Circuit Analysis | 电路分析考点精讲

📚 Circuit Analysis | 电路分析考点精讲

In GCSE OCR Physics, circuit analysis brings together the foundational ideas of current, voltage, resistance, power and energy transfer. Mastering the rules for series and parallel circuits, applying Ohm’s law, and confidently using potential dividers with sensors will give you the toolkit to solve a wide range of exam problems.

在 GCSE OCR 物理中，电路分析融合了电流、电压、电阻、功率和能量传递等基础概念。掌握串联与并联电路的规律，熟练应用欧姆定律，并能在传感器场景下灵活使用分压器，你就拥有了解决大多数考试难题的工具箱。

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1. Current and Charge | 电流与电荷

Electric current is the rate of flow of charge. Charge is measured in coulombs (C) and current in amperes (A). One ampere means one coulomb of charge passes a point every second. In a metal wire, the moving charges are free electrons, which flow from negative to positive, but conventional current is defined as the direction positive charges would move, i.e. from the positive terminal to the negative terminal around a circuit.

电流是电荷流动的速率。电荷以库仑 (C) 为单位，电流以安培 (A) 为单位。1 安培表示每秒有 1 库仑的电荷通过某一点。在金属导线中，运动的电荷是自由电子，它们从负极流向正极，但常规电流的方向被定义为正电荷流动的方向，即从电源正极经过电路流向负极。

I = Q ÷ t

where I is current (A), Q is charge (C) and t is time (s). This equation is central to calculating current in simple circuits and appears regularly in both multiple‑choice and calculation questions.

其中 I 为电流 (A)，Q 为电荷量 (C)，t 为时间 (s)。该公式是计算简单电路中电流的核心方程，经常出现在选择题和计算题中。

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2. Potential Difference and Electromotive Force | 电势差与电动势

Potential difference (p.d.) is the work done per unit charge when charge moves between two points. It is measured in volts (V), where 1 V = 1 J / C. The electromotive force (e.m.f.) of a source is the total energy supplied per unit charge that passes through the source. Although e.m.f. is also measured in volts, it describes the energy transferred to the circuit, while p.d. describes energy transferred by components.

电势差 (p.d.) 是单位电荷在两点之间移动时所做的功，单位为伏特 (V)，1 V = 1 J / C。电源的电动势 (e.m.f.) 是每单位电荷通过电源时所提供的总能量。尽管电动势也以伏特为单位，但它描述的是转移到电路中的能量，而电势差描述的是元件消耗或转换的能量。

V = W ÷ Q

Remember: for a cell with negligible internal resistance, the terminal p.d. equals its e.m.f. In a closed loop, the sum of all p.d.s equals the sum of the e.m.f.s — this is Kirchhoff’s voltage law, often used implicitly in OCR problems.

记住：对于内阻可忽略的电池，端电压等于其电动势。在一个闭合回路中，所有电势差的代数和等于所有电动势的代数和——这就是基尔霍夫电压定律，常隐含在 OCR 考题中。

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3. Resistance and Ohm’s Law | 电阻与欧姆定律

Resistance is a measure of how much a component opposes the flow of current. The unit of resistance is the ohm (Ω). Ohm’s law states that, for a metallic conductor kept at a constant temperature, the current through it is directly proportional to the potential difference across it, giving the relationship V = I × R.

电阻是衡量元件对电流阻碍程度的物理量，单位为欧姆 (Ω)。欧姆定律指出，对于温度保持恒定的金属导体，通过它的电流与其两端的电势差成正比，得到关系式 V = I × R。

Any component that obeys Ohm’s law is called an ohmic conductor; its I–V graph is a straight line passing through the origin. A filament lamp does not obey Ohm’s law because its resistance increases as it heats up — the I–V graph curves. The equation R = V ÷ I defines resistance for any component, even if it is non‑ohmic.

任何满足欧姆定律的元件都称为欧姆导体，其 I–V 图像是一条通过原点的直线。白炽灯灯丝不遵从欧姆定律，因为其电阻随温度升高而增大，I–V 图像呈曲线状。公式 R = V ÷ I 定义了任何元件（即使是非欧姆导体）的电阻。

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4. Series Circuits | 串联电路

In a series circuit, components are joined one after another, so there is only one loop for current. This leads to three key rules:

• The current is the same at all points: I₁ = I₂ = I₃ …
• The total resistance is the sum of individual resistances: R_total = R₁ + R₂ + …
• The supply voltage is shared between components: V_total = V₁ + V₂ + …

在串联电路中，元件逐一连接，只有一条电流通路。这产生了三条重要规律：

• 各处电流都相等：I₁ = I₂ = I₃ …
• 总电阻等于各个电阻之和：R_total = R₁ + R₂ + …
• 电源电压在元件间分配：V_total = V₁ + V₂ + …

Adding more resistors in series increases the total resistance and reduces the current for a fixed supply voltage. Energy is conserved because the total voltage supplied equals the sum of the p.d.s across all components.

