📚 GCSE WJEC Physics: Circuit Analysis Exam Focus | GCSE WJEC 物理：电路分析考点精讲
Mastering circuit analysis is a cornerstone of the WJEC GCSE Physics specification. This topic links charge, current, voltage and resistance into a unified framework, leading to practical applications such as potential dividers, sensor circuits and domestic electricity safety. A clear understanding of these principles will not only help you solve calculation problems but also allow you to explain how real electrical systems behave, from simple torch circuits to the circuits that protect your home.
掌握电路分析是 WJEC GCSE 物理考试的核心板块。这部分内容将电荷、电流、电压和电阻统一在一个框架中，并延伸到分压器、传感器电路和家庭用电安全等实际应用。透彻理解这些原理不仅能帮助你解决计算题，还能让你解释从简单手电筒电路到家庭保护电路的各类真实电学系统是如何工作的。
1. Charge and Current | 电荷与电流
Electric current is the rate of flow of electric charge. In a metal conductor, the charge carriers are free electrons that drift through the lattice of positive ions. Charge is measured in coulombs (C) and current in amperes (A). One ampere is defined as one coulomb of charge passing a point per second.
电流是电荷流动的速率。在金属导体中，电荷载体是自由电子，它们在正离子晶格中漂移。电荷的单位是库仑 (C)，电流的单位是安培 (A)。一安培定义为每秒有一库仑的电荷通过某一点。
I = Q ÷ t or Q = I x t
where I is current (A), Q is charge (C) and t is time (s).
其中 I 是电流 (A)，Q 是电荷 (C)，t 是时间 (s)。
Conventional current flows from the positive to the negative terminal of a cell, opposite to the direction of electron flow. In circuit analysis we always use conventional current direction.
传统电流方向是从电池的正极流向负极，与电子流动的方向相反。在电路分析中我们始终使用传统电流方向。
2. Potential Difference and EMF | 电位差与电动势
Potential difference (p.d.) is the energy transferred per unit charge between two points in a circuit. Electromotive force (emf) is the total energy supplied per unit charge by a source such as a cell or battery. Both are measured in volts (V), where 1 V = 1 J/C.
电位差 (p.d.) 是电路中两点之间单位电荷所转移的能量。电动势 (emf) 是电源（如电池）向单位电荷提供的总能量。两者的单位都是伏特 (V)，1 V = 1 J/C。
V = W ÷ Q
Here V is the p.d. (V), W is the energy transferred (J) and Q is the charge (C). A voltmeter is always connected in parallel across the component.
这里 V 是电位差 (V)，W 是转移的能量 (J)，Q 是电荷 (C)。电压表总是并联在元件两端。
3. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance is the opposition to current. It is defined as the ratio of p.d. across a conductor to the current through it. The unit of resistance is the ohm (Ω).
电阻是对电流的阻碍作用。它被定义为导体两端的电位差与通过导体的电流之比。电阻的单位是欧姆 (Ω)。
R = V ÷ I
Ohm’s law states that, for an ohmic conductor at constant temperature, the current is directly proportional to the p.d. across it. The relationship V = I x R is used throughout circuit calculations.
欧姆定律指出，对于温度恒定的欧姆导体，电流与加在它两端的电位差成正比。关系式 V = I x R 在整个电路计算中都会用到。
A fixed metal resistor at constant temperature follows Ohm’s law exactly, giving a straight‑line I–V graph through the origin. The gradient of the I–V graph represents 1/R.
在恒定温度下，定值金属电阻严格遵循欧姆定律，其 I–V 图像是通过原点的直线。I–V 图像的斜率代表 1/R。
4. Factors Affecting Resistance | 影响电阻的因素
The resistance of a wire depends on its length, cross‑sectional area and the material from which it is made. Resistance is directly proportional to length: a longer wire means electrons must travel further, causing more collisions. Resistance is inversely proportional to cross‑sectional area: a thicker wire offers more pathways and thus lower resistance.
导线的电阻取决于它的长度、横截面积和材料。电阻与长度成正比：导线越长，电子需要运动的路程越长，碰撞越多。电阻与横截面积成反比：较粗的导线提供更多通路，因此电阻更低。
Resistivity is a material property. Copper has a low resistivity and is widely used for connections, while nichrome has a higher resistivity and is used in heating elements. For most metallic conductors, resistance increases with temperature because the lattice ions vibrate more, making collisions with electrons more frequent.
