Understanding Voltmeter Resolution

The resolution of a digital measuring instrument, like a voltmeter, is the smallest change in the measured quantity that the instrument can detect and display. It essentially defines the precision of the instrument.

The resolution is directly related to the number of digits the display can show.

Decoding "$4\frac{1}{2}$-Digit" Display

A "$4\frac{1}{2}$-digit" display means the voltmeter has:

• Four digits that can display any value from 0 to 9.
• One "half-digit" which can typically only display '0' or '1'. This half-digit is usually the most significant digit (leftmost).

This configuration allows the voltmeter to display readings with a higher degree of precision compared to a simple 4-digit meter. The total number of possible discrete readings is determined by this setup.

Calculating the Resolution

For a "$4\frac{1}{2}$-digit" voltmeter:

1. The most significant digit can be '0' or '1'.
2. The other four digits can range from '0' to '9'.
3. This means the voltmeter can display numbers from 00000 up to 19999.
4. The total number of distinct counts is therefore 20,000 (from 0 to 19999).

The resolution is determined by the place value of the least significant digit (LSB) when the voltmeter is set to its most sensitive range. For a $4\frac{1}{2}$-digit display showing a maximum value like $1.9999$ V:

• The digits represent place values relative to the decimal point.
• The reading $1.9999$ V involves place values: Units ($10^0$), Tenths ($10^{-1}$), Hundredths ($10^{-2}$), Thousandths ($10^{-3}$), and Ten-thousandths ($10^{-4}$).
• The least significant digit (the last '9') is in the ten-thousandths place.

Therefore, the smallest increment the voltmeter can display is:

Resolution = $1 \times 10^{-4}$

Resolution = $0.0001$

Conclusion

The resolution of a $4\frac{1}{2}$-digit voltmeter corresponds to the value represented by its least significant digit on the most sensitive scale, which is $0.0001$.