在串联电路中增加更多电阻会增大总电阻，若电源电压不变则电流减小。能量是守恒的，因为提供的总电压等于各元件两端电势差之和。

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5. Parallel Circuits | 并联电路

In a parallel circuit, each component is connected on its own separate branch between the same two points. The rules for parallel circuits are:

• The p.d. across each branch is the same as the supply voltage: V₁ = V₂ = V_supply
• The total current from the source is the sum of the branch currents: I_total = I₁ + I₂ + …
• The total resistance is lower than the smallest branch resistance and is found using: 1/R_total = 1/R₁ + 1/R₂ + …

在并联电路中，每个元件连接在相同的两点之间形成独立支路。并联电路规律如下：

• 各支路两端电势差等于电源电压：V₁ = V₂ = V_supply
• 电源总电流等于各支路电流之和：I_total = I₁ + I₂ + …
• 总电阻小于任一支路电阻，计算公式为：1/R_total = 1/R₁ + 1/R₂ + …

Adding extra branches in parallel provides additional paths for current and therefore decreases the total resistance. This is why connecting too many appliances in parallel can draw a dangerously large current and blow a fuse.

并联增加支路会提供更多电流路径，因此总电阻减小。这也是为什么并联接入过多电器会导致电流过大，烧断保险丝。

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6. Power and Energy in Circuits | 电路中的功率与能量

Power is the rate at which energy is transferred. In an electrical component, power can be calculated using three equivalent forms derived from P = VI and V = IR:

P = V × I = I² × R = V² ÷ R

Electrical energy transferred is given by E = P × t, or equivalently E = V × I × t. The standard unit for energy is the joule (J). In power grid contexts, energy may be quoted in kilowatt‑hours (kWh).

功率是能量传递的速率。在电器元件中，功率可由 P = VI 及 V = IR 导出三种等价形式：P = V × I = I² × R = V² ÷ R。

电能传递量由 E = P × t 或 E = V × I × t 给出。能量的标准单位是焦耳 (J)。在电网场景中，能量可能以千瓦时 (kWh) 表示。

These relationships allow you to compare the energy efficiency of different components, or to explain why a high‑resistance device on a fixed voltage source dissipates less power (using P = V²/R).

利用这些关系，你可以比较不同元件的能量效率，或解释定电压下高电阻器件为何消耗功率更小（使用 P = V²/R）。

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7. Potential Dividers | 分压器

A potential divider is a simple circuit that uses two resistors in series to produce a fraction of the input voltage. It is widely employed as a control or sensing circuit. The output voltage is taken across one of the resistors, usually R₂:

V_out = V_in × (R₂ ÷ (R₁ + R₂))

If R₂ is replaced by a variable resistor or a sensor such as an LDR or thermistor, the output voltage changes in response to environmental conditions. The fixed resistor R₁ is often chosen so that the divider is most sensitive near a particular threshold.

分压器是一个简单的电路，利用两个串联电阻获得输入电压的一部分。它广泛用作控制或传感电路。输出电压通常取自 R₂ 两端：V_out = V_in × (R₂ ÷ (R₁ + R₂))。

如果 R₂ 替换为可变电阻或光敏/热敏传感器，输出电压就会随环境条件而变。固定电阻 R₁ 常被选取为使分压器在特定阈值附近最灵敏的值。

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8. Sensors: LDR and Thermistor | 传感器：光敏电阻与热敏电阻

An LDR (light‑dependent resistor) has a resistance that decreases as light intensity increases. In the dark, its resistance can be several megaohms; in bright light it may drop to a few hundred ohms. A thermistor is a temperature‑dependent resistor; most common are NTC (negative temperature coefficient) thermistors whose resistance falls as temperature rises.

光敏电阻 (LDR) 的阻值随光照强度增大而减小。黑暗中其电阻可能达数兆欧，强光下可能降至几百欧。热敏电阻是一种温度敏感的电阻；常见的是负温度系数 (NTC) 热敏电阻，温度升高时阻值降低。

When used in a potential divider, an LDR can trigger a light‑sensing switch; a thermistor can form part of a temperature alarm or thermostat circuit. The output voltage rises when the sensor’s resistance increases, and OCR questions frequently ask you to describe and explain such behaviour.

