E E 1205 Measurements Data Accuracy Measurements Essential

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 Voltage Current Power/Energy Luminosity

Representing Data • Significant Digits – 3. 14159 – 2. 73 (6 sig. digits) (3 sig. digits) • Decimal Places – 3. 14159 – 0. 036 (5 dec. places) (3 dec. places)

Representing Data • Scientific Notation – 7. 382 x 10 -8 – -4. 690 x 105 • Engineering Notation – 45. 2 x 10 -6 – -613. 8 x 103

Rounding Off Numbers • 52. 3691 – 52. 369 – 52. 37 – 52. 4 • 73. 85 – 73. 8 • 27. 55 – 27. 6

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 cm 2 , not 509. 64

Measurement Accuracy and Precision

Voltage Divider Circuit

Loaded Voltage Divider

Voltage Divider Equations Unloaded: Loaded: If RL >> R 2:

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

Current Divider Circuit (2/2) In general:

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

A D’Arsonval Voltmeter

D’Arsonval Voltmeter • Small voltage rating on movement (~50 m. V) • Small current rating on movement (~1 m. A) • Must use voltage dropping resistor, Rv

Example: 1 Volt F. S. Voltmeter Note: d’Arsonval movement has resistance of 50 W Scale chosen for 1. 0 volt full deflection.

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

D’Arsonval Ammeter • Small voltage rating on movement (~50 m. V) • Small current rating on movement (~1 m. A) • Must use current bypass conductor, Ga

Example: 1 Amp F. S. Ammeter Note: d’Arsonval movement has conductance of 0. 02 S Ga = 19. 98 S has ~50. 050 m. W resistance. Scale chosen for 1. 0 amp full deflection.

Example: 10 Amp F. S. Ammeter Ga = 199. 98 S has ~5. 0005 m. W resistance. Scale chosen for 10 amp full deflection.

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

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

Example: Voltage Measurement Measured Voltage:

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

Another Voltage Measurement (2/2) Measured Voltage:

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

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

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

Another Current Measurement (2/2) Measured Current:

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

How the DVM Works

DVM Example If

Hall Effect Transducer • Use as Gaussmeter • Use as Wattmeter

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

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

Ohmmeter Example 10 m. A Full Scale (Outer Numbers) Rb+Radj+Rd’A=150 W Inner (Nonlinear) Scale in Ohms Vb=1. 5 V

Wheatstone Bridge Vab= 0 and Iab= 0 Vad = Vbd I 1 = I 3 I 2 = I x R 1 I 1=R 2 I 2 R 3 I 3=Rx. Ix

Example: Wheatstone Bridge I=2 A