Multimeter Accuracy Calculation

To compute the accuracy of a digital multimeter, we first need to understand what accuracy represents in the context of measurement instruments. Accuracy refers to how close a measured value is to the true or actual value. In this question, we are given a nominal reading and a range within which the actual value might fall.

Understanding Digital Multimeter Range

A digital multimeter reading of 100V is given. The problem states that this reading can actually range from 97V to 103V. This range indicates the uncertainty or tolerance associated with the measurement. The deviation from the nominal reading helps us calculate the accuracy.

• Nominal Reading: This is the value displayed on the digital multimeter, which is 100V.
• Lower Limit: The lowest possible value for the 100V reading is 97V.
• Upper Limit: The highest possible value for the 100V reading is 103V.

The deviation is the maximum difference between the nominal reading and the limits of the range.

• Deviation from the lower limit: $\left| 97\text{V} - 100\text{V} \right| = \left| -3\text{V} \right| = 3\text{V}$
• Deviation from the upper limit: $\left| 103\text{V} - 100\text{V} \right| = \left| 3\text{V} \right| = 3\text{V}$

So, the maximum deviation or uncertainty in the reading is $\pm 3\text{V}$.

Computing Accuracy Percentage

The accuracy of an instrument or a measurement is often expressed as a percentage of the true value or the full-scale reading. In this case, we use the nominal reading as our reference (true value) to compute the accuracy percentage.

The formula to compute accuracy in percentage is:

$$ \text{Accuracy (}\% \text{)} = \frac{\text{Maximum Deviation}}{\text{Nominal Reading}} \times 100\% $$

Let's substitute the values we have:

• Maximum Deviation = $3\text{V}$
• Nominal Reading = $100\text{V}$

Now, let's perform the calculation:

$$ \text{Accuracy (}\% \text{)} = \frac{3\text{V}}{100\text{V}} \times 100\% $$

$$ \text{Accuracy (}\% \text{)} = 0.03 \times 100\% $$

$$ \text{Accuracy (}\% \text{)} = 3\% $$

Since the deviation can be both positive and negative (from 97V to 103V), the accuracy is expressed as $\pm 3\%$. This means the digital multimeter reading of 100V is accurate to within $\pm 3\%$ of the actual value.

Therefore, the accuracy of the digital multimeter reading is $\pm 3\%$.