(Solved): 4. a) An RTD (Resistance Temperature Detector) sensor forms one arm of a Wheatstone bridge circuit ...

4. a) An RTD (Resistance Temperature Detector) sensor forms one arm of a Wheatstone bridge circuit as shown in Figure Q4. The values of the fixed resistors are as shown in the figure. b) c) Assume the RTD is a PT100 sensor (implying its resistance is 10002 at 0°C). The resistance of the RTD RRTD at temperature T can be expressed as: RRTD= Ro(1 + a(T-To)) where Ro = 1000, To = 0°C and sensor temperature coefficient a = 0.003925°C-1. 10V 1kQ2 Vo 10092 out 1kQ RTD Figure Q4 i) Determine ambient temperature T when the bridge is balanced. ii) If the RTD is immersed in a temperature calibration bath maintained at T = 100°C, determine the output voltage Vout. iii) Determine the sensitivity of the measurement, in terms of bridge output versus ambient temperature. Consider a Type K thermocouple used to measure engine exhaust gas temperature in an automotive application. While taking a measurement, an emf of 28.963mV is recorded relative to the reference junction temperature of 23°C. Determine the measured temperature. An absolute rotary optical encoder is used to accurately position multiple stabilizers for a crane. If the encoder has 13 tracks, determine its angular resolution. F 0=17 =A ?? ? = ±? V= Adla Al/ AR/F E G=1+2v=- Damping Ratio Peak Magnitude (dB) Damping Ratio Peak Magnitude (dB) 73.144471 33.979771 67.734829 27.960535 64.336221 24.440882 61.881412 21.945154 59.963713 58.391265 57.059082 55.903632 54.883594 53.970599 47.956898 44.436352 41.938025 40.000032 38.416519 37.077651 35.917856 34.894836 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 0.3 0.4 0.5 0.6 0.7 20.01087 18.432037 17.098772 15.945483 14.929871 14.023048 8.1360878 4.8465611 2.6954074 1.2493874 0.35457534 0.001737526 F (s) 1. 2. 4. 5. 6. 3.-—-/ 7. 8. 9. 10. 11. 12. 13. 1 1 3 --- S S 1 s+a 1 (s+a)" 1 s(s+a) Laplace Table 1 s(s+ a)(s+b) s+a s(s+ a)(s+b) 1 (s+a)(s+b) S (s+ a)(s+b) Laplace Transform Table (1) 5 (1) 1 or u(1) 1-u(t) or f 1 (n-1)! 1 (n-1)! -(1-e") a u(t)-(-a) rectangular pulse 051 -(1- ab 1 la ab b-a 1 a-b unit impulse at 1=0 unit step starting at 1 = 0 ramp function - n = positive integer unit step starting at 1 = a b(a-a) b-a exponential decay -e + b-a b-a n=positive integer -M (ae -be") a(a?b)] b-a