📚 Control Variables in A-Level Physics Practicals | A-Level 物理实验中的控制变量
In A-level Physics, a practical investigation is only valid if you deliberately change one variable, measure another, and keep all other relevant variables constant. The variables that are kept constant are called control variables. This article explains how to identify, manage and describe control variables across the AQA required practicals, and how to use them to gain marks in written and practical assessments.
在 A-level 物理中，只有当你刻意改变一个变量、测量另一个变量，并让所有其他相关变量保持不变时，实验探究才有效。这些保持不变的变量称为控制变量。本文将解释如何在 AQA 要求实验中识别、管理和描述控制变量，以及如何利用它们在笔试和实验评估中获得分数。
1. What is a Control Variable? | 什么是控制变量？
A control variable is a quantity that could affect the outcome of an experiment but is deliberately kept constant so that it does not interfere with the relationship being tested. In a fair test, only the independent variable is changed and only the dependent variable is measured as a result. Any other quantity that might change the dependent variable must be controlled.
控制变量是可能影响实验结果、但被刻意保持不变的量，以免干扰正在检验的关系。在公平实验中，只改变自变量，只测量因变量，其余可能影响因变量的量都必须加以控制。
For example, when investigating how the length of a pendulum affects its time period, the mass of the bob and the initial amplitude must be controlled. If you changed the mass and length at the same time, you would not know whether a change in the period was caused by length or mass.
例如，在研究单摆长度如何影响周期时，摆球质量和初始振幅必须保持不变。如果同时改变质量和摆长，你就无法判断周期的变化是由摆长还是质量引起的。
2. Independent, Dependent and Control Variables | 自变量、因变量与控制变量
In any AQA practical, you should be able to state the independent variable, the dependent variable and the relevant control variables. The independent variable is the one you deliberately change. The dependent variable is the one you measure. Control variables are all the other quantities that could influence the dependent variable.
在任何 AQA 实验中，你都应该能够说出自变量、因变量和相关的控制变量。自变量是你刻意改变的量，因变量是你测量的量，控制变量是其他所有可能影响因变量的量。
| Role | What happens | Example: resistance of a metal wire |
|---|---|---|
| Independent variable | Changed by the experimenter | Length L of the wire |
| Dependent variable | Measured in response | Resistance R |
| Control variables | Kept constant | Cross-sectional area, material, temperature |
ed in This table shows the core language used in AQA mark schemes. You should use the words independent, dependent and control precisely, rather than saying 'the thing I change' or 'the thing I keep the same' length and resistivity matter, so area, material and temperature must be controlled when only length is changed.
这张表展示了 AQA 评分方案中使用的核心术语。你应该准确使用自变量、因变量和控制变量这些词，而不是说“我改变的东西”或“我保持不变的东西”。公式 R = ρL/A 说明了面积、长度和电阻率为何重要，因此当只改变长度时，面积、材料和温度必须保持不变。
3. Why Control Variables Matter in AQA Practicals | 为什么控制变量在 AQA 实验中很重要
If a control variable changes, the graph of dependent variable against independent variable may show extra scatter, a false trend, or the wrong gradient. This reduces the validity of the conclusion because the observed relationship may not be due only to the independent variable.
如果控制变量发生变化，因变量对自变量的图像可能会出现额外的散点、虚假趋势或错误的斜率。这会降低结论的有效性，因为观察到的关系可能并非仅由自变量引起。
For example, when measuring the resistance of a metal wire, a high current can raise the temperature of the wire. Since resistance increases with temperature for a metal, the measured resistance will rise even if the length is unchanged. This could produce a non-linear graph or an incorrect value for resistivity. Keeping the current low and switching off between readings controls the temperature.
例如，在测量金属丝电阻时，较大的电流会使金属丝温度升高。由于金属的电阻随温度升高而增大，即使长度不变，测得的电阻也会增大。这可能产生非线性图像或错误的电阻率数值。保持电流较小并在读数之间断开电路可以控制温度。
Controlling variables also improves repeatability and reproducibility. If another student repeats the experiment using the same controls, they should obtain similar results. AQA practical assessment often asks you to explain how a control variable improves accuracy or reliability.
控制变量还能提高重复性和再现性。如果另一位学生使用相同的控制条件重复实验，他们应该得到相似的结果。AQA 实验评估经常要求你解释控制变量如何提高准确度或可靠性。
4. How to Identify Control Variables | 如何识别控制变量
To identify control variables, first write down the relevant physics equation or law. Then ask: apart from the independent variable, what other quantities in the equation could change the dependent variable? These are the quantities that must be controlled.
