance R_total = 4 + 8 = 12 Ω
Step 2: Current I = V / R_total = 12 / 12 = 1.0 A
Step 3: V1 = I × R1 = 1.0 × 4 = 4.0 V; V2 = I × R2 = 1.0 × 8 = 8.0 V
Check: 4.0 + 8.0 = 12.0 V. The larger resistor takes more voltage. This is the principle behind potential dividers. 电阻大的分得更多电压，这就是分压器的原理。

5. Potential Dividers and Sensor Circuits

A potential divider is one of the most practical circuit arrangements in the Edexcel syllabus. It uses two or more resistors in series to produce a fraction of the input voltage. The output voltage formula is: Vout = Vin × R2 / (R1 + R2). By replacing one resistor with a sensor (thermistor or LDR), the circuit becomes a sensing device. 分压器是Edexcel考纲中最实用的电路配置之一。输出电压公式为Vout=Vin×R2/(R1+R2)。用一个传感器替换其中一个电阻，电路就变成了感应装置。

Thermistor circuit: An NTC thermistor's resistance drops as temperature rises. Place it as R1 in a potential divider: when temperature increases, Vout increases (since R1 drops, R2 gets a larger share). LDR circuit: An LDR's resistance drops as light intensity increases. The same logic applies: as light increases, LDR resistance drops, changing Vout. 热敏电阻电路中温度升高导致NTC电阻下降，输出电压变化。光敏电阻同理。

6. EMF, Internal Resistance and Terminal PD

Every real power source has internal resistance (r). The EMF (ε) is the total energy supplied per unit charge, while the terminal p.d. is what actually appears across the battery terminals when current flows: V = ε - Ir. The "lost volts" Ir are the energy dissipated inside the battery itself as heat. 每个真实电源都有内阻r。EMF是每单位电荷提供的总能量，而端电压是实际测量到的电压：V=ε-Ir。"损失电压"Ir在电池内部以热能消散。

Worked Example: A battery of EMF 6.0V and internal resistance 0.50Ω is connected to an external resistor of 2.5Ω. Find the terminal p.d. and the power delivered to the load.
Step 1: Total resistance = r + R = 0.50 + 2.5 = 3.0 Ω
Step 2: Current I = ε / R_total = 6.0 / 3.0 = 2.0 A
Step 3: Terminal p.d. V = ε - Ir = 6.0 - (2.0 × 0.50) = 5.0 V
Step 4: Power to load P = I²R = 2.0² × 2.5 = 10 W
Note: the internal resistance dissipates P_r = I²r = 2.0² × 0.50 = 2.0 W as waste heat. 内阻消耗了2W功率。

7. Electrical Power, Energy and Efficiency

Power in an electrical circuit can be expressed in three equivalent forms: P = IV = I²R = V²/R. Choose the most convenient one based on what is known. Energy transferred is E = Pt, often measured in kilowatt-hours (kWh) for practical applications. One kWh = 3.6 × 106 J. 电功率有三种等价形式：P=IV=I²R=V²/R。根据已知条件选择最方便的一种。能量转换E=Pt，实际应用中常用千瓦时计算。

Efficiency of an electrical device is the ratio of useful power output to total power input: efficiency = Puseful / Ptotal × 100%. For a motor lifting a mass, the useful power is the mechanical work done per second against gravity. The total power includes heat losses in the coils. 效率=有用功率/总功率×100%。对于一个提升重物的电机，有用功率是克服重力的机械功，总功率包括线圈中的热损耗。

8. Alternating Current (AC) Basics

Edexcel introduces AC at A-Level with the concept of rms (root mean square) values. For a sinusoidal AC supply, Vrms = V0 / √2 and Irms = I0 / √2, where V0 and I0 are peak values. The UK mains supply is 230V rms at 50 Hz, which means the peak voltage is actually 230 × √2 ≈ 325V. A 230V UK mains bulb behaves, on average, like it is connected to 230V DC in terms of power output. Edexcel A-Level引入交流电，重点是rms值。正弦交流电中Vrms=V0/√2。英国市电230V rms，峰值约325V。

9. Edexcel Exam Technique and Top 5 Mistakes

Edexcel Paper 1 electricity questions reward structured working. Always write the formula, substitute values with units, calculate, and state the answer with correct units and significant figures. For multi-step circuit problems, draw a simplified equivalent circuit first. Edexcel Paper 1 电学题目奖励结构化解题。总是先写公式，代入数值带单位，计算，然后给出带单位和有效数字的答案。

Top 5 Edexcel Electricity Mistakes 五大常见错误

1. Forgetting internal resistance when calculating current: use I = ε / (R + r), not I = V / R. 忘记内阻，计算电流时分母漏掉r。

2. Confusing series and parallel formulas: for series, resistances add; for parallel, use 1/R = 1/R1 + 1/R2. 混淆串并联公式。

3. Mixing up power formulas: P = I²R is best for series (same I), P = V²/R is best for parallel (same V). 功率公式用错：串联用P=I²R，并联用P=V²/R。

4. Misidentifying ammeter and voltmeter connections: ammeters in SERIES, voltmeters in PARALLEL. 电流表串联接入，电压表并联接入。

5. Ignoring significant figures: Edexcel expects 2 or 3 sf matching the given data precision. 忽略有效数字规则。

Key Bilingual Terms 关键双语术语

Current 电流 | Potential Difference 电势差 | Resistance 电阻 | Resistivity 电阻率 | Ohm's Law 欧姆定律 | Ohmic Conductor 欧姆导体 | Filament Lamp 白炽灯 | Diode 二极管 | Electromotive Force 电动势 | Internal Resistance 内阻 | Terminal PD 端电压 | Series Circuit 串联电路 | Parallel Circuit 并联电路 | Kirchhoff's First Law 基尔霍夫第一定律 | Kirchhoff's Second Law 基尔霍夫第二定律 | Potential Divider 分压器 | Thermistor 热敏电阻 | LDR 光敏电阻 | Power 功率 | Efficiency 效率 | Alternating Current 交流电 | rms Value 均方根值 | Peak Voltage 峰值电压 | Semiconductor 半导体

Quick Revision Checklist 快速复习清单

1. Define current and p.d., state units. 定义电流和电势差。
2. Sketch I-V graphs for ohmic conductor, filament lamp, and diode. 画出三种元件的I-V图。
3. Derive R = ρL/A and explain each term. 推导电阻率公式并解释各项。
4. State and apply Kirchhoff's two laws. 陈述并应用基尔霍夫两条定律。
5. Derive Vout formula for a potential divider. 推导分压器输出电压公式。
6. Describe the EMF and internal resistance experiment. 描述EMF和内阻测定实验。
7. Relate P = IV, I²R, V²/R and know when to use each. 掌握三种功率形式的使用场景。
8. Calculate efficiency of an electrical device. 计算电器效率。
9. Convert between peak and rms values. 在峰值和rms值之间转换。
10. Practice at least 3 Edexcel past-paper multi-step circuit problems. 练习至少3道历年真题。

🛍️ 微信小店好物推荐

fx-991CN X 中文版计算器-老王推荐

¥168.00 🛒 微信小店购买

直击高考专项突破 高中物理+高中数学二级公式快解

¥59.80 🛒 微信小店购买

🎓 Need one-on-one tutoring? 需要一对一辅导?

📱 16621398022 同微信

Follow tutorhao on WeChat for more learning resources 关注公众号获取更多学习资源

更多咨询请联系16621398022（同微信）