Electrical and Electronic Measurements

ELECTRONIC INSTRUMENTATION AND MEASUREMENTS Second Edition David A. Bell

UNITS,DIMENSIONS, AND STANDARDS CHAPTER ONE UNITS,DIMENSIONS, AND STANDARDS

Units, Dimensions, and Standards Objectives: Discuss the three fundamental mechanical units in the System International (SI) . Define the SI units for some electrical and magnetic quantities. Identify the various metric prefixes اختصارات قياس. Identify the dimensions of various quantities. Define the various measurement standards المعايير القياسية and their applications.

SI - ELECTRICAL UNITS I= dq /dt The ampere (A) is the unit of electric current. The coulomb (C) is the unit of electric charge. 1 coulomb = total charge carried by 6.24x1018 electrons Charge of electron =1/ 6.24x1018 =1.602x10-19 C I= dq /dt

Emf, Potential Difference, and Voltage [ Volt (V) ] Potential Deference = power / current = P / I [ V, Watt / Ampere ] The Volt (V) is defined as the potential difference between two points on a conductor carrying a current of 1 A when the power dissipated between these two points is 1 watt.

SI ELECTRICAL UNITS Resistance [ohm (Ω)], and conductance [ Siemens (S) ] Resistance (R) = voltage / current = V / I [ Ω ] The ohm (Ω) is the unit of resistance which defined as the resistance which permits a current flow of 1 ampere when a potential difference of 1 volt is applied to the resistance . Unit of conductance is Siemens (S), where: Conductance (G)=1/Resistance =1/R [S]

Magnetic Flux(Ф) And Flux Density (B) The Weber (Wb) is the SI unit of Flux Ф. Where as , Tesla (T) is the SI unit of Flux Density B E = N dФ/dt [V, Turns Wb/Sec] The Weber is define as: The magnetic flux which linking a single turn coil produces an emf of 1V, when the flux is reduced to zero at a constant rate in 1 Sec.

Flux Density (B) As Flux Density (B) is define as the magnetic flux per unit area: B = Ф / Area [ T, Wb/m2 ] Then Tesla is define as: the flux density in a magnetic field when 1 Weber of flux occurs in a plane of 1 square meter.

INDUCTANCE (L) The SI unit of inductance is the henry (H). The inductance of a circuit is 1 henry, when an emf of 1 volt is induced by the current changing at the rate of 1 A/sec. V = L di /dt

CAPACITANCE (C) The SI unit of capacitance is the farad (F) The farad is the capacitance of a capacitor that contains a charge of 1 coulomb when the potential difference between its terminals is 1 volt. C = Q / V

Temperature Scales Celsius scale (°C) is divided to 100 divisions between the freezing temperature (0°C) and the boiling temperature (100°C) of water. Kelvin scale (°K) starts at absolute zero of temperature, which corresponds to -273.15°C: (i.e. 0°C Ξ 273.15°K, and100°C Ξ 373.15°C)

Other System of Units English (American / Imperial) system of units: It is measured in (Foot for length- Pound رطل for mass- Second for time) CGS systems of units : It is measured in (Cm-Gram-Second) Appendix 1 provides a list of conversion table between one system to SI or vice versa.

Example (1): A bar magnet with a 1 inch square cross section is used to have a total magnetic flux of 500 Maxwell. Determine the flux density in Tesla. Solution: From Appendix 1, Total flux, Ф = (500 Maxwell) x 10-8 Wb =5 µ Wb area, A = (1 inch square )x (2.54 x 10-2)2m2 = (2.54)2 x 10-4 m2 flux density, = β = Ф/A = 5 µ wb / 2.542 x 10-4 m2 = 7.75 mT

Example(2): The normal human body temperature is given as 98.7°F. Determine the equivalent Celsius and Kelvin scale temperatures. Solution: From Appendix 1, Celsius temperature = °F – 32 / 1.8 = 98.7-32/ 1.8 = 37°C Kelvin temperature =(°F – 32 / 1.8) + 273.15 = 310.15°K

DIMENSIONS The dimension are useful in deriving some relations between the used quantities in equations. The dimension of both sides of the equation must be equal. area = length x length The dimension of area are [L2]

DIMENSIONS Similarly, Force= mass x acceleration = mass x (Length/Time)/time = [M] [LT-2] Work= Force x distance = [ MLT-2 ] [ L ] =[ML2T-2]

STANDARDS Working standards: Electrical measurement standards are precise resistors, capacitors, inductors, voltage sources, and current sources, which can be used for comparison purposes when measuring electrical quantities .

Working standards For example, resistance can be accurately measured by means of Wheatstone bridge which uses a standard resistor. Standard resistors, capacitors, inductors usually found in an electronics laboratory are classified as working standards.

Working standards Working standard resistors are normally constructed of manganin, which have a very low temperature coefficient. e.g. precise resistors, capacitors, inductors, voltage sources. Their typical accuracies are better than ±1%.

Standards Classifications International Standards (Class A) are the highest level of accuracy. They are used to check the accuracy of Primary Standards. Primary Standards (Class B) are maintained at institutions in various countries. They have high accuracy. They are used to check the accuracy of Secondary Standards.

Secondary standards (Class C) are employed in industries for to check the accuracy of the working standards. Working standards are used as a measurement references on a day to day basis in all electronics Laboratories.

Sheet (1) Review Question: (1)- State the SI units and unit symbols for force, and work, then define each unit. (2)- State the SI units and unit symbols for energy and power, then define each unit. (3)- State the SI units and unit symbols for electric current , and charge, then define each unit. (4)- State the SI units and unit symbols for electrical resistance, and conductance, then define each unit. (5)- State the SI units and unit symbols for magnetic flux, and flux density, then define each unit.

(5)- State the SI units and unit symbols for magnetic flux, and flux density, then define each unit. (6)- State the SI units and unit symbols for inductance, and capacitance, then define each unit . (7)- Name the two SI temperature sales, and identify the freezing and boiling temperatures of water for each scale. (8)- List the various levels of measurement standards, and discuss the application of each classification.

(1)- perform the following conversion: Problems: NOTE: Use the Appendix 1 to perform all required unit conversions (1)- perform the following conversion: a)- 6215 miles to kilometers. b)- 50 miles per hour to kilometers per hour. c)- 12 square feet to square centimeters. (2)- Determine how long it takes light to travel to earth from a star 1 million miles Away if the speed of light is 3 x 108 m/s. (3)- The speed of sound in air is 345 m/s. Calculate the distance in miles from a thunderstorm when the thunder is heard 5 s after the lightning flash.

(4)- A 140 Ib person has a height of 5 ft 7 in (4)- A 140 Ib person has a height of 5 ft 7 in. Convert these measurements into kilograms and centimeters. (5)- Calculate the Celsius and Kelvin scale equivalent of 80° F. (6)- Determine the dimension of area, volume, velocity and acceleration. (7)- Determine the dimension of: Force – Work – energy and power. (8)- Determine the dimension of charge, voltage and resistance. (9)- Determine the dimension of: Capacitance and inductance.