Yi's Blog

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不确定度 的计算公式

单次测量没有 A 类不确定度,只有 B 类不确定度。

$$
U_{R’} = \frac{\Delta R’{s}}{3} = \frac{R’{s} \times 0.1%}{3}
$$

根据公式 ,两边取对数:

$$
\frac{\partial \ln R_{x}}{\partial R_{s}} = \frac{1}{2R_{s}}, \quad \frac{\partial \ln R_{x}}{\partial R’{s}} = \frac{1}{2R’{s}}
$$

$$
\frac{U_{Rx}}{R_{x}} = \sqrt{\left( \frac{\partial \ln R_{x}}{\partial R_{s}} \right)^2 U_{R}^{2} + \left( \frac{\partial \ln R_{x}}{\partial R’{s}} \right)^2 U{R’}^{2}} = \sqrt{\left( \frac{U_{R}}{2R_{s}} \right)^2 + \left( \frac{U_{R’}}{2R’_{s}} \right)^2}
$$

其中, 表示交换位置前的电阻箱阻值, 表示交换位置后的电阻箱阻值。

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