The following observations on the measurement of electric currents are condensed from J. N. Shool - bred's paper on the ." Measurement of Electricity" (J1. Soc. Arts,' Ap. 6, 1883), and one by Professors Ayrton and Perry on " Measuring Instruments used in Electric Lighting and Transmission of Power."
The measurement of all physical quantities rests upon 3 fundamental units - length, mass, and time. All others can be deduced from these. The fundamental units chosen for electrical measuring are: length, 1 centimetre; mass, 1 gramme; time, 1 second; and the term "C.G.S." was applied to the whole system.
As, with the use of a scale common to all quantities, both very large and very small numbers must often be represented, it is advocated in the C.G.S, system to express each number as the product of 2 factors, 1 of them being a power of 10; also to effect this in such a way that the exponent of the power of 10 shall be the characteristic of the logarithm of the number. Thus, 1,280,000 would be written as 1.28X106, and .000128 as 1.28xlO4.
The following table contains some of the units based upon the C.G.S. system:-
C.G.S. Units of Measurement.
Length, 1 centimetre; mass, 1 gramme; time, 1 second.
Unit length in unit time
Rate of increase of velocity per second: In gravitation measure = g. g, in latitude of London = 981 C.G.S. units.
Momentum of 1 gramme with a velocity of 1 centimetre per second.
Force which, acting upon 1 gramme for a second, generates a velocity of 1 centimetre per second.
Amount of work done by 1 dyne working through 1 centimetre of distance.
Electro - magnetic.
A pole which, at 1 centimetre distance from a similar pole, gives a force of 1 dyne.
The intensity of a field which acts on unit magnetic pole with a force of 1 dyne.
A current flowing along 1 centimetre of a circuit in form of a circular arc, of 1 centimetre radius; and exerting a force of 1 dyne on a unit pole placed at the centre.
The quantity conveyed by unit current in 1 second.
The difference of the electric condition between 2 conductors, or 2 points of a conductor, when the transference of electricity from one to the other is proceeding at the rate of 1 erg of work per unit of electricity transferred.
A resistance such that, with unit of difference of potential between the ends of conductor, 1 unit of current is conveyed along it.
N.B. - 'The estimation of resistance actually resolves itself into a question of velocity, i.e. - Lenght / Time.
Some of the above C. G. S. electromagnetic units being found to be inconveniently large, and others to be far too small, the following " practical" units, for general use, have been deduced from them, and are now being universally adopted.
" Practical" Electrical Units.
The ohm (109 C. G. S. units of resistance), as the unit of resistance, is that of a column of mercury having 1 sq. millimetre of section, and of a length hereafter to be determined by a commission specially appointed for the purpose. Note. - The length is supposed, however, to be between 104 and 105 centimetres.
The ampere (10 - 1 C.G.S. units of current), as the unit of current; which is the current produced by 1 volt through 1 ohm.
The coulomb (10 - 1 C. G. S. units of quantity), as the unit of quantity of electricity; which is defined by the condition that an ampere yields 1 coulomb per second.
The farad (10 - 9 C. G. S. units of capacity), as the unit of capacity; which is such that 1 coulomb in a farad shall give 1 volt.
Or, to quote the words of Sir Wm. Thomson, " The volt acting through an ohm gives a current of 1 ampere, that is to say, 1 coulomb per second; and the farad is the capacity of a condenser, which holds 1 coulomb, when the difference of potential of its 2 plates is 1 volt."
The following was suggested by Dr.
C. W. Siemens to be added to the above units: -
The watt (107 C. G. S. units of power), as the unit of power; being the power conveyed by a current of 1 ampere in 1 second through a conductor whose ends differ in potential by 1 volt.
The joule (107 C. G. S. units of work), as the unit of work, or heat, being the heat generated by a watt in a second.
In the construction of instruments for the generation and measurement of electric currents, great advantage is taken of the inducting action of magnets upon coils; of the effect of the passage of the electric current through a coil upon a magnetic needle in its vicinity; and of the result of electric currents of different intensities upon each other,' in their passage through conductors in the form of coils.
The evaluation of the electrical energy of a supply depends upon the exact measurement of 2 factors - the amount of the supply and the pressure under which it is given; or the quantity of the current and the elect romotivc force. The product of the current expended, in ampere seconds, or of this amount of quantity expressed in coulombs, by the electrical pressure of the same, expressed in volts, gives the electrical energy expended, or the power of the supply. The electrical energy is therefore represented by the product of volts x amperes x time; or by the product of volts X coulombs; or, expressed algebraically, W = ECt = EQ.
Following are equivalent expressions for the same amount of power, expressed in other terms, some of which may be more familiar: -
Hate of expending Energy.
1 volt - ampere
107 ergs per second. 1 watt.
1/1.33 foot - pounds per second.
1/ 0.81 kilogrammetres per second.
1/736 force - cheval (French horsepower).
1/716 horse - power.
The Board of Trade suggest that the unit of price to be charged should be based on "the energy contained in a current of 1000 amperes flowing under an electromotive force of 1 volt during 1 hour;" or in other words, the unit might be put as 1000 volt - ampere hours. The ampere hour is another way of saying 3600 coulombs of quantity of electricity supplied. It may be of interest to state in other more conventional terms the equivalent of the amount of work implied in the above unit: -
Work done, or Energy expended.
1000 volt - ampere hours=
/1010 erg hours.
3,600,000 volt - coulombs.
1000 watt hours.
2,645,000 foot - pounds.
1.35 force - cheval heures.
\l . 34 horse - power hours.
Put in terms more in accordance with actual practice, the above unit might mean the supply for 1 hour of a current of 10 amperes with an electromotive force of 100 volts; or a 5 - ampere current with an E. M. F. of 200 volts; or a 10 - ampere current at 200 volts for only 1/2 hour; and so on, provided that the product of the 3 factors is always 1000.
To arrive at an evaluation of the supply of electric energy, the measurement of each of these 2 factors (in volts and amperes respectively), must be effected either separately or combined, and a continuous and cumulative record must be kept of the supply as it proceeds. To' measure with completeness, for commercial purposes, a supply of electricity, entails a continuous record of current and pressure, either separately or combined. In the supply of towns, the question for the consumer will probably be much simplified by causing one element, pressure, to remain constant. If so, it becomes the duty of suppliers to keep up that pressure under penalty; and instruments for recording such pressure will have to be installed where required, and placed tinder proper supervision. For the customer, it will then generally suffice to have an exact record of the quantity of his individual consumption of electric supply.
Some of the non - recording instruments in more general use, by the addition of recording apparatus, by which the element of time can be integrated, may be made into registering meters. Thus, any current or ampere measurer may be converted into a record of quantity; or a coulomb - meter, by the integration of the time during which the current has flowed; and, similarly, any power or volt-ampere measurer may become a register of work done by means of the addition of the elements of time. Again, volt or pressure measurers will always be required in any case where a check is needed upon the actual difference of potential or electromotive force of the supply; and this may arise from a variety of causes.