Article – 3



Chapter-3

Measurement and Measuring Systems.

3.1 Measurements.

3.2 Fundamental units of Measurement.

3.3 Derived units of Measurement.

3.4 Fundamental Systems of Measurements, with merits and de-merits.

3.5 Unit of Force. / Force on a current carrying conductor.

3.6 Unit of Power. Power in an electric circuit

3.7 Unit of Work or Energy.

3.8 S.I Electrical Units.

3.9 Electrical reference Standards.

3.1 Measurements.

Measurement have got very important role in every walk of life. Measurement is considered to be an essential tool for Metering as the sophistication in metering advances, the old aged to modern age metering encompasses mercury meters, electromechnical, electronic, numerical and digital meters with multi functional and multi purpose features. These features are responsible for latest advances like multi-functionality and gave birth to cordless (Wireless) tele-metering and internet / Web metering employing GSM, GPRS, EATHER NET and MODEMS ( Modulator and Demodulator) technology. Information technology have played and playing a vital role in Remote Controlled Metering / Tele-Metering like Tele-Protection.

Modern day energy meters incorporate microprocessors, registers (separate registers for maintaining time scaled energy log, Mw log, events log, for measurements and registrations / recordings), not only the energy in one direction i.e. uni-directional, they are bi-directional i.e. measure energy in both the directions and act as an import energy meter and also as an export energy meter as and when the change has occurred in direction of flow of the energy.

The same meter is multifunctional, and is being, in use as power meter, MDI (Maximum Demand Indication, even recording), single and three phase voltmeters, ammeters, frequency and power factor meter in a single module.

Transient, harmonic and phasor analysis features have also been added for in-depth analysis of the inputs (Measurands). Inputs to the Energy Meters have been received via C.T’s and P.T’s and are immune to Transients, whereby CT’s and P.T’s may generate transients, as they have gone trough change of energy level i.e. switch from one steady state condition to an-other one. The unsymmetrical waveforms may be over-damped, under-damped or critically damped.

The Transient analysis feature provides a in-depth analysis of these transients by recording / measuring the transients and an Engineer can device a methodology to over come from this situation. The transitory state also is accompanied by harmonics generated by C.Ts and P.Ts (Current and Potential transformers used as range extension / insulation providers) as a result of distorted waveforms at the inputs to the energy meters.

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When these distorted wave forms have been disintegrated / broken down to its constituents i.e. components called as harmonics. Harmonics are multiples or submultiples of basic frequency (i.e. Power Frequency of 50 Hertz or Cycles per Second). Then first, second, third, fourth, … harmonics are 100 Hz, and 150, 200, 250 Hz and so on respectively. Accordingly in-feed contains harmonics, which ultimately affect the meter behavior so is the need of harmonic analyzers. To get rid of the most severe harmonic, filters have been suggested by engineers to safeguard the gadgetry from ill-effects of most prominent harmonic. Yet remaining harmonics may affect the behavior of the meter as input to the meter may get corrupted.

Additionally, energy meters are not meant for active energy only, instead they also register “Apparent” and “Reactive” energy in four quadrants. Further recording feature includes, capability to register all of the three types of electrical energies (Active, Reactive, and Apparent) in single gadgetry,

In order to have a master of Energy Meters, and their testing, necessitates to acquire knowledge of Measurements and Measuring Systems, which will be helpful as you will encounter/ gone through the testing phase of the energy meters catering for other measurands also. Hence author wishes / advise the reader to get appropriate knowledge of the measurements that is required for both Metering and Standardizations.( In some instances, accuracy class of the energy meters used, demand new standard i.e. from +2 ℅ to either +1 % , or + 0.5 % or + 0.2 % etc or 0.2S means accuracy is 0.2.% at specific loading condition and S stands for precise / accurate measurement purpose ).

Knowledge of Measurements is also important from the view point, that as the gadgetry to measure multiple measurands, supplied as input to the metering, is of what quality. Its importance can be more pronounced by way of analogy, where by, the food supplied as input to human beings / animals determines the healthiness plus proper dose of food as input quantities, determine the life expectancy of living beings.

