📚 Edexcel A-Level Physics Combined 203: Mechanics and Electric Circuits | Edexcel A-Level 物理综合203：力学与电路
This revision article combines two core Edexcel A-Level Physics topics: Mechanics (Topic 2) and Electric Circuits (Topic 3). You will review the essential definitions, equations and problem-solving strategies needed to tackle both short-answer and multi-step questions.
本篇复习文章综合了 Edexcel A-Level 物理两个核心主题：力学（主题2）和电路（主题3）。你将复习关键定义、方程与解题策略，以应对简答题和多步骤计算题。
1. Scalars, Vectors and SI Units | 标量、矢量与国际单位制
A scalar quantity has magnitude only, such as distance, speed, mass and energy. A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration and force.
标量只有大小，例如路程、速率、质量和能量。矢量既有大小又有方向，例如位移、速度、加速度和力。
The SI base units used in mechanics and electricity include the metre (m), kilogram (kg), second (s), ampere (A) and kelvin (K). You can check whether an equation is homogeneous by expressing each derived unit in base units.
力学和电学中使用的国际单位制基本单位包括米（m）、千克（kg）、秒（s）、安培（A）和开尔文（K）。你可以将每个导出单位写成基本单位，来检验一个方程是否量纲一致。
For example, the newton is expressed as kg m s⁻², and the volt is expressed as kg m² s⁻³ A⁻¹. Using base units helps to identify errors in a formula before numerical substitution.
例如，牛顿可表示为 kg m s⁻²，伏特可表示为 kg m² s⁻³ A⁻¹。使用基本单位有助于在代入数值前发现公式中的错误。
2. Kinematics: Motion with Constant Acceleration | 运动学：匀加速运动
For motion in a straight line with uniform acceleration, the four SUVAT equations link displacement s, initial velocity u, final velocity v, acceleration a and time t.
对于匀加速直线运动，四个运动学方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系起来。
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = ½ (u + v) t
When an object is in free fall near the Earth’s surface, the acceleration a is replaced by g = 9.81 m s⁻² acting downwards. Choose a positive direction and assign signs consistently.
当物体在地球表面附近自由下落时，加速度 a 用向下的 g = 9.81 m s⁻² 代替。选定正方向后，要一致地确定各量的正负号。
Projectile motion can be analysed by resolving into horizontal and vertical components. The horizontal velocity remains constant, while the vertical motion follows SUVAT with a = g.
抛体运动可以分解为水平分量和竖直分量进行分析。水平速度保持不变，而竖直运动遵循加速度为 g 的运动学方程。
3. Newton’s Laws and Momentum | 牛顿定律与动量
Newton’s first law states that an object remains at rest or in uniform motion unless acted on by a resultant force. Newton’s second law states that resultant force equals rate of change of momentum, which simplifies to F = ma for constant mass.
牛顿第一定律指出，除非受到合外力作用，物体将保持静止或匀速直线运动。牛顿第二定律指出，合外力等于动量的变化率，当质量恒定时简化为 F = ma。
Newton’s third law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These forces act on different objects and do not cancel out in a single free-body diagram.
牛顿第三定律指出，若物体 A 对物体 B 施加力，则物体 B 对物体 A 施加大小相等、方向相反的力。这两个力作用在不同物体上，不会在同一受力图中相互抵消。
Momentum p is defined as mass × velocity, so p = mv. The principle of conservation of momentum states that in a closed system with no external resultant force, total momentum before a collision or explosion equals total momentum after.
动量 p 定义为质量 × 速度，即 p = mv。动量守恒定律指出，在没有外合力的封闭系统中，碰撞或爆炸前的总动量等于碰撞或爆炸后的总动量。
Impulse is the change in momentum and equals force × time, giving the equation FΔt = Δp = mv − mu. The area under a force–time graph represents impulse.
冲量是动量的变化量，等于力 × 时间，方程写作 FΔt = Δp = mv − mu。力—时间图线下面积表示冲量。
4. Work, Energy and Power | 功、能量与功率
Work done W is the product of force and displacement in the direction of the force: W = Fd cos θ, where θ is the angle between force and displacement. Work is measured in joules (J).
