GATE 2025 IN Q.23: solution and answer

GATE 2025 · INQ.23 · 1 mark · MCQ

A $3 \frac{1}{2}$ digit digital voltmeter has a specified accuracy of $\pm (0.5% + 1)$ . If it is used to measure $10 V$ DC voltage, the error in the measurement would be

Note: Accuracy of the digital voltmeter is expressed as $\pm$ (% of reading + digit).

(A)
$\pm 0.4%$
(B)
$\pm 1.5%$
(C)
$\pm 0.6%$
(D)
$\pm 1%$

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Answer and solution

ANSWER

The error is $\pm 0.06 V$ , which is $\pm 0.6%$ of the $10 V$ reading. The answer is option (C).

Official answer: CSource: Official answer key, GATE 2025 IN (IIT Roorkee)

A $3 \frac{1}{2}$ digit display has three full digits (each 0 to 9) and one leading half digit (0 or 1), so its largest reading is $1999$ counts.
The ranges of such a meter are $1.999 V$ , $19.99 V$ , $199.9 V$ , and so on. $10 V$ is too large for the $1.999 V$ range, so the lowest range that can show it is $19.99 V$ . There it reads $10.00$ , which is $1000$ counts.
Resolution on this range (the value of one count in the last digit): $1 digit = 0.01 V$
Percentage-of-reading part: $0.5% \times 10 V = 0.05 V$
Digit part: $+ 1 digit = 0.01 V$ .
The two parts add, because a specification gives the worst case: $Δ V = \pm (0.05 + 0.01) V = \pm 0.06 V$
As a percentage of the reading: $\frac{0.06 V}{10 V} \times 100% = \pm 0.6%$ Check in counts: $0.5%$ of $1000$ counts is $5$ counts, plus $1$ count gives $6$ counts out of $1000$ , which is $0.6%$ . This is option (C).

KEY IDEA

For a DVM spec of $\pm (% of reading + n digits)$ , first find the range the reading sits on. On that range one digit is one count of the last displayed place. Change the digit term into volts, add it to the percentage-of-reading term, then divide by the reading. For a $3 \frac{1}{2}$ digit meter, $10 V$ sits on the $19.99 V$ range, so $1 digit = 0.01 V$ .

WATCH OUT FOR

There are three common mistakes. The first is to answer $\pm 0.5%$ and forget the digit term, but that is not one of the options. The second is to add the "1" as $1%$ , which gives $\pm 1.5%$ (option B). The third is to take one digit as $0.1 V$ by assuming the wrong range, which gives $0.05 + 0.1 = 0.15 V$ , or $1.5%$ . The digit term has to be turned into volts using the resolution of the range actually in use, which here is $0.01 V$ on the $19.99 V$ range.

From the GATE 2025 IN paper. Every question of this paper · Download the full paper · All 2 Digital instruments questions, with notes