Question

Resolution of a \(3\frac{1}{2}\) digit DVM is

• A. \(\frac{1}{100}\)
• B. \(\frac{1}{1000}\)
• C. \(\frac{1}{2000}\)
• D. \(\frac{1}{10000}\)

Hint:

For any digital meter, a \(3\frac{1}{2}\)-digit display can count from 0000 up to 1999. This gives a total span of 2000 counts, making the base resolution exactly \(\frac{1}{2000}\) (or \(0.05%\)).

Answer 1

The Correct Option is C

Concept: The resolution (\(R\)) of a Digital Voltmeter (DVM) represents the smallest change in input voltage that the instrument can reliably detect and display. For an instrument display characterized by \(N\) full digits alongside a fractional leading digit, resolution can be evaluated using the maximum count capacity: \[ \text{Resolution } (R) = \frac{1}{\text{Total Number of Distinct Steps/Counts}} = \frac{1}{\text{Maximum Full-Scale Reading Count}} \]

Step 1: Determine the digit display configurations. For a \(3\frac{1}{2}\) digit instrument display layout:
• There are 3 full digits that can display any integer value from 0 through 9.
• The leading fractional digit (\(\frac{1}{2}\) digit) can only display either 0 or 1.

Step 2: Calculate the maximum display count capacity range. The highest number this screen can display is when the half-digit is at its maximum value (1) and all full digits are at their highest value (9): \[ \text{Maximum display state} = 1999 \] Including the zero state (\(0000\)), the total number of distinct display intervals or steps from zero up to the maximum capacity is exactly: \[ \text{Total steps} = 2000 \]

Step 3: Define resolution. Thus, the base structural resolution limit fraction is given by: \[ R = \frac{1}{2000} \] This matches option (C).