Similarly proper input of the quantity to be measured, gadgetry will behave similarly. A competent engineer should undermine this aspect too, as he will be given responsibility to verify the accuracy of measurements while testing of the energy meters, in particular, will be carried out. He should be gone through different phases in order to fix the problem i.e weather the energy meter under test is malfunctioning, due to some problem with the energy meter. In order to pin point the problem, i.e. is there any problem with the measuring instrument / testing equipment, or their may be some problem with the input quantities to be measured.

Hence well acquainted engineer must have sufficient knowledge of measurements prior to proceed for testing. It has been a experience that in more than 20 % cases, while going through testing phase, that input quantity variations may create hindrances in achieving the required test results.

One should also realize its importance of measurements for research work in the field of science i.e. use of the fundamental units of measurements and other derived units from the fundamental units, to describe quantitatively the parameter to be measured (measurands). The analogy came from knowledge, which is of two types i.e. 1-Acquired Knowledge, 2- Revealed Knowledge. First one is being acquired through worldly means, where as second one is not an acquire-able; instead it is being revealed / gifted by the All Mighty GOD, to selected ones through his angels.

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Analogy and Duality theories were also came from this thought. “Analogy means similarity” and-“Duality means second or duplicate with all the features inverted”. Spiral /Wired charged spring is the mechanical analog of electrically charged Inductor or Capacitor from electricity components as both analog being momentary energy storage devices. Similarly electricity Energy Meters and mechanical Energy Meters are analog to each other and involve measurement of energy in their relevant fields and is being used for better understanding of one or the other.

Duality theory, provide the means to identify the features of the duals with inversion. By way of duality, more comprehension, better understanding of the more complex phenomenon can be had, which will be used for both i.e. for better planning, design features as well as in R&D work (Research and development work).

Following example will clarify it. In electric circuits, duality theory is being adopted in connection with the “constant current source” and “constant voltage source”, where-in, switch is connected in series with the load for constant voltage source where as for constant current source, switch is being connected in parallel with load. All loads are connected in parallel to the constant voltage source where as all loads are connected in series to the constant current source. The source voltage of the constant voltage source remains constant and is applied to all the loads in parallel, in order to have almost constant voltages. For the case of constant current source, all of the loads are connected in series, to have the constant currents. This theory is being used in describing the salient features of each dual with inversion.

It is interesting and also important to know that Measurement had started since long, as the development of different civilizations kept in pace with the need to meet with the requirements of the human beings. It dates back to B.C (before chariest) period even earlier than that.

In the field of Physics, the earliest recorded facts in connection with the subject of “Electricity” were obtained as a result of experiments carried out by the ancient Greek Philosopher “Thales of Miletus”, about 600 B.C. , related to the forces of repulsion and attraction between bodies charged with static electricity. Those facts were qualitative only, and it was left for “Coulomb” , many centuries later, to state them in a quantitative form by his Inverse Square Law, which is the most fundamental law of electrostatics i.e.:-

F ≈ Q1 X Q2 . . . . . 3.1.1

ε X r²

Where F is the force between two small bodies charged respectively with Q1 and Q2 units of electricity, their centers being a distance r apart and ε is a constant depending upon the medium in which the bodies are situated, and is called the “Permittivity” of the medium.

In the rationalized M.K.S system of units this expression is written as:-

F = Q1 X Q2 newtons, . . . 3.1.2

4 Π ε X r²

Where F is the force in newtons, between two small bodies charged respectively with Q1 and Q2 Coulombs (units of electricity), their centers being a distance r apart in meters

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and ε = εo X εr , is a constant depending upon the medium in which the bodies are situated, and is called the “ Permittivity” of the medium with εo is the primary electric constant having a value of _____________1_____________ 36 Π X 109.

and εr is the permittivity of the medium relative to that of a vacuum. εr = 1 for a vacuum, and air may be considered to have the same value. In this system, two infinitely small bodies each having unit charge and being 01 (one ) meter apart in air experience a force of 9 X 10 raised to the power of 9 newtons.