要识别控制变量，首先写下相关的物理公式或定律。然后问自己：除了自变量之外，公式中还有哪些量可能改变因变量？这些就是必须控制的量。
For a simple pendulum, the period is given by T = 2π√L/g. This equation contains only L and g. Therefore, when investigating how L affects T, the gravitational field strength g must be kept constant by staying in the same location. In addition, the equation assumes a small angle, so the amplitude should be kept small and constant to avoid a changing period.
对于单摆，周期由 T = 2π√L/g 给出。这个公式只包含 L 和 g。因此，在研究 L 如何影响 T 时，重力场强度 g 必须通过在同一地点实验来保持不变。此外，该公式假设小角度，因此振幅应保持较小且恒定，以避免周期发生变化。
In more complex experiments, there may be several control variables. For example, in the inverse square law for gamma radiation, the count rate C depends on distance x and source activity. The activity, background count rate, detector position and absorber thickness must all be controlled while distance is changed.
在更复杂的实验中，可能有多个控制变量。例如，在伽马辐射的平方反比定律中，计数率 C 取决于距离 x 和放射源活度。在改变距离时，放射源活度、背景计数率、探测器位置和吸收体厚度都必须控制。
5. Common Control Techniques in A-Level Physics | A-Level 物理中常见的控制方法
AQA mark schemes reward specific methods of controlling variables, not just naming them. Saying 'keep the temperature constant' is usually too vague. You should state how the temperature is controlled, for example 'use a water bath', 'keep the current small to reduce heating' or 'wait for thermal equilibrium before each reading'.
AQA 评分方案奖励控制变量的具体方法，而不仅仅是说出变量名称。说“保持温度不变”通常过于笼统。你应该说明如何控制温度，例如“使用水浴”、“保持电流较小以减少发热”或“在每次读数前等待热平衡”。
| Control variable | Common technique | Typical AQA context |
|---|---|---|
| Temperature | Use a water bath, low current, open circuit between readings | Resistivity, IV characteristics |
| Mass | Use the same object or transfer masses carefully | Newton's second law, pendulum |
| Cross-sectional area | Use the same wire and measure diameter with a micrometer | Resistivity |
| Angle or amplitude | Use a protractor, keep angle below about 10° | Pendulum, diffraction |
| Potential difference or current | Use the same cell, variable resistor, or keep current constant | Internal resistance, components |
| Background radiation | Measure background count and subtract from each reading | Gamma inverse square law |
This table can be used as a checklist when planning any AQA required practical. Always link the control to the physics equation so that your answer shows understanding rather than memorisation.
这张表可以用作规划任何 AQA 要求实验时的检查清单。始终将控制变量与物理公式联系起来，这样你的答案就能表现出理解，而不是死记硬背。
6. Control Variables in Mechanics Practicals | 力学实验中的控制变量
In the simple pendulum experiment, the period T is measured for different lengths L. The control variables are the mass of the bob, the amplitude of the swing, and the gravitational field strength g. The mass is controlled by using the same bob throughout. The amplitude is controlled by using a small angle, typically less than 10°, and by measuring the same initial displacement each time.
在单摆实验中，测量不同摆长 L 下的周期 T。控制变量是摆球质量、摆动幅度和重力场强度 g。通过始终使用同一个摆球来控制质量。通过使用小角度（通常小于 10°）并每次测量相同的初始位移来控制振幅。
T = 2π√L/g
For a free-fall experiment to determine g, the initial velocity must be controlled by releasing the object from rest. Air resistance should be minimised by using a small, dense object such as a steel ball. If the object is dropped from different heights, the same object and the same release mechanism should be used each time.
在测定 g 的自由落体实验中，必须通过从静止释放物体来控制初速度。应使用小而致密的物体（如钢球）以尽量减少空气阻力。如果从不同高度释放物体，每次应使用相同的物体和相同的释放机构。
In Newton's second law, when investigating how acceleration depends on force, the total mass of the system must be controlled. This is done by transferring masses from the trolley to the hanger, keeping the total mass of trolley plus hanger and masses constant. When investigating how acceleration depends on mass, the accelerating force must be kept constant by using the same hanger and masses.
