ARITHMETIC OF ELECTRICITY. CHAPTER I. INTRODUCTORY. SPACE is the lineal distance from one point to another. Time is the measure of duration. Force is any cause of change of motion of matter. It is expressed practically by grams, volts, pounds or other unit. Resistance is a counter-force or whatever opposes the action of a force. Work is force exercised in traversing a space against a resistance or counter-force. Force multiplied by space denotes work as foot-pounds. Energy is the capacity for doing work and is measurable by the work units. Mass is quantity of matter. Weight is the force apparent when gravity acts upon mass. When the latter is prevented from moving under the stress of gravity its weight can be appreciated. Physical and Mechanical calculation, are based on three fundamental units of dimension, as follows: the unit of time-the second, T; the unit of length -the centimeter, L; the unit of mass-the gram, M. Concerning the latter it is to be distinguished from weight. The gram is equal to one cubic centimeter of water under standard conditions and is invariable; the weight of a gram varies slightly with the latitude and with other conditions. Upon these three fundamental units are based the derived units, geometrical, mechanical and electrical. The derived units are named from the initials of their units of dimension, the C. G. S. units, indicating centimeter-gram-second units. In practical electric calculations we deal with certain quantities selected as of convenient size and as bearing an easily defined relation to thefundamental units. They are called practical units. The cause of a manifestation of energy is force; if of electromotive energy, that is to say of electric energy in the current form, it is called electromotive force, E. M. F. or simply E. or difference of potential D. P. What this condition of excitation may be is a profound mystery, like gravitation and much else in the physical world. The practical unit of E. M. F. is the VOLT, equal to one hundred millions (100,000,000) C. G. S. units of E. M. F. The last numeral is expressed more briefly as the eighth power of 10 or 108. Thus the volt is defined as equal to 10° C. G. S. units of E. M. F. This notation in powers of 10 is used throughout C. G. S. calculations. Division by a power of 10 is expressed by using a negative exponent, thus 10-* means rooooooo. The exponent indicates the number of ciphers to be placed after 1. When electromotive force does work a current is produced. The practical unit of current is the AMPERE, equal to C. G. S. unit, or 101 C. G. S. unit, being expressed by 10. A current of one ampere passing for one second gives a quantity of electricity. It is called the COULOMB and is equal to 10 C. G. S. units. A coulomb of electricty if stored in a recipient tends to escape with a definite E. M. F. If the recipient is of such character that this definite E. M. F. is one volt, it has a capacity of one FARAD equal to 1ooooooooo or 10° C. G. S. unit. In A current of electricity passes through some substances more easily than through others. The relative ease of passage is termed conductance. calculations its reciprocal, which is resistance, is almost universally used. A current of one ampere is maintained by one volt through a resistance of one practical unit. This unit is called the Онм and is equal to 10° C. G. S. units. Sometimes, where larger units are wanted, the prefix deka, ten times, heka, one hundred times, kilo, one thousand times, or mega, one million times are used, as dekalitre, ten liters, kilowatt, one thousand watts, megohm, one million ohms. Sometimes, where smaller units are wanted, the prefixes, deci, one tenth, centi, one hundredth, milli, one thousandth, micro, one millionth, are used. microfarad is one millionth of a farad. A For the concrete conception of the principal units the following data are submitted. A Daniell's battery maintains an E. M. F. of 1.07 volt. A current which in each second deposits .00033 grams copper (by electro-plating) is of one ampere intensity and from what has been said the copper deposited by that current in one second corresponds to one coulomb. A column of mercury one millimeter square and 106.24 centimeters long has a resistance of one ohm at 0° C. The capacity of the earth is 1088800 farad. A Leyden jar with a total coated surface of one square meter and glass one mm. thick has a capacity of microfarad. The last is the more generally used unit of capacity. These practical units are derived from the C. G. S. units by substituting for the centimeter (C.) one thousand million (109) centimeters and for the gram, the one hundred thousand millionth (10-1) part of a gram. CHAPTER II. OHM'S LAW. THIS law expresses the relation in an active electric circuit (circuit through which a current of electricity is forced) of current, electromotive force, and resistance. These three factors are always present in such a circuit. Its general statement is as follows: In an active electric circuit the current is equal to the electromotive force divided by the resistance. This law can be expressed in various ways as it is transposed. It may be given as a group of rules, to be referred to under the general title of OHM'S LAW. Rule 1. The current is equal to the electromotive force divided by the resistance. E C = - Rule 2. The electromotive force is equal to the current multiplied by the resistance. E = CR Rule 3. The resistance is equal to the electromotive force divided by the current. E R= с Rule 4. The current varies directly with the electromotive force and inversely with the resistance. |