3.2 Fundamental Units of Measurement.

There are two types of Units of Measurements, namely

a- Fundamental units.

b- Derived units.

Fundamental units consist of three basic units i.e. “Length”, “Mass” and “Time”.

There are numerous measuring systems including few following systems i.e.

1- “Apothecaries” System. (Fluid ounces, pint,.etc.)

2- “Avoirdupies” System. (tola, ounce, pound, seer, hundredweight and ton )

3- “F.P.S” (Foot, Pound, Seconds) System.

4- “C.G.S” (Centimeter, grams, Seconds) System.

5- “M.K.S” (Meter, Kilogram, Seconds) System.

6- “S.I” (International Standards) System. (In 1950, the Int’l Electro technical Commission adopted the “ampere” as basic electric unit as a fourth dimension. That is LENGTH, MASS, TIME, ELECTRIC CURRENT as basic units of measurements, having units of Meter, Kilogram, Seconds and Ampere respectively.

Each system has got its own scales for each of the fundamental and derived units.

Another classification comprises of the following measurement systems :-

a- Un-rationalized System of Measurements.

b- Rationalized System of Measurements.(M.K.S) system.

All systems of measurements depend upon the adoption of certain absolute or fundamental units.

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A - In the meter-kilogram-second (M.K.S) system, the unit of length is the meter-which is defined as equal to 1 650 763.73 wavelengths of the orange line emitted from the internationally specified Krypton discharge lamp. The meter was formerly defined as the distance between two lines on a platinum-iridium bar preserved at the International

Bureau of Weights and Measures at Sevres, France. This bar is still used as a reference standard and its exact length is periodically verified in terms of wavelengths of the radiation from the krypton lamp.

By Act of the Parliament,

1 yard = 0.9144 meter exactly.

B - The unit of “mass” is the kilogram, as defined by the platinum-iridium standard rod of mass one Kg, at mean site condition i.e. at specified gravitational force, kept at “sevres” in France (Standards Lab),

Again, by Act of Parliament,

1 pound = 0.453 592 37 kilogram exactly ≈ 0.4536 kg.

C - The unit of the” time” is the second, defined as the interval occupied by 9 192 631 770 cycles of the radiation corresponding to the transition of the caesium-133 atom and is approximately 1 / 86 400 of the mean solar day.

3.3 Derived Units of Measurement.

A - Unit of force.

In the M.K.S system, the unit of force is the Newton (in commemoration of the great English scientist, “Sir Isaac Newton”,(1642-1727) and is defined as the force, acting on a mass of 1 kilogram, gives it an acceleration of 1 meter per second per second.

Hence the force, F (Newton), required to give a mass of m (kilogram) an acceleration of a (meters/second²) is:

F (N) = m (kg) X a (m/s²)………………………………..(3.3.1)

An alternative unit of force in M.K.S system is the kilogram force. It has been decided by the international Organization for Standardization to define the unit in terms of the gravitational force on unit mass at a point on the earth’s surface (approximately at latitude 45º N), where the acceleration due to gravity is 9.806 65 m/s²; hence 1 kilogram-force is the force which, acting on a mass of I kilogram, gives it an acceleration of 9.806 65 m/s².

The British Standards institution recommends the abbreviation “kgf” for “kilogram-force” to distinguish it from “kg” for “kilogram-mass”. (Like wise, the abbreviation for “pound-force” is “lbf”).

Since the acceleration produced by I kgf acting upon a given mass is 9.806 65 times that due to 1 newton.

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Hence M.K.S system of measurement is more practical and realistic. (Like wise bar pressure for gases is more practical and realistic as 1-bar barometric pressure =14.7 lbf /square inch, at mean sea level, of F.P.S system). Similarly 200-bar CNG gas filling pressure is equivalent to:

14.7 lbf /sq-inch X 200 bars = 2940 lbf / sq-inch ≈ 3,000 lbf / sq-inch

i.e. 200-bar gas pressure means, it is 200 times greater than the normal barometric pressure. So bar-gas pressure is merely indicative of, how many times grater is the gas pressure as compared to 1- bar atmospheric / barometric pressure.

