A-Level AQA Physics: Circuit Analysis | A-Level AQA 物理：电路分析考点精讲

📚 A-Level AQA Physics: Circuit Analysis | A-Level AQA 物理：电路分析考点精讲

Mastering circuit analysis is essential for A-Level AQA Physics. This revision guide covers every key concept — from Ohm’s law and Kirchhoff’s rules to potential dividers, the Wheatstone bridge and practical measurement techniques. Understanding how to combine resistors, analyse multi-loop circuits and use sensors will prepare you for both the written papers and required practicals.

掌握电路分析是 AQA 物理 A-Level 的核心能力。本篇精讲覆盖所有关键考点，包括欧姆定律、基尔霍夫定律、分压电路、惠斯通电桥以及实验测量技巧。透彻理解电阻组合、多回路分析和传感器应用，将帮你从容应对笔试与必做实验。

1. Current, Charge and Drift Velocity | 电流、电荷与漂移速度

Electric current I is defined as the rate of flow of charge. In a metal conductor, current arises from the directed motion of free electrons, and the fundamental relation is I = ΔQ / Δt, where ΔQ is the charge passing a point in time Δt. The direction of conventional current is taken as the flow of positive charge, opposite to the electron flow.

电流 I 被定义为电荷流动的速率。在金属导体中，电流源于自由电子的定向运动，基本关系式为 I = ΔQ / Δt，其中 ΔQ 是时间 Δt 内通过某点的电荷量。约定电流方向为正电荷流动方向，与电子流动方向相反。

When charge carriers move through a conductor, their average drift velocity v is given by I = n A v q, where n is the number density of charge carriers, A is the cross‑sectional area and q is the charge on each carrier. This relationship explains why a thin wire has a smaller current for the same drift velocity, because A is reduced.

当载流子穿过导体时，其平均漂移速度 v 满足 I = n A v q，其中 n 为载流子数密度，A 为横截面积，q 为每个载流子的电荷量。该关系说明在相同漂移速度下，细导线的电流较小，因为 A 较小。

2. Ohm’s Law and Resistance | 欧姆定律与电阻

Ohm’s law states that for an ohmic conductor at constant temperature, the potential difference V across it is directly proportional to the current I through it: V ∝ I. The constant of proportionality is the resistance R, so V = I R. Resistance is measured in ohms (Ω).

欧姆定律指出，对于温度恒定的欧姆导体，其两端的电势差 V 与通过它的电流 I 成正比：V ∝ I。比例常数为电阻 R，因此 V = I R。电阻的单位为欧姆 (Ω)。

Not all components obey Ohm’s law. A component that does is called an ohmic conductor; its I–V graph is a straight line through the origin. For a filament lamp, the resistance increases as the current rises because the metal filament heats up, causing more frequent collisions between electrons and ions. A diode has a very high resistance in one direction and a very low resistance in the other, producing a characteristic non‑linear I–V curve.

并非所有元件都遵守欧姆定律。遵守的称为欧姆导体，其 I–V 图为一条过原点的直线。对于灯丝灯泡，电阻随电流增大而升高，因为金属灯丝变热，电子与离子碰撞更加频繁。二极管在单个方向上电阻极高，在另一方向上电阻极低，形成非线性的特征 I–V 曲线。

3. I–V Characteristics of Circuit Components | 电路元件的 I–V 特性

The I–V characteristic of a fixed resistor is a straight line through the origin, confirming that resistance is constant. For a filament lamp, the graph shows a shallow curve at low currents and a steeper slope at higher currents, illustrating increasing resistance. A thermistor’s resistance decreases as temperature rises, so its I–V characteristic depends on the thermistor’s heating.

固定电阻的 I–V 特性为一条过原点的直线，验证了其电阻恒定。灯丝灯泡的曲线在低电流时较平缓，高电流时斜率增加，反映出电阻的增大。热敏电阻的电阻随温度升高而减小，因此其 I–V 特性与自身发热有关。

A diode only allows current to pass when the potential difference exceeds a small threshold (about 0.6 V for a silicon diode) in the forward direction. Below this threshold, practically no current flows; in reverse bias, only a negligible leakage current passes until breakdown occurs. This property makes diodes ideal for rectification.