电阻率是材料属性。铜的电阻率很低，广泛用于连接线；镍铬合金的电阻率较高，用于加热元件。对于大多数金属导体，电阻随温度升高而增大，因为晶格离子振动更剧烈，电子与之碰撞更频繁。
5. I–V Characteristics of Components | 元件的电流‑电压特性
The shape of an I–V graph reveals how a component behaves in a circuit.
I–V 图形的形状揭示了元件在电路中的行为。
Fixed resistor: At constant temperature the I–V graph is a straight line through the origin, confirming Ohm’s law. The resistance is constant and equals the inverse of the gradient.
固定电阻：在温度恒定下 I–V 图是通过原点的直线，验证了欧姆定律。电阻恒定且等于斜率的倒数。
Filament lamp: As current increases, the filament heats up and its resistance rises. The I–V graph is a curve that bends towards the voltage axis, showing a decreasing gradient. The lamp is non‑ohmic because the temperature change alters resistance.
灯丝灯泡：随着电流增大，灯丝变热，电阻升高。I–V 图是一条向电压轴弯曲的曲线，斜率减小。灯丝灯泡是非欧姆元件，因为温度变化改变了电阻。
Diode: A diode only allows current to flow in one direction. In the forward direction, a silicon diode requires about 0.7 V to start conducting, after which the current rises steeply. In the reverse direction the current is practically zero. The I–V graph is flat along the horizontal axis until the threshold voltage, then shoots upward.
二极管：二极管只允许电流沿一个方向流动。在正向，硅二极管需要约 0.7 V 才开始导通，之后电流急剧上升。在反向，电流几乎为零。I–V 图在达到阈值电压前沿水平轴平坦，然后陡然上升。
6. Series Circuits | 串联电路
In a series circuit components are connected end‑to‑end in a single loop. Key rules must be memorised:
在串联电路中，元件首尾相连形成单一回路。以下重要规则必须记住：
| Property | Series Behaviour |
|---|---|
| Current | The current is the same at all points: I = I₁ = I₂ |
| Potential difference | The supply p.d. is shared: V = V₁ + V₂ |
| Total resistance | Rₜ = R₁ + R₂ + … |
These facts follow from charge conservation and energy conservation. The current is the same because charge does not build up or leak out; voltage divides because energy is transferred in each resistance.
这些结论源于电荷守恒和能量守恒。电流处处相等是因为电荷不会堆积或泄漏；电压被分配是因为每一段电阻都转移了能量。
7. Parallel Circuits | 并联电路
In a parallel circuit components are connected on separate branches. The following rules apply:
在并联电路中，元件连接在不同的支路上。适用以下规则：
| Property | Parallel Behaviour |
|---|---|
| Current | Total current = sum of branch currents: I = I₁ + I₂ |
| Potential difference | The p.d. across each branch is the same: V = V₁ = V₂ |
| Total resistance | 1/Rₜ = 1/R₁ + 1/R₂; the combined resistance is less than the smallest individual resistance |
Adding more resistors in parallel reduces the total resistance because extra pathways are provided for current. The mains supply in homes is a parallel circuit so that each appliance receives the full 230 V.
在并联电路中增加更多电阻会降低总电阻，因为为电流提供了更多的通路。家庭中的市电供电是并联电路，这样每个用电器都能获得完整的 230 V 电压。
8. Potential Dividers | 分压器
A potential divider consists of two or more resistors in series, across a supply voltage. It is used to obtain a desired fraction of the input voltage.
分压器由两个或多个电阻串联组成，跨接在电源电压上，用于获得输入电压的某一预定比例。
Vₒᵤₜ = Vᵢₙ x (R₂ ÷ (R₁ + R₂))
Here R₂ is the resistor across which the output voltage is taken, and R₁ is the other resistor. By replacing one fixed resistor with a variable resistor, the output voltage can be adjusted continuously.
这里 R₂ 是提取输出电压所跨接的电阻，R₁ 是另一个电阻。若将其中一个固定电阻替换为可变电阻，就能连续调节输出电压。
A simple potential divider can be constructed using a single rheostat or potentiometer. The sliding contact divides the track into two variable resistances, giving an output that varies from 0 V up to the supply voltage.