Therefore 1 kilogram-force = 9.806 65 Newtons.

It follows that the force, F, in kilogram-force, required to give a mass of 1 kilogram, an acceleration of a meters/ second² is given by:

F = m (kg) X a (m/s²)

9.806 65(Newtons/kilogram-force).

F = m X a kilogram-force ………………….…..(3.3.2)

9.806 65

F ≈ m X a kilogram-force …..………………….(3.3.3)

9.81

Example 3.1: Calculate the numerical relationship between the pound-force and the Newton. Assume 1 kgf = 9.81 N

Solution:

Since 1 lb = 0.4536 kg.

1 lbf = 0.4536 kgf

= 0.4536 X 9.81 = 4.45 Newton,

or 1 N = 0.225 lbf

* In the foot-pound-second (F.P.S) system of units, a force of 1 poundal, applied to a mass of 1 lb, gives an acceleration of 1 ft / second², and a force of 1 pound-force gives an acceleration of 32.174 ft / second² (= 9.806 65 m/s² ). Hence 1 lbf = 32.174 poundals and

F (in pounds) = m (lb) X a (ft/s²)

32.174 (poundals/pound-force).

F = m X a pounds-force………………………..(3.3.4)

32.174

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F ≈ m X a pound-force…………………….…..(3.3.5)

32.2

The relative magnitudes of the Newton, the kilogram-force and the pound force are indicated by the lengths of lines in fig 3.1

1 Newton ------

1 kgf ----------------------------------------------------------------

1 lbf --------------------

Fig.3.1: The relative magnitudes of the Newton, the kilogram-force and the pound-force.

Example 3.2 : A force of 50 N is applied to a mass of 200 kg. Calculate:

a) The force in pounds-force, and,

b) The acceleration in meters/second², assuming the frictional resistance to be negligible.

(a) Since 1 lbf = 4.45 Newton

Therefore: 1 N = 0.225 lbf

Therefore Accelerating force = 50 X 0.225 = 11.25 lbf

(b) From expression (3.2.2.1),

50 = 200 a.

a = 50 / 200 = 0.25 m/second²

B – Unit of Turning Moment or torque.

If a force of F Newtons is acting at right angle to a radius of d meters from a point ;

Turning moment or torque about that point = F X d Newton-meter… …..(3.3.6)

≈ F X d kilogram-force-meters

9.81

C – Unit of Work or Energy .

In the M.K.S system, the unit of energy is the joule ( after an English physicist, James P, Joule, 1818-89), namely thr work done when a force of 1 newton acts for a distance of 1 meter in the direction of the force.

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Hence if a force of F newtons acts for a distance of d meters in its own direction ;

Work done in joules = F (newtons) X d ( meters).

= F X d newton-meters……………………..(3.3.7)

If a body of mass m kilograms has a velocity of v meters/second,

Kinetic Energy = ½ mv² …………………(3.3.8)

By experiments, it has been found that 1 kilocalorie = 4187 joules.

* The summary of numerical relationships between the various units of energy used in engineering are appended on page ___15______as a ready reference ;

Example 3.3 : Derive the mathematical relationship between the foot pound-force and the joule.

Solution ;

Since 1 ft = 0.3048 m

1 lbf = 4.45 N

Therefore 1 ft lbf = 0.3048 X 4.45

= 1.356 meter-newton or joule

Or 1 joule = 1/1.356 = 0.7374 ft lbf.

D – Unit of Power.

Since power is the rate of doing work, it follows that in M.K.S system, the unit of power is the joule/second or “watts” (after the famous Scottish engineer, James Watt, 1736-1819).