功 W 是力与沿力方向位移的乘积：W = Fd cos θ，其中 θ 为力与位移之间的夹角。功的单位是焦耳（J）。
Kinetic energy is given by Eₖ = ½ mv², and gravitational potential energy by Eₚ = mgΔh. In ideal systems without friction or air resistance, total mechanical energy is conserved.
动能公式为 Eₖ = ½ mv²，重力势能公式为 Eₚ = mgΔh。在没有摩擦或空气阻力的理想系统中，总机械能守恒。
Power is the rate of doing work or transferring energy: P = W/t = Fv for constant velocity. Efficiency is useful output energy divided by total input energy, often expressed as a percentage.
功率是做功或传递能量的速率：P = W/t = Fv（速度恒定时）。效率为有用输出能量除以总输入能量，通常以百分比表示。
5. Electric Current and Charge | 电流与电荷
Electric current I is the rate of flow of charge: I = Q/t, where Q is charge in coulombs and t is time in seconds. Current is measured in amperes (A).
电流 I 是电荷流动的速率：I = Q/t，其中 Q 为电荷（库仑），t 为时间（秒）。电流的单位是安培（A）。
The elementary charge e = 1.60 × 10⁻¹⁹ C. The total charge transferred by a number n of electrons or protons is Q = ne, which can be used with I = Q/t.
元电荷 e = 1.60 × 10⁻¹⁹ C。n 个电子或质子所传递的总电荷为 Q = ne，可与 I = Q/t 一起使用。
In metals, current is carried by free electrons moving in the opposite direction to conventional current. The drift velocity v of electrons is linked by I = nAvq, where n is charge carrier density and A is cross-sectional area.
在金属中，电流由自由电子携带，其运动方向与常规电流方向相反。电子漂移速度 v 满足 I = nAvq，其中 n 为载流子密度，A 为横截面积。
6. Potential Difference, Resistance and Ohm’s Law | 电势差、电阻与欧姆定律
Potential difference V between two points is the energy transferred per unit charge: V = W/Q. It is measured in volts (V). The e.m.f. of a source is the energy supplied per unit charge, while terminal p.d. can be lower due to internal resistance.
两点之间的电势差 V 是每单位电荷所转移的能量：V = W/Q。其单位是伏特（V）。电源的电动势是每单位电荷所提供的能量，而端电压由于内阻可能较低。
Resistance R is defined as R = V/I and is measured in ohms (Ω). A component obeys Ohm’s law when current is directly proportional to potential difference at constant temperature.
电阻 R 定义为 R = V/I，单位是欧姆（Ω）。当温度恒定时，若电流与电势差成正比，则该元件服从欧姆定律。
The I–V characteristic of a fixed resistor at constant temperature is a straight line through the origin. A filament lamp curves because its resistance increases with temperature, and a diode only conducts in one direction.
恒温下固定电阻器的 I–V 特性是一条过原点的直线。白炽灯的曲线弯曲是因为电阻随温度升高而增大，二极管则只能单向导通。
7. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the same current flows through every component, while the total potential difference is shared. The total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + R₃.
在串联电路中，所有元件流过相同的电流，而总电压被各元件分配。总电阻等于各电阻之和：R总 = R₁ + R₂ + R₃。
In a parallel circuit, the potential difference across each branch is the same, while the total current is shared. The total resistance is found from 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃.
在并联电路中，各支路两端的电势差相同，而总电流被分摊。总电阻由 1/R总 = 1/R₁ + 1/R₂ + 1/R₃ 求得。
Series circuits are useful for sharing voltage, such as in potential dividers, while parallel circuits keep the same voltage across each branch and are used in household wiring.
