Training Resistive Sensors Practice Test — Resistive Sensors
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Practice Test — Resistive Sensors

24 min Resistive Sensors

Practice Test — Resistive Sensors

This practice test pulls together the resistive-sensor content: RTDs, thermistors, strain gauges, potentiometers, and photoresistors. Work through the twenty questions without looking back at the lesson notes, then check your answers against the key at the bottom.

Aim to explain each step as you go, in the analytical style used throughout Webster and Pallàs-Areny. If a problem stumps you, revisit the worked example in the corresponding lesson before moving on.

Practice Problems

1. Compute $R$ for a Pt100 at 150 °C (linear model).
2. What is the sensitivity of a Pt1000 near 0 °C?
3. A Pt100 reads 92 Ω. Estimate $T$ (linear).
4. With $\delta = 3\,\text{mW}/^\circ\text{C}$ and $I = 1\,\text{mA}$ through 110 Ω, estimate ΔT_self-heating.
5. NTC: $R_0 = 10\,\text{k}\Omega$ at 25 °C, $\beta = 4000$. Find $R$ at 60 °C.
6. Same NTC: $R = 3\,\text{k}\Omega$. Find $T$ (°C).
7. Why does the β model break down at extreme temperatures?
8. What is the gauge factor definition?
9. Steel beam ($E = 200\,\text{GPa}$), $\epsilon = 400\,\mu\epsilon$. Find $\sigma$.
10. 350 Ω foil gauge, $GF = 2.0$, $\epsilon = 800\,\mu\epsilon$. Find $\Delta R$.
11. Semiconductor gauge with $GF = 100$, same strain. Find $\Delta R$.
12. Unloaded 20 kΩ pot, $V_s = 3.3\,\text{V}$, $x = 0.25$. $V_{\text{out}} =$?
13. Same pot, $R_L = 10\,\text{k}\Omega$, $x = 0.5$: find loading error.
14. LDR: $R_1 = 1\,\text{k}\Omega$ at 100 lux, $\gamma = 0.9$. Find $R$ at 1000 lux.
15. What causes the loading error in a potentiometer?
16. Name one sensor where the resistance decreases as temperature rises.
17. Name one sensor where the resistance increases with temperature.
18. What is Callendar–Van Dusen named after?
19. Why is Pt100 more accurate than a typical thermistor for absolute temperature?
20. Why are strain gauges almost never used alone (single resistor)?
Show Answer Key

1. $R = 100(1 + 3.85\times10^{-3}\cdot 150) = 157.75\,\Omega$.

2. $S = 3.85\,\Omega/^\circ\text{C}$.

3. $T = (0.92 - 1)/3.85\times10^{-3} \approx -20.8\,^\circ\text{C}$.

4. $P = (10^{-3})^2(110) = 1.1\times10^{-4}\,\text{W} = 0.11\,\text{mW}$. $\Delta T = 0.11/3 \approx 0.037\,^\circ\text{C}$.

5. $\ln(R/10\text{k}) = 4000(1/333.15 - 1/298.15) = 4000(-3.52\times10^{-4}) = -1.408$. $R = 10000 e^{-1.408} \approx 2.45\,\text{k}\Omega$.

6. $\ln(0.3)/4000 = -3.01\times10^{-4}$. $1/T = 3.354\times10^{-3} - 3.01\times10^{-4} = 3.053\times10^{-3}$. $T \approx 327.5\,\text{K} \approx 54.4\,^\circ\text{C}$.

7. Because $\beta$ itself varies with temperature; the model fits only a limited range well.

8. $GF = (\Delta R/R)/\epsilon$.

9. $\sigma = 200\times10^9\cdot 4\times10^{-4} = 8\times10^7\,\text{Pa} = 80\,\text{MPa}$.

10. $\Delta R = 350\cdot 2\cdot 8\times10^{-4} = 0.56\,\Omega$.

11. $\Delta R = 350\cdot 100\cdot 8\times10^{-4} = 28\,\Omega$.

12. $V_{\text{out}} = 0.25\cdot 3.3 = 0.825\,\text{V}$.

13. Denom $= 1 + 0.25\cdot 2 = 1.5$. $V_{\text{out}} = 3.3\cdot 0.5/1.5 = 1.10\,\text{V}$ vs. 1.65 V ideal → error $\approx 33\%$.

14. $R = 1000\cdot 10^{-0.9} = 1000\cdot 0.126 = 126\,\Omega$.

15. Current drawn by the load makes the wiper-to-ground and wiper-to-supply sections no longer behave as a simple divider.

16. NTC thermistor (and all intrinsic semiconductor sensors).

17. Platinum RTD, copper RTD, PTC thermistor.

18. British engineers Hugh Callendar and Milton Van Dusen, who characterized platinum resistance thermometry.

19. Platinum has a well-defined, internationally standardized temperature coefficient (ITS-90); NTC β varies part-to-part.

20. Signal is only millivolts; a bridge is needed to amplify and reject common-mode drift.

Potentiometers and Photoresistors Back to Module