In practice, the watt is often found to be inconveniently small and so the Kw (Kilo-Watt = 1000 Watts) is frequently used by the general consumers of electricity, but for bulk power kilowatt is still a small unit, so Mw (Mega-Watt = 1000 Kw = 1000000 Watts) or Gw(Giga-Watts = 1000 * 1000 * 1000 Watts).

Similarly, when we are dealing with a large amount of energy, it is more convenient to express the later in Kilowatt-hour rather than in joules.

1 Kilowatt-hour (or Kwh ) = 1000 Watt-hours,

= 1000 X 60 X 60,

= 3 600 000 watt-second or joule.

1 megewatt (or MW) = 1000 KW = 1 000 000 W.

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If T newton meters be the torque due to force acting about an axis of rotation, then for an angular displacement of θ radians in the direction of the force, the work done = W = T θ joules,

Therefore, T newton meters = W / θ joules / radians.

i.e. 1 newton meter = 1 joule radian.

If ω = angular velocity in radians / second.

Then, Power = d W / dt = T, d θ / dt = ω T Watts.

* The summary of numerical relationships between the various units of energy used in engineering are appended as below (for ready reference) ;

Summary of important formulae and relationships ;

F = m (kg) X a (m/s²) ……………...(3.3.1)

Work done in joules = F (newtons) X d ( meters)….…………..(3.3.7)

= F X d newton-meters.

Kinetic Energy (joules) = ½ m (kg) X v² (m/s)² …………………(3.3.8)

Power(Watts) = 2 Π T (newton-meter) X n (rev/second)………(3.3.9)

1 lbf = 4.45 N

1 N = 0.225 lbf

1 kgf = 9.806 65 N

1 ft lbf = 1.356 J

1 KWh = 3 600 000 J

1 hp = 746 Watts

1 Kcal = 4187 J

1 British Thermal Unit (B.T.U) = 0.252 Kcal

= 1055 J

Q (coulombs) = I (amperes) X t (seconds).

Mass of element liberated from electrolyte ;

= z (g/C) X I (amperes) X t (seconds).

= z (g/C) X Q (coulombs).

Ohm’s Law : I = V / R, V = I R or R = V /I

Electrical Power = I² R = I V = V² / R (Watts).

Electrical Energy = I V t (joules).

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3.4 Fundamental Systems of Measurement.

Measuring Systems along with there dimensions, are essential tool for the proof of the validity / correctness of any mathematical equation, specially newly formulated mathematical equations in the field of Physics ( specially for Electrical / Mechanical Engineering) incorporating units and dimensions.

When one will be familiar with Measuring Systems and unit used in, can easily transform his day to day engineering needs and also be considered as well acquainted with respect to quantities to be measured (measurands) and determine the scope and need of the measuring instruments, their class of accuracy, specs (specifications), there ratings and other features necessary to complete his tasks in a stipulated time frame with ease, better accuracy, precision etc. He would be better conversant with other fellows in the same field and can convey his ideas to others, easily.

.

In the present age, when we look back to measuring systems, we find “ Apothecaries” and “ Avoirdupies” systems of measurements though little bit older documented systems - still applied generally in different countries and are seldom used in electrical engineering and are described as below :-

3.4-a. Measuring Systems of ordinary Quantities.

1-Apothecaries System of Measurements.

1 fluid ounce = 8 fluid drams = 28.413 cm³.

1 pint = 20 fluid ounces = 568.26 cm³.

2- Avoirdupies System of Measurements.

1 tola = 0.41 ounces = 11.6363 grams.

1 ounce = 437.5 grains = 28.350 grams.

1 pound = 16 ounces = 0.4536 kg.

1 seer = 16 chattak = 0.93 kg.

1 stone = 14 pounds 6.3503 kgs.

1 hundredweight = 112 pounds = 50.802 kgs.

1 ton = 20 cwt = 1.0161 tonnes.

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3.4-b. Measuring Systems of Electrical Quantities.

3- F.P.S. ( Foot, Pound, Seconds) System.