二极管仅在正向偏压下，电势差超过一个小子阈值（硅管约 0.6 V）时才允许电流通过。低于该阈值时几乎无电流；反向偏压时，只有极小的漏电流，直至发生击穿。这一特性使二极管非常适合用于整流。

4. Resistors in Series and Parallel | 串联与并联电阻

For resistors connected in series, the total resistance R_total is the sum of the individual resistances: R_total = R₁ + R₂ + R₃ + …. The same current flows through each resistor, and the total p.d. is shared according to each resistance.

串联电阻的总电阻 R_total 等于各电阻之和：R_total = R₁ + R₂ + R₃ + …。通过每个电阻的电流相同，总电势差按各电阻比例分配。

For resistors in parallel, the reciprocal of the total resistance equals the sum of the reciprocals: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …. The p.d. across each parallel branch is the same, and the total current divides among the branches. The total resistance is always less than the smallest individual resistance.

并联电阻的总电阻倒数等于各电阻倒数之和：1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …。各并联支路两端电势差相同，总电流在支路间分配。总电阻始终小于最小的单个电阻。

Quantity	Series	Parallel
Current	Same through all	Splits among branches
P.d.	Divided across resistors	Same across each branch
Resistance	R_total = R₁ + R₂ + …	1/R_total = 1/R₁ + 1/R₂ + …

5. Potential Divider Circuits | 分压电路

A potential divider uses two resistors in series to produce a fraction of the input voltage. For two resistors R₁ and R₂ connected across a supply of voltage V_in, the output voltage across R₂ is V_out = V_in × (R₂ / (R₁ + R₂)). This is derived from the ratio of resistances and the fact that the same current flows through both.

分压器利用两个串联电阻来获得输入电压的一部分。若 R₁ 和 R₂ 串接在电压 V_in 两端，则 R₂ 两端的输出电压为 V_out = V_in × (R₂ / (R₁ + R₂))。该公式源自电阻比例和串联电流相同的原理。

V_out = V_in × R₂ / (R₁ + R₂)

The potential divider is the basis of many sensor circuits. If R₂ is replaced by a thermistor, the output voltage changes with temperature. If R₂ is an LDR, V_out varies with light intensity. These circuits allow a change in a physical quantity to produce a measurable voltage change.

分压器是许多传感器电路的基础。若用热敏电阻替换 R₂，输出电压将随温度变化；若用光敏电阻 (LDR)，V_out 则随光照强度改变。这类电路可将物理量的变化转变为可测量的电压变化。

6. Electromotive Force (EMF) and Internal Resistance | 电动势与内阻

The electromotive force (ε) of a source is the energy supplied per unit charge in converting non‑electrical energy into electrical energy. It is measured in volts. A real power source, such as a battery, has internal resistance r, which causes the terminal p.d. to drop when current flows.

电源的电动势 (ε) 是每单位电荷在将非电能转换为电能时获得的能量，单位为伏特。真实的电源（如电池）具有内阻 r，当有电流流过时，端电压会下降。

The relationship between terminal p.d. V, emf ε, current I and internal resistance r is ε = I (R + r) or V = ε − I r. The ‘lost volts’ inside the source equal I r. A graph of terminal p.d. against current yields a straight line with gradient −r and y‑intercept ε.

端电压 V、电动势 ε、电流 I 和内阻 r 之间的关系为 ε = I (R + r) 或 V = ε − I r。电源内部损耗的“势降”为 I r。绘出端电压对电流的关系图，可得到一条斜率为 −r、y 截距为 ε 的直线。

V = ε – I r

7. Kirchhoff’s Laws | 基尔霍夫定律

Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering any junction is zero, or equivalently, the total current entering a junction equals the total current leaving it: ∑I_in = ∑I_out. This is a consequence of charge conservation.

基尔霍夫电流定律 (KCL) 指出，流入任一节点的电流代数和为零，或者说，进入节点的电流之和等于离开节点的电流之和：∑I_in = ∑I_out。这是电荷守恒的结果。

Kirchhoff’s voltage law (KVL) states that the algebraic sum of the emfs and potential differences around any closed loop is zero: ∑ε + ∑(I R) = 0. Energy gained per unit charge equals energy lost per unit charge around a complete loop. KVL is used to write loop equations for complex circuits.