当它们用在分压器中时，LDR 可触发感光开关；热敏电阻可构成温度报警或恒温电路的一部分。传感器阻值增大时输出电压上升，OCR 考题经常要求你描述并解释这一行为。

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9. Circuit Symbols and Diagrams | 电路符号与图

Being able to read and draw standard circuit symbols quickly is essential for interpreting exam diagrams. Below is a quick reference for components that regularly appear.

能够快速识读和绘制标准电路符号对理解考试图表至关重要。下面是常考元件的速查表。

Component | 元件	Symbol description | 符号描述
Cell | 单节电池	Long line (+), short line (–), labelled
Battery | 电池组	Two or more cells in series
Fixed resistor | 定值电阻	Rectangle, often labelled R
Variable resistor | 可变电阻	Rectangle with arrow crossing diagonally
Lamp | 灯泡	Circle with a cross inside
Ammeter | 电流表	Circle with A
Voltmeter | 电压表	Circle with V
Diode | 二极管	Triangle touching vertical line, arrow shows forward direction
LED | 发光二极管	Diode symbol with two outward arrows
LDR | 光敏电阻	Resistor symbol with circle around and two arrows pointing inwards
Thermistor | 热敏电阻	Resistor symbol with a slanted line through it, often with annotation θ
Fuse | 保险丝	Rectangle with wire passing through, often marked with current rating

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10. Measuring Current and Voltage | 测量电流与电压

An ammeter measures current and must be placed in series so that all the current flows through it. An ideal ammeter has negligible resistance. A voltmeter measures potential difference and is connected in parallel with the component being investigated; it should have a very high resistance so it draws minimal current.

电流表测量电流，必须串联在电路中，使所有电流都通过它。理想电流表的内阻可忽略。电压表测量电势差，并联在被测元件两端；它应当具有很高的电阻，以汲取极小的电流。

When drawing circuits or planning experiments, remember that reversing this arrangement will give incorrect readings or may damage the meters. The OCR practical endorsement tasks often require you to justify where meters are placed.

绘制电路或规划实验时，记得接反会导致读数错误甚至损坏仪表。OCR 实验评估任务经常要求你论证电表的接入位置。

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11. Safety and Fuses | 安全与保险丝

A fuse is a safety device containing a thin wire that melts if the current exceeds a rated value, opening the circuit. Fuses are rated in amps (e.g. 3 A, 5 A, 13 A) and should be chosen just above the normal operating current of the appliance. A circuit breaker performs a similar function but can be reset.

保险丝是一种安全装置，内含细金属丝，当电流超过额定值时熔断，断开电路。保险丝以安培为额定值（如 3 A、5 A、13 A），应选在略高于电器正常工作电流的规格。断路器功能类似，但可复位。

Excessive current can be caused by short circuits or overloading. Earth wires and double insulation provide additional protection, but understanding current ratings and fusing helps you evaluate why circuits are designed the way they are.

过电流可由短路或过载引发。地线和双重绝缘可提供额外保护，但理解额定电流和熔断原理能帮助你评价电路设计的原因。

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12. Worked Example: Series‑Parallel Combination | 实例：串并联组合电路

Consider a 12 V battery connected to a 10 Ω resistor in series with a parallel pair of 20 Ω and 30 Ω resistors. Calculate the total current drawn from the battery.

考虑一个 12 V 电池，连接一个 10 Ω 电阻，然后与一个 20 Ω 和一个 30 Ω 电阻的并联组合串联。计算电池提供的总电流。

Step 1: Find the equivalent resistance of the parallel pair. Using 1/R_par = 1/20 + 1/30 gives 1/R_par = 3/60 + 2/60 = 5/60, so R_par = 12 Ω.

第一步：计算并联部分的等效电阻。1/R_par = 1/20 + 1/30 = 3/60 + 2/60 = 5/60，因此 R_par = 12 Ω。

Step 2: Total circuit resistance R_total = 10 Ω + 12 Ω = 22 Ω.

第二步：电路总电阻 R_total = 10 Ω + 12 Ω = 22 Ω。

Step 3: Apply Ohm’s law to the whole circuit: I = V / R_total = 12 V / 22 Ω ≈ 0.545 A.

第三步：对整个电路应用欧姆定律：I = V / R_total = 12 V ÷ 22 Ω ≈ 0.545 A。

You could further calculate the p.d. across each section or the branch currents, demonstrating the systematic approach that GCSE OCR examiners expect.

你可以进一步计算各段电压或支路电流，这一系统步骤正是 GCSE OCR 考官期待的方法。

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Published by TutorHao | Physics Revision Series | aleveler.com

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