 |
APPENDIX.
UNITS OF MEASUREMENT.
(From Munro and Jamieson's Pocket-book of Electrical Rules and Tables).
I. FUNDAMENTAL UNITS.—The electrical units are derived from the following mechanical units:—
The Centimetre as a unit of length; The Gramme as a unit of mass; The Second as a unit of time.
The Centimetre is equal to 0.3937 inch in length, and nominally represents one thousand-millionth part, or 1/1,000,000,000 of a quadrant of the earth.
The Gramme is equal to 15.432 grains, and represents the mass of a cubic centimetre of water at 4 degrees C. Mass is the quantity of matter in a body.
The Second is the time of one swing of a pendulum making 86,164.09 swings in a sidereal day, or 1/86,400 part of a mean solar day.
II. DERIVED MECHANICAL UNITS.-
Area.-The unit of area is the square centimetre.
Volume.—The unit of volume is the CUBIC CENTIMETRE.
VELOCITY is rate of change of position. It involves the idea of direction as well as that of magnitude. VELOCITY is UNIFORM when equal spaces are traversed in equal intervals of time The unit of velocity is the velocity of a body which moves through unit distance in unit time, or the VELOCITY OF ONE CENTIMETRE PER SECOND.
MOMENTUM is the quantity of motion in a body, and is measured by mass x velocity.
ACCELERATION is the rate of change of velocity, whether that change take place in the direction of motion or not. The unit of acceleration is the acceleration of a body which undergoes unit change of velocity in unit time, or an acceleration of one centimetre-per-second per second The acceleration due to gravity is considerably greater than this, for the velocity imparted by gravity to falling bodies in one second is about 981 centimetres per second (or about 32.2 feet per second). The value differs slightly in different latitudes. At Greenwich the value of the acceleration due to gravity is g=981.17; at the Equator g=978.1; at the North Pole g=983.1.
FORCE is that which tends to alter a body's natural state of rest or of uniform motion in a straight line.
FORCE is measured by the acceleration which it imparts to mass—i. e., mass x acceleration.
THE UNIT OF FORCE, or DYNE, is that force which, acting for one second on a mass of one gramme, gives to it a velocity of one centimetre per second. The force with which the earth attracts any mass is usually called the "weight" of that mass, and its value obviously differs at different points of the earth's surface The force with which a body gravitates—i e, its weight (in dynes), is found by multiplying its mass (in grammes) by the value of g at the particular place where the force is exerted.
Work is the product of a force and a distance through which it acts. The unit of work is the work done in overcoming unit force through unit distance—i e, in pushing a body through a distance of one centimetre against a forch of one dyne. It is called the Erg. Since the "weight" of one gramme is 1 X 981 or 981 dynes, the work of raising one gramme through the height of one centimetre against the force of gravity is 981 ergs or g ergs. One kilogramme-metre = 100,000 (g) ergs = 9 8 1 X 10^7 ergs. One foot- pound = 13,825 (g) ergs, = 1 356 X 10^7 ergs.
Energy is that property which, possessed by a body, gives it the capability of doing work. Kinetic energy is the work a body can do in virtue of its motion. Potential energy is the work a body can do in virtue of its position. The unit of energy is the Erg.
Power or Activity is the rate of work; the practical unit is called the Watt—10^7 ergs per second.
A Horse-power = 33,000 ft—Ibs per minute = 550 ft—Ibs per second, but as seen above under Work, 1 ft—Ib = 1 356 X 10^7 ergs, and under Power, 1 Watt = 10^7 ergs per sec a Horsepower = 550 X 1 356 X 10^7 ergs = 746 Watts; or, EC/746C^2R/746=E^2/(746 R) =HP where E = volts, C = amperes, and R = ohms.
The French "force de cheval" = 75 kilogramme metres per sec = 736 Watts = 542 48 ft—lbs. per sec. = .9863 H.P.; or one H.P. = 1.01385 "force de cheval."
DERIVED ELECTRICAL UNITS.—There are two systems of electrical units derived from the fundamental "C.G.S." units, one set being based upon the force exerted between two quantities of electricity, and the other upon the force exerted between two magnetic poles. The former set are termed electro-static units, the latter electro-magnetic units.
III. ELECTROSTATIC UNITS.—
UNIT QUANTITY of electricity is that which repels an equal and similar quantity at unit distance with unit force in air.
UNIT CURRENT is that which conveys unit quantity of electricity along a conductor in a second.
UNIT ELECTROMOTIVE FORCE, or unit DIFFERENCE OF POTENTIAL exists between two points when the unit quantity of electricity in passing from one to the other will do the unit amount of work.
UNIT RESISTANCE is that of a conductor through which unit electromotive force between its ends can send a unit current.
UNIT CAPACITY is that of a condenser which contains unit quantity when charged to unit difference of potential.
IV. MAGNETIC UNITS.—
UNIT MAGNETIC POLE is that which repels an equal and similar pole at unit distance with unit force in air.
STRENGTH OF MAGNETIC FIELD at any point is measured by the force which would act on a unit magnetic pole placed at that point.
UNIT INTENSITY OF FIELD is that intensity of field which acts on a unit pole with unit force.