简单的分压器可以用单个变阻器或电位器搭建。滑动触点将轨道分成两个可变电阻，输出电压从 0 V 到电源电压之间变化。
9. Sensing Circuits: LDRs and Thermistors | 传感电路：光敏电阻与热敏电阻
Light‑dependent resistors (LDRs) and thermistors are variable resistors whose resistance changes with environmental conditions. In darkness an LDR has a very high resistance, often several megohms; as light intensity increases, its resistance drops to a few hundred ohms. A negative temperature coefficient (NTC) thermistor behaves similarly with heat: at low temperatures its resistance is high, and when heated its resistance falls significantly.
光敏电阻 (LDR) 和热敏电阻是电阻值随环境条件变化的可变电阻。在黑暗中 LDR 的电阻很高，常达几兆欧；随着光照增强，其电阻下降到几百欧。负温度系数 (NTC) 热敏电阻对热量的反应类似：低温时电阻高，受热时电阻显著下降。
These components are typically placed in potential‑divider arrangements. For example, an LDR in the R₂ position of a potential divider can be connected to a transistor switch to turn on a lamp automatically when it gets dark. As light fades, the LDR resistance increases, so Vₒᵤₜ rises and activates the switching circuit. Thermistors are used in fire alarms, thermostats and incubator temperature controls.
这些元件通常被放置在分压器结构中。例如，将 LDR 放在分压器的 R₂ 位置，并连接到晶体管开关，就能在天黑时自动点亮电灯。随着光线变暗，LDR 电阻增大，Vₒᵤₜ 升高，触发开关电路。热敏电阻常用于火灾报警器、恒温器和孵育器温度控制中。
10. Electrical Power and Energy | 电功率与电能
Power is the rate of energy transfer. In electric circuits, power can be calculated using the current and the p.d. across a component.
功率是能量转移的速率。在电路中，功率可以利用流过元件的电流和元件两端的电位差来计算。
P = I x V
where P is power in watts (W), I is current (A) and V is p.d. (V). By combining with V = I x R we derive two alternative forms:
其中 P 是功率 (W)，I 是电流 (A)，V 是电位差 (V)。结合 V = I x R 可以推出两个替代公式：
P = I² x R and P = V² ÷ R
Electrical energy transferred is given by E = P x t. The joule is a very small unit for domestic consumption, so energy is often measured in kilowatt‑hours (kWh). 1 kWh is the energy used by a 1 kW appliance running for one hour (1 kWh = 3.6 x 10⁶ J). Electricity bills are calculated in kilowatt‑hours.
电能转移量为 E = P x t。焦耳对于家庭用电来说是非常小的单位，因此电能常用千瓦时 (kWh) 计量。1 kWh 是 1 kW 的用电器工作一小时所消耗的能量 (1 kWh = 3.6 x 10⁶ J)。电费按千瓦时计算。
11. Electrical Safety in Circuits | 电路安全
Circuit safety features protect both equipment and users from overheating, short circuits and electric shock. A fuse is a thin piece of wire that melts and breaks the circuit if the current exceeds its rated value. The correct fuse for an appliance is chosen based on the normal operating current. For example, a 700 W heater running on 230 V draws about 3 A, so a 5 A or 3 A fuse is appropriate.
电路安全装置可以保护设备和用户免受过热、短路和触电的危害。保险丝是一段细金属丝，当电流超过其额定值时它就会熔断并切断电路。选用保险丝时应依据用电器的正常工作电流。例如，一台 700 W 的取暖器接在 230 V 上电流约为 3 A，因此选用 3 A 或 5 A 的保险丝是合适的。
Earthing is used for appliances with metal casings. The earth wire connects the casing to the ground, providing a low‑resistance path for current should a live wire touch the casing. This large current blows the fuse, disconnecting the appliance and preventing electric shock. Double‑insulated appliances (marked with a square‑within‑a‑square symbol) have no earth wire because their outer case is non‑conductive and the internal wiring is protected by an extra layer of insulation.
接地线用于带有金属外壳的电器。接地线将外壳与大地相连，如果火线碰到外壳，它会为电流提供一条低电阻通路。这个瞬间大电流会烧断保险丝，断开电路，防止触电。双重绝缘电器（标有回字形符号）没有接地线，因为它们的外壳不导电，而且内部线路有额外绝缘保护。
Modern domestic circuits are also protected by residual current devices (RCDs) which detect an imbalance between live and neutral currents and disconnect the supply within milliseconds, offering extra personal protection.
现代家庭电路还通过剩余电流装置 (RCD) 来进行保护，它能检测火线与零线之间的电流不平衡，并在毫秒内切断电源，提供额外的人身保护。
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