Combining Uncertainties (Edexcel A-Level Physics 1.15) | 不确定度的合成（爱德思 A-Level 物理 1.15）

📚 Combining Uncertainties (Edexcel A-Level Physics 1.15) | 不确定度的合成（爱德思 A-Level 物理 1.15）

In Edexcel A-Level Physics, every measurement has an uncertainty. Knowing how to combine uncertainties allows you to estimate the total uncertainty in a final calculated quantity, such as speed, resistance or density, from the uncertainties in the raw measurements.

在爱德思 A-Level 物理中，每一次测量都存在不确定度。学会如何合成不确定度，可以帮助你估算最终计算量（如速度、电阻或密度）的总不确定度，这些不确定度来自原始测量。

1. Why Uncertainties Matter | 为什么不确定度很重要

An uncertainty is not a mistake; it is the range within which the true value is expected to lie. For example, a ruler measurement of 12.5 cm has an absolute uncertainty of ±0.1 cm, so the true length is likely between 12.4 cm and 12.6 cm.

不确定度不是错误，而是真值预期所在的范围。例如，用直尺测得 12.5 cm，绝对不确定度为 ±0.1 cm，因此真实长度很可能在 12.4 cm 到 12.6 cm 之间。

When two or more measurements are used in a formula, the uncertainties in each measurement combine to produce an uncertainty in the final result. This is called propagation of uncertainties.

当两个或多个测量值用于公式时，每个测量值的不确定度会合成，产生最终结果的不确定度，这称为不确定度传递。

2. Absolute and Percentage Uncertainty | 绝对不确定度与百分比不确定度

Absolute uncertainty is the range of a measurement, written as ±Δx, and has the same units as the measurement itself. Percentage uncertainty is calculated by (Δx / x) × 100% and is dimensionless.

绝对不确定度是测量范围，写作 ±Δx，单位与测量值相同。百分比不确定度用 (Δx / x) × 100% 计算，无量纲。

For a current of 2.0 A with an absolute uncertainty of ±0.1 A, the percentage uncertainty is (0.1 / 2.0) × 100% = 5%.

对于电流 2.0 A、绝对不确定度 ±0.1 A，百分比不确定度为 (0.1 / 2.0) × 100% = 5%。

3. Adding and Subtracting Measurements | 测量值的加减

When measurements are added or subtracted, their absolute uncertainties add directly. If q = a + b or q = a – b, then Δq = Δa + Δb.

当测量值相加或相减时，其绝对不确定度直接相加。若 q = a + b 或 q = a – b，则 Δq = Δa + Δb。

Δq = Δa + Δb

Suppose a = (5.0 ± 0.2) cm and b = (3.0 ± 0.1) cm. The difference a – b = 2.0 cm has an uncertainty Δq = 0.2 + 0.1 = 0.3 cm, so q = (2.0 ± 0.3) cm.

假设 a = (5.0 ± 0.2) cm，b = (3.0 ± 0.1) cm。差值 a – b = 2.0 cm 的不确定度为 Δq = 0.2 + 0.1 = 0.3 cm，因此 q = (2.0 ± 0.3) cm。

Even though the two measured values are subtracted, the absolute uncertainties still add. This is because one value may be at its upper limit while the other is at its lower limit, making the maximum possible difference larger.

即使两个测量值相减，绝对不确定度仍然相加。这是因为一个值可能处于上限，另一个处于下限，从而使最大可能差值更大。

4. Multiplying and Dividing Measurements | 测量值的乘除

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