Question

A DC current is measured by using a digital multimeter. The display reads xx.yymA on 100 mA range. The error of the meter is given by the manufacturer as: ±(1%rdg+0.3%fs+3dgt). Here, the figures xx and yy are your birth day as the following format xx (day). yy (month). [Example; If your birth day is 15.06.2000 the display reads 15,06 mA]

a) Calculate the absolute and relative errors of the measurement.

Answer 1

To calculate the absolute and relative errors of a DC current measurement using a digital multimeter, apply the manufacturer's error formula to the measured reading, with the full scale value being 100 mA for this range.

Step-by-step explanation:

The measurement error for a DC current measured with a digital multimeter involves three components: a percentage of the reading (rdg), a percentage of the full scale (fs), and a count of the least significant digits (dgt). The error given by the manufacturer is ±(1%rdg + 0.3%fs + 3dgt). To calculate both the absolute and relative errors, we will apply these percentages and counts to the displayed reading.

Assuming the digital multimeter reads xx.yymA (where xx and yy represent the day and month of your birthday respectively), we first convert this reading into a numerical value the formula can use. The full scale (fs) value for the 100 mA range is 100 mA.

The absolute error is calculated by taking 1% of the reading, adding 0.3% of the full scale, and then adding 3 digits of the least significant figure (which, on the 100 mA range, is 0.01 mA). The relative error is the absolute error expressed as a percentage of the actual reading.

For a reading of xx.yymA, the absolute error = (1% of xx.yy mA) + (0.3% of 100 mA) + (3 × 0.01 mA), and the relative error = (Absolute error / xx.yy mA) × 100%.