Digital Voltmeters Questions and Answers

Answer: B

The bandwidth is 1.25 Hz.

A dual slope voltmeter integrates the input over a fixed time and so behaves like an averaging filter. For an integration (measurement) time T, the effective bandwidth of such an averaging process is taken as \(1/2T\):

\[ \begin{aligned} B &= \frac{1}{2T} = \frac{1}{2 \times 0.4\ \text{s}} \\ &= 1.25\ \text{Hz} \end{aligned} \]

The option 2.5 Hz is \(1/T\), the measurement rate, not the bandwidth. The values 0.8 Hz and 0.6 Hz do not follow from the gate time.

Answer: B

The correct matching is a-iii, b-ii, c-i, d-iv.

An n-bit ADC can show the codes 0 to 2ⁿ - 1, so a display reading needs the smallest ADC whose top code is not exceeded:

\[ \text{8-bit: }0\text{ to }255 \]

\[ \text{10-bit: }0\text{ to }1023 \]

\[ \text{12-bit: }0\text{ to }4095 \]

\[ \text{16-bit: }0\text{ to }65535 \]

132 is at most 255, so an 8-bit ADC is enough: (c) with (i). 893 is above 255 and at most 1023, so 10-bit: (b) with (ii). 1072 is above 1023 and at most 4095, so 12-bit: (a) with (iii). 59705 is above 4095 and at most 65535, so 16-bit: (d) with (iv).

The other codes break at least one of these ranges, for example putting 893 on an 8-bit ADC, which cannot show a number above 255.

Answer: D

The reading that needs a 4½ digit meter is 1.4856 mV.

A 4½ digit display has four full digits (0-9) and a leading half digit that can only be 0 or 1, so its maximum count is 19999. The reading 1.4856 has five digits with a leading 1, which fits exactly.

1.999 mA and -1.999 µV have four digits with a leading 1, which a 3½ digit meter (maximum count 1999) can already show, and so can 1000 V. Only 1.4856 mV requires the extra digit.

Answer: D

The resolutions are 0.001 V and 0.01 V.

A 3½ digit meter has a maximum count of 1999, so its resolution is one count in the last digit. On the 1 V range the display reads up to 1.999 V, so the smallest step is 0.001 V. On the 10 V range it reads up to 19.99 V, so the smallest step is 0.01 V.

\[ \begin{aligned} \frac{1\ \text{V}}{1000} &= 0.001\ \text{V} \\ \frac{10\ \text{V}}{1000} &= 0.01\ \text{V} \end{aligned} \]

The other options are ten or a hundred times too coarse on one or both ranges.