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Practice Test — Sensors & Measurement Math
Practice Test — Sensors & Measurement
Practice Test — 20 Questions
1. A sensor: $V = 0.03T + 0.2$. Output at 80°C?
2. Same sensor reads 1.7 V. Temperature?
3. Amplifier gain: input 2 mW, output 200 mW. dB?
4. −20 dB in power. What fraction remains?
5. Voltage triples. How many dB?
6. $25.0 \pm 0.5$ m. Relative error?
7. $a = 10 \pm 0.5$, $b = 4 \pm 0.2$. Error in $a \times b$?
8. 10-bit ADC, 0–5 V. Resolution?
9. Nyquist rate for 8 kHz signal?
10. 12-bit ADC, value 2048 out of range 0–4096, range 0–3.3 V. Voltage?
11. SNR = 50 dB. Power ratio?
12. Chain: +15 dB amp, −5 dB cable, +20 dB amp. Total?
13. $r = 3.0 \pm 0.1$. Error in $r^3$?
14. Strain gauge: $R = 350(1 + 2\epsilon)$. $R$ at $\epsilon = 0.005$?
15. How many bits for at least 10000 levels?
16. $v = d/t$, $d = 50 \pm 1$ m, $t = 5.0 \pm 0.1$ s. $v$ and error?
17. What does "sensitivity" mean for a sensor?
18. Is a thermocouple linear or exponential?
19. $2^{14} = ?$
20. If you don't sample fast enough, what artifact appears?
Show Answer Key
1. $0.03(80) + 0.2 = 2.6$ V
2. $T = (1.7-0.2)/0.03 = 50$°C
3. $10\log(100) = 20$ dB
4. $10^{-2} = 1/100$ (1%)
5. $20\log(3) \approx 9.5$ dB
6. $0.5/25 = 2\%$
7. Relative: $5\% + 5\% = 10\%$. Absolute: $0.10 \times 40 = 4$
8. $5/1024 \approx 4.88$ mV
9. 16 kHz
10. $2048 \times 3.3/4096 = 1.65$ V
11. $10^5 = 100{,}000$
12. 30 dB
13. $3 \times 0.1/3.0 = 10\%$ relative error
14. $350(1.01) = 353.5$ Ω
15. $2^{14} = 16384 \geq 10000$ → 14 bits
16. $v = 10$, relative error = $2\% + 2\% = 4\%$, $\Delta v = 0.4$ → $10.0 \pm 0.4$ m/s
17. Output change per unit input change (slope of transfer function).
18. Approximately linear over moderate ranges.
19. 16384
20. Aliasing — false low-frequency signals appear.