在牛顿第二定律实验中，当研究加速度如何依赖于力时，系统的总质量必须保持恒定。这可以通过将砝码从小车转移到挂钩上来实现，使小车加挂钩和砝码的总质量保持不变。当研究加速度如何依赖于质量时，必须通过使用相同的挂钩和砝码来保持加速力恒定。
F = ma
7. Control Variables in Electrical Practicals | 电学实验中的控制变量
In the resistivity experiment, the resistance R of a metal wire is measured for different lengths L. The cross-sectional area A, the material of the wire, and the temperature must be controlled. The cross-sectional area is controlled by using the same wire throughout and measuring its diameter at several places with a micrometer.
在电阻率实验中，测量不同长度 L 下金属丝的电阻 R。必须控制横截面积 A、金属丝材料和温度。通过始终使用同一根金属丝并用千分尺在多个位置测量其直径来控制横截面积。
ρ = RA/L
Temperature is controlled by keeping the current small and switching the circuit off between readings. A large current would heat the wire and increase its resistance, making the data unreliable. Some students also use a water bath around the wire to maintain a constant temperature.
通过保持电流较小并在两次读数之间断开电路来控制温度。大电流会加热金属丝并增大其电阻，使数据不可靠。有些学生还会在金属丝周围使用水浴来保持恒定温度。
s of the cell, so the same cell should be used throughout and its temperature should not change significantly.
在内阻实验中，测量电池在不同电流 I 下的端电压 V。控制变量是电池的温度和电池本身。公式 ε = V + Ir 表明 ε 和 r 是电池的性质，因此整个实验应使用同一个电池，并且电池温度不应明显变化。
ε = V + Ir
8. Control Variables in Waves and Radiation Practicals | 波动与辐射实验中的控制变量
In Young's double-slit experiment, the fringe spacing w is related to the wavelength λ, the distance D to the screen, and the slit separation s. If you measure w for different values of D, you must keep λ and s constant. Use the same laser so λ is constant, and use the same double slit so s is constant.
在杨氏双缝实验中，条纹间距 w 与波长 λ、到屏幕的距离 D 以及缝间距 s 有关。如果在不同 D 值下测量 w，则必须保持 λ 和 s 不变。使用同一激光器使 λ 保持不变，并使用同一个双缝使 s 保持不变。
w = λD/s
For the inverse square law with gamma radiation, the count rate C is measured at different distances x from the source. The activity of the source, the background count rate, the detector settings and the absorber thickness must all be controlled. Background count should be measured separately and subtracted from each reading. The source should be handled with tongs and kept in the same position while the detector is moved.
对于伽马辐射的平方反比定律，在离放射源不同距离 x 处测量计数率 C。放射源活度、背景计数率、探测器设置和吸收体厚度都必须控制。背景计数应单独测量并从每次读数中减去。应使用钳子操作放射源并将其保持在相同位置，同时移动探测器。
C ∝ 1/x²
9. Control Variables in Gas Laws and Thermal Physics | 气体定律与热学实验中的控制变量
In Boyle's law, the pressure p of a fixed mass of gas is measured as its volume V is changed. The control variables are the mass of gas and the temperature. The mass is controlled by using a sealed syringe or airtight container. The temperature is controlled by compressing or expanding the gas slowly and waiting for the reading to stabilise, so that the gas can exchange heat with its surroundings.
在玻意耳定律实验中，测量一定质量气体在体积 V 改变时的压强 p。控制变量是气体的质量和温度。通过使用密封的注射器或气密容器来控制质量。通过缓慢压缩或膨胀气体并等待读数稳定来控制温度，使气体能够与周围环境进行热交换。
pV = constant at constant temperature
In Charles's law, the volume V of a fixed mass of gas is measured as its temperature T changes. The mass of gas and the pressure must be controlled. The mass is kept constant by trapping air in a sealed capillary tube. The pressure is kept constant by using a mercury bead or by ensuring the gas is open to the atmosphere and the apparatus is not tilted.
在查理定律实验中，测量一定质量气体在温度 T 改变时的体积 V。必须控制气体的质量和压强。通过在密封的毛细管中封入空气来控制质量。通过使用水银珠或确保气体与大气相通且装置不倾斜来保持压强恒定。
V/T = constant at constant pressure
10. Exam Answers, Common Mistakes and Checklist | 考试答案、常见错误与清单
A common mistake is to give a vague control variable such as 'keep the temperature the same' without saying how. For example, in a resistance experiment, a weak answer is
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