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E E 1205

E E 1205. Measurements, Data & Accuracy. Measurements. Essential to Engineering Multitude of Sensors Electromagnetic Hall Effect Photonic Simple Yardstick Spring Scales Measuring cups. Measurements. Electrical Conductivity Field Strength Electric Magnetic Frequency/Timing

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E E 1205

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  1. E E 1205 Measurements, Data & Accuracy

  2. Measurements • Essential to Engineering • Multitude of Sensors • Electromagnetic • Hall Effect • Photonic • Simple • Yardstick • Spring Scales • Measuring cups

  3. Measurements • Electrical • Conductivity • Field Strength • Electric • Magnetic • Frequency/Timing • Voltage • Current • Power/Energy • Luminosity

  4. Representing Data • Significant Digits • 3.14159 (6 sig. digits) • 2.73 (3 sig. digits) • Decimal Places • 3.14159 (5 dec. places) • 0.036 (3 dec. places)

  5. Representing Data • Scientific Notation • 7.382 x 10-8 • -4.690 x 105 • Engineering Notation • 45.2 x 10-6 • -613.8 x 103

  6. Rounding Off Numbers • 52.3691 • 52.369 • 52.37 • 52.4 • 73.85 • 73.8 • 27.55 • 27.6

  7. Excessive Significant Digits • Do not display more significant digits than can be justified • Area calculation: l = 27.4 cm, w = 18.6 cm A = l x w = 510 cm2 , not 509.64

  8. Voltage Divider Circuit

  9. Loaded Voltage Divider

  10. Voltage Divider Equations Unloaded: Loaded: If RL >> R2:

  11. Current Divider Circuit (1/2) If there are only two paths:

  12. Current Divider Circuit (2/2) • In general:

  13. D’Arsonval Meter Movement • Permanent Magnet Frame • Torque on rotor proportional to coil current • Restraint spring opposes electric torque • Angular deflection of indicator proportional to rotor coil current

  14. A D’Arsonval Voltmeter

  15. D’Arsonval Voltmeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use voltage dropping resistor, Rv

  16. Example: 1 Volt F.S. Voltmeter Note: d’Arsonval movement has resistance of 50 W Scale chosen for 1.0 volt full deflection.

  17. Example: 10V F.S. Voltmeter Scale chosen for 10 volts full deflection.

  18. D’Arsonval Ammeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use current bypass conductor, Ga

  19. Example: 1 Amp F.S. Ammeter Note: d’Arsonval movement has conductance of 0.02 S Ga = 19.98 S has ~50.050 mW resistance. Scale chosen for 1.0 amp full deflection.

  20. Example: 10 Amp F.S. Ammeter Ga = 199.98 S has ~5.0005 mW resistance. Scale chosen for 10 amp full deflection.

  21. Measurement Errors • Inherent Instrument Error • Poor Calibration • Improper Use of Instrument • Application of Instrument Changes What was to be Measured • Ideal Voltmeters have Infinite Resistance • Ideal Ammeters have Zero Resistance

  22. Example: Voltage Measurement True Voltage: (If voltmeter removed)

  23. Example: Voltage Measurement Measured Voltage:

  24. Another Voltage Measurement (1/2) True Voltage: (If voltmeter removed)

  25. Another Voltage Measurement (2/2) Measured Voltage:

  26. Example: Current Measurement (1/2) True Current: (If ammeter replaced by short circuit)

  27. Example: Current Measurement (2/2) Measured Current:

  28. Another Current Measurement (1/2) True Current: (If ammeter replaced by short circuit)

  29. Another Current Measurement (2/2) Measured Current:

  30. A Digital Voltmeter • Integrating Converter • Dependent on Vref • Dependent on Temperature • Independent of RC

  31. How the DVM Works

  32. DVM Example If

  33. Measuring Resistance • Indirect • Measure Voltage across Resistor • Measure Current through Resistor • Calculate Resistance (Inaccurate) • d’Arsonval Ohmmeter • Very Simple • Inaccurate • Wheatstone Bridge (Most Accurate)

  34. D’Arsonval Ohmmeter Need to adjust Radj and zero setting each scale change.

  35. Ohmmeter Example 10 mA Full Scale (Outer Numbers) Rb+Radj+Rd’A=150 W Vb=1.5 V Inner (Nonlinear) Scale in Ohms

  36. Wheatstone Bridge Vab= 0 and Iab= 0 Vad = Vbd I1 = I3 I2 = Ix R1I1=R2I2 R3I3=RxIx

  37. Example: Wheatstone Bridge I = 2 A

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