基尔霍夫电压定律 (KVL) 指出，绕任一闭合回路，电动势与电势差的代数和为零：∑ε + ∑(I R) = 0。单位电荷在闭环中获得的能量等于其损失的能量。KVL 可用于列出复杂电路的回路方程。

When applying Kirchhoff’s laws, choose a consistent direction for the current in each branch and follow the loop in a specified direction. A rise in potential (from – to + of a battery) is positive; a drop across a resistor (in the direction of current) is negative. Solving the simultaneous equations yields the branch currents.

应用基尔霍夫定律时，为每条支路规定一致的电流方向，并按指定方向环绕回路。电势升高（从电池的负到正）取正；沿电流方向经过电阻的电势降落取负。联立求解方程组即可得到各支路电流。

8. Electrical Power and Energy Dissipation | 电功率与能量耗散

Electrical power P delivered to a component is given by P = I V. Using Ohm’s law, this can be rewritten for a resistor as P = I² R or P = V² / R. Power is measured in watts (W), and energy transferred in time t is E = P t = I V t.

输送给元件的电功率 P 为 P = I V。利用欧姆定律，可改写为 P = I² R 或 P = V² / R。功率的单位为瓦特 (W)，在时间 t 内转移的能量为 E = P t = I V t。

P = I V = I² R = V² / R

In a circuit, energy is dissipated as heat in resistive components. The rate of heating determines how components behave; for example, a resistor’s temperature may rise, changing its resistance. When calculating energy, always use the appropriate formula based on known quantities, and remember to convert time to seconds.

在电路中，能量以热的形式在电阻元件上耗散。发热速率决定了元件的行为；例如电阻的温度可能上升，从而改变阻值。计算能量时，务必根据已知量选用合适公式，并将时间换算为秒。

9. Using a Potential Divider as a Sensor | 分压器在传感器中的应用

Replacing one fixed resistor in a potential divider with a variable‑resistance sensor creates a sensing circuit. A thermistor (whose resistance falls as temperature rises) placed as R₂ will cause V_out to increase with temperature if it is in the lower position, or decrease if in the upper position. Careful choice of the fixed resistor sets the sensitivity and range.

将分压器中的一个固定电阻换成可变电阻传感器即可构成传感电路。将热敏电阻（阻值随温度升高而减小）作为 R₂ 接入较低位置时，V_out 随温度升高而增大；若接在较高位置，则 V_out 随温度升高而减小。合理选择固定电阻可调节灵敏度和量程。

Similarly, a light‑dependent resistor (LDR) exhibits decreasing resistance with increasing light intensity. When used as R₂ in the lower branch, the output voltage rises as the light gets brighter. These voltage changes can be fed into a comparator or a data‑logger to trigger an action, such as switching on a lamp at dusk.

类似地，光敏电阻 (LDR) 的阻值随光照强度增加而减小。当其作为 R₂ 接入下支路时，输出电压随光线变亮而升高。这些电压变化可输入比较器或数据记录器以触发动作，例如在黄昏时点亮电灯。

10. The Potentiometer and Measurement of EMF | 电位计与电动势的测量

A potentiometer is a null‑measurement device used to compare potential differences or to measure the emf of a cell without drawing current. It consists of a long uniform resistance wire AB with a known voltage applied across it. A sliding contact can tap off a fraction of the total p.d. proportional to the length of wire selected.

电位计是一种零测量设备，用于比较电势差或在无电流抽取的情况下测量电池电动势。它由一根长均匀电阻丝 AB 构成，其两端施加已知电压。滑动触点可按选用长度比例分取总电势差。

To measure an unknown emf εₓ, the cell is connected via a galvanometer to the sliding contact. The contact is adjusted until the galvanometer reads zero (null point). At balance, εₓ equals the p.d. across the selected length ℓₓ of the wire. Using a standard cell of emf εₛ and its balance length ℓₛ, the unknown emf is found from εₓ / εₛ = ℓₓ / ℓₛ.