串联电路可用于分配电压，例如分压器；并联电路各支路保持相同电压，常用于家庭布线。
8. Kirchhoff’s Laws and Circuit Analysis | 基尔霍夫定律与电路分析
Kirchhoff’s first law (current law) states that the sum of currents entering a junction equals the sum of currents leaving the junction. This is a consequence of conservation of charge.
基尔霍夫第一定律（电流定律）指出，流入节点的电流之和等于流出节点的电流之和。这是电荷守恒的结果。
Kirchhoff’s second law (voltage law) states that the sum of e.m.f.s around any closed loop equals the sum of potential differences across the components. This follows from conservation of energy.
基尔霍夫第二定律（电压定律）指出，沿任意闭合回路的电动势之和等于各元件上电势差之和。这是能量守恒的结果。
A real cell has internal resistance r, so terminal p.d. V = ε − Ir, where ε is the e.m.f. and I is the current. The lost volts are Ir within the cell.
真实电池具有内阻 r，因此端电压 V = ε − Ir，其中 ε 为电动势，I 为电流。损失电压为电池内部的 Ir。
- Use KCL to write equations for currents at junctions.
- Use KVL to write loop equations in the direction of current.
- Solve simultaneous equations to find unknown currents and p.d.s.
- 利用 KCL 在节点处写出电流方程。
- 沿电流方向利用 KVL 写出回路方程。
- 解联立方程求出未知电流和电势差。
9. Resistivity and Thermistors | 电阻率与热敏电阻
Resistivity ρ is a material property defined by R = ρL/A, where L is length and A is cross-sectional area. The unit of resistivity is Ω m.
电阻率 ρ 是材料的属性，定义为 R = ρL/A，其中 L 为长度，A 为横截面积。电阻率的单位是 Ω m。
Metals have low resistivity and their resistance increases with temperature because lattice vibrations scatter electrons more. Semiconductors often show the opposite behaviour.
金属的电阻率较低，其电阻随温度升高而增大，因为晶格振动对电子的散射增强。半导体则常表现出相反的行为。
A thermistor is a temperature-dependent resistor. For a negative temperature coefficient (NTC) thermistor, resistance decreases as temperature rises, making it useful in temperature sensors.
热敏电阻是一种随温度变化的电阻。对于负温度系数（NTC）热敏电阻，温度升高时电阻减小，这使它可用于温度传感器。
A light-dependent resistor (LDR) has resistance that decreases with increasing light intensity. Combining an LDR or thermistor with a fixed resistor forms a potential divider for sensing circuits.
光敏电阻（LDR）的电阻随光照强度增加而减小。将 LDR 或热敏电阻与固定电阻组合可构成用于传感电路的分压器。
10. Combining Mechanics and Circuits: Sensors and Applications | 力学与电路综合：传感器与应用
Many examination questions link mechanics to electric circuits through sensors. For example, a strain gauge changes resistance when stretched or compressed, allowing force or acceleration to be measured.
许多考题通过传感器将力学与电路联系起来。例如，应变片在拉伸或压缩时电阻发生变化，从而可以测量力或加速度。
A potential divider uses two resistors in series. The output voltage across one resistor is Vout = Vin × R₂ / (R₁ + R₂). Replacing R₂ with a sensor gives a voltage that varies with physical conditions.
分压器由两个串联电阻组成。其中一个电阻上的输出电压为 Vout = Vin × R₂ / (R₁ + R₂)。将 R₂ 换成传感器，可得到随物理条件变化的电压。
When analysing a sensor circuit, first identify how the sensor resistance changes, then apply the potential divider equation or Ohm’s law to determine the output p.d.
分析传感器电路时，首先判断传感器电阻如何变化，然后应用分压器公式或欧姆定律来确定输出电压。
A typical combined problem may give a mass on a spring, a strain gauge attached to the spring, and ask you to calculate the output voltage for a given acceleration or force. Start by using mechanics to find the force, then use circuit rules to find the electrical output.
典型的综合题可能给出弹簧上的质量块、贴在弹簧上的应变片，并要求计算给定加速度或力下的输出电压。首先用力学求出力，然后用电路规律求电学输出。
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