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Problem #6:

A technician in an electronics lab is measuring the resistance of a critical electrical component. The component specification calls for a minimum resistance of 97.3 Ω. The technician makes twelve measurements of resistance with a sample mean of 98.0 Ω and a sample deviation of 0.78 Ω. The multi-meter used to perform the measurements has a stated accuracy of 200 mΩ + 0.5% (one-sided confidence interval).

Based on this information, determine:

a) The total measurement uncertainty at a confidence level of 99%. State the resistance value to the proper number of significant digits and uncertainty.

b) The confidence level that the component meets the specification.

Answer :

Final answer:

In the scenario, the measurement uncertainty of the component's resistance is calculated using statistical methods considering the sample deviation and the precision of the multi-meter. The confidence level that the component meets specifications is determined by comparing the measured values to the minimum resistance specification.

Explanation:

The problem given involves the concept of measurement uncertainty, commonly dealt with in Physics and Engineering. This concept involves calculating the deviation of measured values from an expected or standard value. In this case, we have a critical electrical component with a specification for minimum resistance, and the technician has made several measurements.

The total measurement uncertainty is derived from the combination of the sample deviation and the accuracy of the multi-meter. This uncertainty helps to quantify just how precise and accurate the measurements are.

Counting on the measurements given, the answer to the part a) of the problem would typically involve using statistical methods to calculate the total uncertainty at a 99% confidence interval. The exact computation depends on the statistical model assumed for the underlying resistance values and the measurement process.

For part b), the analysis involves comparing the specification's minimum resistance and the measurements taken. If the measured values fall within the minimum specifications, taking uncertainty into account, we'd be confident that it meets specifications

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