测量未知电动势 εₓ 时，将待测电池通过检流计与滑触头相连。调节触头至检流计读数为零（平衡点）。在平衡时，εₓ 等于所选丝长 ℓₓ 两端的电势差。借助已知电动势 εₛ 的标准电池及其平衡长度 ℓₛ，可由 εₓ / εₛ = ℓₓ / ℓₛ 求得未知电动势。

εₓ / εₛ = ℓₓ / ℓₛ

The potentiometer method is highly accurate because at balance no current flows through the cell under test, eliminating errors due to internal resistance. It is also used to calibrate voltmeters and ammeters.

电位计法精度很高，因为平衡时无电流流过被测电池，从而消除了内阻引起的误差。它还可用于校准电压表和电流表。

11. Wheatstone Bridge Circuit | 惠斯通电桥电路

The Wheatstone bridge consists of four resistors arranged in a diamond shape, with a galvanometer connected between the two mid‑points. When the bridge is balanced, the galvanometer reads zero, meaning that the ratio of the two resistors in one branch equals the ratio in the other: R₁ / R₂ = R₃ / R₄.

惠斯通电桥由四个电阻呈菱形排列构成，两中点间接入检流计。当电桥平衡时，检流计读数为零，这意味着一个支路中两电阻之比等于另一支路相应电阻之比：R₁ / R₂ = R₃ / R₄。

R₁ / R₂ = R₃ / R₄ (balanced)

This condition arises because the potential at the two mid‑points is equal. The Wheatstone bridge is commonly used to determine an unknown resistance precisely. By using a known variable resistor in one arm and adjusting it until null is achieved, the unknown resistance can be calculated without needing to measure current or voltage directly.

该平衡条件源自两个中点电势相等。惠斯通电桥常用于精确测量未知电阻。在一条臂中使用已知的可变电阻并调节至零点，即可在无需直接测量电流或电压的条件下计算未知阻值。

A strain gauge often employs a Wheatstone bridge arrangement. As the gauge’s resistance changes with mechanical deformation, the bridge becomes unbalanced, producing a small voltage output proportional to the strain. This principle is widely applied in force and pressure sensors.

应变片通常采用惠斯通电桥结构。随着应变片阻值随机械形变改变，电桥失去平衡，输出与应变成正比的微小电压。这一原理广泛应用于力和压力传感器。

12. Practical Skills and Experimental Techniques | 实验技能与测量方法

In AQA practicals you are expected to set up circuits from diagrams, choose appropriate meters and ranges, and record measurements with correct precision. When measuring internal resistance, you will vary a variable resistor (rheostat) and record terminal p.d. and current, then plot a graph to find ε and r.

在 AQA 实验考核中，你需要能根据电路图搭建实际电路，选择合适的电表及量程，并以正确精度记录测量值。在测量内阻的实验中，你需要改变可变电阻（变阻器）并记录端电压与电流，再绘制曲线以求得 ε 和 r。

For investigating the I–V characteristic of a filament lamp or diode, you should use a potential divider to vary the p.d. smoothly and include a protective resistor to limit the current. Always take readings for both positive and negative directions where appropriate, and allow components to cool between measurements to ensure repeatability.

在研究灯丝灯泡或二极管的 I–V 特性时，应使用分压器均匀改变电势差，并接入保护电阻以限制电流。务必在合适的情况下记录正向和反向两类读数，并在测量之间让元件冷却以确保可重复性。

When using a potentiometer or Wheatstone bridge, care must be taken to achieve a sensitive null point. This requires a sensitive centre‑zero galvanometer and careful adjustment of the sliding contact or variable resistor. Systematic errors, such as non‑uniformity of the resistance wire or contact resistance, should be considered and minimised.

使用电位计或惠斯通电桥时，必须细致操作以获得灵敏的平衡点。这需要一台灵敏的中央零位检流计，并仔细调节滑触头或可变电阻。诸如电阻丝不均匀或接触电阻等系统误差，应加以考虑并尽量减小。

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A-Level AQA Physics: Circuit Analysis | A-Level AQA 物理：电路分析 考点精讲