MOMENT OF A MAGNET is the strength of either pole multiplied by the distance between the poles.
INTENSITY OF MAGNETISATION is the magnetic moment of a magnet divided by its volume.
MAGNETIC POTENTIAL.—The potential at a point due to a magnet is the work that must be done in removing a unit pole from that point to an infinite distance against the magnetic attraction, or in bringing up a unit pole from an infinite distance to that point against the magnetic repulsion.
UNIT DIFFERENCE OF MAGNETIC POTENTIAL.—Unit difference of magnetic potential exists between two points when it requires the expenditure of one erg of work to bring an (N. or S.) unit magnetic pole from one point to the other against the magnetic forces.
V. ELECTRO-MAGNETIC UNITS.—
UNIT CURRENT is that which in a wire of unit length, bent so as to form an arc of a circle of unit radius, would act upon a unit pole at the centre of the circle with unit force.
UNIT QUANTITY of electricity is that which a unit current conveys in unit time.
UNIT ELECTRO-MOTIVE FORCE or DIFFERENCE OF POTENTIAL is that which is produced in a conductor moving through a magnetic field at such a rate as to cut one unit line per second.
UNIT RESISTANCE is that of a conductor in which unit current is produced by unit electro-motive force between its ends.
UNIT CAPACITY is that of a condenser which will be at unit difference of potential when charged with unit quantity.
Electric and magnetic force varies inversely as the square of the distance.
PRACTICAL UNITS OF ELECTRICITY.
RESISTANCE-R.—The Ohm is the resistance of a column of mercury 106.3 centimetres long, 1 square millimetre in cross-section, weighing 14.4521 grammes, and at a temperature of 0 degrees centigrade. Standards of wire are used for practical purposes. The ohm is equal to a thousand million, 10^9, electromagnetic or Centimetre-Gramme-Second ("C. G. S.") units of resistance.
The megohm is one million ohms.
The microhm is one millionth of an ohm.
ELECTROMOTIVE FORCE—E.—The Volt is that electromotive force which maintains a current of one ampere in a conductor having a resistance of one ohm. The electromotive force of a Clark standard cell at a temperature of 15 degrees centigrade is 1.434 volts. The volt is equal to a hundred million, 10^8, C. G. S. units of electromotive force.
CURRENT—C.—The Ampere is that current which will decompose 0.09324 milligramme of water (H2O) per second or deposit 1.118 milligrammes of silver per second. It is equal to one-tenth of a C. G. S. unit of current.
The milliampere is one thousandth of an ampere.
QUANTITY—Q.—The Coulomb is the quantity of electricity conveyed by an ampere in a second. It is equal to one-tenth of a C. G. S. unit of quantity.
The micro-coulomb is one millionth of a coulomb.
CAPACITY—K.—The farad is that capacity of a body, say a Leyden jar or condenser, which a coulomb of electricity will charge to the potential of a volt. It is equal to one thousand-millionth of a C. G. S. unit of capacity.
The micro-farad is one millionth of a Farad.
By Ohm's Law, Current = Electromotive Force/ Resistance,
or C = E/R
Ampere = Volt/Ohm
Hence when we know any two of these quantities, we can find the third. For example, if we know the electromotive force or difference of potential in volts and the resistance in ohms of an electric circuit, we can easily find the current in amperes.
POWER—P.—The Watt is the power conveyed by a current of one ampere through a conductor whose ends differ in potential by one volt, or, in other words, the rate of doing work when an ampere passes through an ohm. It is equal to ten million, 10^7, C. G. S. units of power or ergs per second, that is to say, to a Joule per second, or 1/746 of a horse-power.
A Watt = volt X ampere, and a Horse-power = Watts/746.
HEAT OR WORK—W.—The Joule is the work done or heat generated by a Watt in a second, that is, the work done or heat generated in a second by an ampere flowing through the resistance of an ohm. It is equal to ten million, 10^7, C. G. S. units of work or ergs. Assuming "Joule's equivalent" of heat and mechanical energy to be 41,600,000, it is the heat required to raise .24 gramme of water 1 degrees centigrade. A Joule = Volt x ampere x second. Since 1 horse-power = 550 foot pounds of work per second,
W = 550/746 E. Q. = .7373 E. Q. foot pounds.
HEAT UNITS.
The British Unit is the amount of heat required to raise one pound of water from 60 degrees to 61 degrees Fahrenheit. It is 251.9 times greater than the metric unit, therm or calorie, which is the amount of heat required to raise one gramme of water from 4 degrees to 5 degrees centigrade.
Joule's Equivalent—J.—is the amount of energy equivalent to a therm or calorie, the metric unit of heat. It is equal to 41,600,000 ergs.
The heat in therms generated in a wire by a current = Volt X ampere X time in seconds X 0.24.
LIGHT UNITS
The British Unit is the light of a spermaceti candle 7/8-inch in diameter, burning 120 grains per hour (six candles to the pound). They sometimes vary as much as 10 per cent, from the standard. Mr. Vernon Harcourt's standard flame is equal to an average standard candle.
The French Unit is the light of a Carcel lamp, and is equivalent to 9 T/Z British units.
THE END |
|
