Transducers in Measurement Questions and Answers

Answer: C

The resistance changes by 0.1%.

First find the strain from Hooke's law, then multiply by the gauge factor, \(\frac{\Delta R}{R} = G\varepsilon\).

\[ \begin{aligned} \varepsilon &= \frac{\sigma}{E} = \frac{100 \times 10^{6}}{200 \times 10^{9}} = 5 \times 10^{-4} \\ \frac{\Delta R}{R} &= 2 \times 5 \times 10^{-4} = 10^{-3} \end{aligned} \]

A fractional change of \(10^{-3}\) is 0.1%. 0.01% and 1% come from slipping a factor of ten in the prefixes M and G, and 10% would mean an impossible strain for steel.

Answer: B

The maximum measurable acceleration is 1200 m/s².

The mass hits the stop when the spring is deflected by 0.02 m. At that point the spring force equals the force needed to accelerate the seismic mass:

\[ \begin{aligned} kx &= ma \\ a &= \frac{kx}{m} = \frac{3 \times 10^{3} \times 0.02}{0.05} \\ &= \frac{60}{0.05} = 1200\ \text{m/s}^{2} \end{aligned} \]

The square-root values printed with the question are not needed. 600 and 300 come from halving or quartering the displacement, and 4.9 m/s² is about half of g, which has nothing to do with the data.

Answer: C

A thermistor is suitable for low span but high sensitivity.

A thermistor's resistance changes by several percent per degree, much more than a metal resistance thermometer's, so it is very sensitive. But its resistance-temperature relation is strongly non-linear (exponential), and its usable range is limited to a few hundred degrees, so its span is small.

High span with low sensitivity describes thermocouples or platinum resistance thermometers better. A device with both high span and high sensitivity, or with both low, does not describe the thermistor's characteristic trade-off.

Answer: B

A 3 and a half digit display is the format of a digital voltmeter, so a matches 4. Pt-100 is a platinum resistance sensor that measures temperature, so b matches 3. An RTD is read through a bridge circuit, so c matches 2. Interference is reduced by guarding and shielding, so d matches 1. The code is 4 3 2 1. The code 1 2 3 4 is the reverse, and 3 1 4 2 and 3 4 1 2 mismatch the first pair. The answer is 4 3 2 1.