This system was developed during 19th century, where by most scientists and engineers find their derivations using fundamental units of length, mass and time as foot, pound and second. From on word, due to names of dimensions of measurements of the fundamental units, the system of dimensions was termed as F.P.S (Foot, pound, second) system. In this system

The few derived units are ;

Force = pound force = lbf

= 0.225 lbf = 1 newton.

Speed = ft /second.

Acceleration = ft / second².

4- C.G.S. (Centimeter, grams, Seconds) System.

This system was also developed during 19th century, where by most scientists and engineers find their derivations using fundamental units of length, mass and time as Centimeter, grams, Seconds. From on word, due to names of dimensions of measurements of the fundamental units, the system of dimensions was termed as C.G.S (Centimeter, grams, Seconds) system. In this system

5- M.K.S. ( Meter, Kilogram, Seconds) System.

Or

THE RATIONALIZED M.K.S SYSTEM OF UNITS.

Up till 1960, C.G.S. system of units was used mostly, but the rationalized M.K.S. (meter-kilogram-second) system took its place afterword and is being

used increasingly, specially in the teaching of electrical engineering and it has been adopted through out. The derivation of the system will be discussed soon after covering its advantage over the C.G.S. system, which it replaces.

It has important advantages in that, practical units-ampere, volt, ohm, etc.- are used through out and the conversion factors necessary in the C.G.S. system are eliminated.

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The only complication in this system is the introduction of the primary magnetic constant μo = 4 Π X 10-7 and the primary electric constant εo = 1 / 36 Π X 10 9, which must be memorized.

Each of these constants has a value of unity in the C.G.S. system, but the conversion factors necessary in this system i.e. C.G.S. system, need to be applied in all the derivations of the formulae and difficult to memorize.

In the M.K.S. system, force is measured in “newtons” and length in meters, mass in kilograms, time in seconds. A newton is the force necessary to give a mass of 1 kilogram an acceleration of 1 meter per second per second and it is equivalent to 10 raised to the power of 5 dynes in the C.G.S. system.

With the introduction of M.K.S. system, the view has been expressed, in some quarters, that the classical methods of deriving electromagnetic and electrostatic formulae should be revised. This is because the unit magnetic pole used in the classical derivations has no physical existence.

The author has gone through the same experience and conclusion while decades of years have been invested in research and development. The word “uni” ascribe the singularity and is only attributed to the “Almighty GOD, i.e. Non worthy of him, all alone and the perfect creator of the Universe. All other creatures in reality are bi-polar in nature and only peace prevails with bi-polar existence of these.

Note:

I felt further elaboration at this stage, as to share with the readers, outcome and findings of my very tedious and tiring research work both as a struggle to knowledge based acquisition of “Mater of Engineering” degree in Electrical Power Engineering (as a part time study with U.E.T Taxila with the collaboration and guidance of noble, late Dr.Aftab Ahmad , my immediate boss at “National Power Control” also known as “Central Load Dispatch System of WAPDA”), as well as my involvement as a hobbyist, in order to keep myself determined. I am very much thankful to “Almighty GOD” for enabling me to get my target for the well being of the humanity.

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CONVERSION FORMULEA

FOR

METRIC MEASURES AND EQUIVALENTS.

LENGTH (1-D i.e. One Dimensional)

1 millimeter (mm) = 1 / 1000 meter = 0.0394 inch

1 centimeter (cm) = 10 mm = 0.3937 inch

1 meter = 100 cm = 1000 mm = 1.0936 yards

1 kilometer = 1000 meter = 0.6214 mile

AREA or SURFACE (2-D i.e. Two Dimensional)

1 sq cm (cm²) = 100 mm² = 0.1550 sq inch

1 sq meter (m²) = 10,000 cm² = 1.1960 sq yards

1 are(a) = 100 m² = 119.60 sq. yard

1 sq km (km²) = 100 hectares = 0.3861 sq miles

VOLUME or CAPACITY (3-D i.e. Three Dimensional)

1 cu cm(cm³) = 0.0610 cu inch

1 cu decimeter (dm³) = 1000 cm³ = 0.0351 cu ft

1 cu meter (m³) = 1000 dm³ = 1.3080 cu yds

1 liter (l) = 1 dm³ = 0.2642 U.S.gallon

1 hectoliter (hl) = 100 liters = 2.7497 bushels

WEIGHT ( Mass)

1 milligram (mg) = 0.0154 grain

1 gramme (g) = 1000 mg = 0.0353 oz = 0.017 chattak

1 Kilogram (kg) = 1000 g = 2.2046 lb = 1.07 seers

1 tonne (t) = 1000 kg = 0.9842 ton = 26.75 Maunds

----------------------------------

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6- S.I (International Standards) System.

In 1950, the Int’l Electro technical Commission adopted the “ampere”, namely the unit of electric current, as the basic electrical unit. We may summarize the definitions of the principal electrical units thus :

( a ) – The ampere is that current which when maintained in each of two infinitely long parallel conductors, situated in a vacuum and separated 1 meter between centers, produce on each conductor a force of 2 X 10 raised to power -7 newton per meter length. The conductors are attracted towards each other if the currents are in the same direction, whereas they repel each other if the currents are in opposite directions.

The value of current in terms of this definition can be determined by means of a very elaborate and carefully constructed balance in which the force between the fixed and moving coils carrying the current is balanced by the force of gravity acting on a known mass.

( b ) – The unit of the electrical quantity is the coulomb, namely the quantity of electricity passing a given point in a circuit when a current of 1 ampere is maintained for 1 second. Hence,

Q (coulombs) = I (ampere) X t (seconds),

Also, 1 ampere-hour = 3600 coulombs.

When a current is passed through an electrolyte, chemical decomposition takes place, and the mass of an element liberated by 1 coulomb is termed the electrochemical equivalent of that element.

If z = electrochemical equivalent of an element in grammes per coulomb,

And I = current in amperes for time t seconds,

Mass of an element liberated = z I t grammes.

The electrochemical equivalents of copper and silver are 0.3294 mg/C and 1.1182 mg/C respectively.

The value of the steady direct current can be determined with considerable accuracy by passing the current through either a copper or a silver voltmeter (i.e. two copper plates in a copper sulphate solution or two silver plates in a silver nitrate solution) for a given time and noting the increase in the mass of the negative plate (or cathode).

( c ) – The unit of the resistance is the ohm, namely the resistance of a circuit in which a steady current of 1 ampere generates heat at the rate of 1 watt. If a current of 1 ampere flows through a circuit of resistance R ohms for t seconds,

Power = I² R watts.

And heat energy generated = I² R t joules.

( d ) - The unit of potential difference* is the volt, namely the difference of potential across a circuit of resistance of 1 ohm carrying a current of 1 ampere. If v represents the p.d in volts across a circuit of resistance 1 ohm carrying a current of I ampere, then, by ohm’s law ;

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V = I R or I = V/R or R = V/I

Power = I² R watts.

= I V watts.

= V² / R watts.

* The term voltage originally meant a difference of potential expressed in volts ; but it is now used as a synonym for potential difference irrespective of the unit in which it is expressed. For instance, the voltage between the lines of a transmission system may be 750 kv, while in communication and electronic circuits, the voltage between two points may be 4 μ V.

( e ) - The electromotive force is that which tends to produced an electric current in a circuit , and the unit of e.m..f is the volt, the principal sources of e.m.f. are :

( i ) – the electrodes of dissimilar materials immersed in an electrolyte, as in primary and secondary cells ;

( ii ) - the relative movement of a conductor and a magnetic flux, as in electric generators and transformers; this source could, alternatively, be expressed as the variation of magnetic flux linked with a coil;

( iii ) - the difference of temperature between junction of dissimilar metals, as in thermo-junctions

9. Electical Reference Standards.

V = Voltage in Volts.

I = Current in ampere.

R = Resistance.( Ohms)

L = Inductance.(Henery)

C = Capacitance (Micro Farad)

XL = Inductive Reactance.

XC = Capacitive Reactance.

Z = Impedence.(Ohms)

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