Fig. 3.—Structure and electronic orbit of a positive helium atom.

between the positive and the negative charges are concerned.

The excess of one proton in the nucleus gives the atom a positive charge, and if the previously removed electron is permitted to return to the atom, it will again become neutral as in fig. 2.

A positively charged body therefore is one which has been deprived of some of its electrons, whereas a negatively charged body is one which has a surplus (acquired more than its normal number) of electrons.

In its unbalanced state the atom will tend to attract any free electrons that may be in the vicinity. This is exactly what takes place when a stick of sealing wax or amber is rubbed with pnnnnnnfinnnn nn

ELECTRONS^

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FLANNEL

AFTER RUBBING

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FLANNEL WAX

Fig. 4.—Illustrating how the rubbing process removes electrons from the flannel, and the re-distribution of electrons after contact of the two bodies.

a piece of flannel. The wax becomes negatively charged and the flannel positively charged.

During the rubbing process, the friction rubs off some of the electrons from the atoms composing the flannel and leaves them on the surface of the wax. Since the surface atoms or mole-. cules of the flanttel are left deficient in electrons and the surface atoms of the wax with a surplus, if the wax and the flannel are left together after being rubbed, there will be a readjustment of electrons, the excess on the wax returning to the deficient atoms of the flannel, as shown in fig. 4.

Most of the electrons in the universe exist as component parts of atoms as described, but it is possible for an electron to exist in the free state apart from the atom temporarily at least. Free electrons exist to some extent in gases, in liquids and in solids, but are much more plentiful in some substances than in others.

Conductors and Insulators of Electricity.—In metals for example, enormous quantities of free electrons exist while such substances as glass and rubber contain only small amounts.

It is the presence of free electrons in substances that enables us to account for the conduction of electricity. The more free electrons a substance contains, the better conductor of electricity is it, and it is on account of the great numbers of free electrons in metals, that metals are good conductors of electricity. Again, substances such as glass, rubber, mica, etc., with their comparatively few free electrons are poor conductors of electricity—good insulators.

Flow of Electric Current.—These free electrons are in a state of continual rapid motion, or thermal agitation. The situation is analogous to that in a gas where it is known that the molecules, according to the kinetic theory, are in a state of rapid motion with a random distribution of velocity.

If it were possible at a given instant to examine the individual molecules or electrons, it would be found that their velocities vary enormously and is a function of the temperature. The higher the temperature of a substance the higher the velocity of the atoms and electrons.

Now if by some means, the random motion of the molecules or electrons in a conductor be controlled and be made to flow in one direction, there results what is called a flow of electric current. Such means of controlling or directing the electron motion is provided by an electric battery or a generator. See fig. 5.

DIRECTION OF

DIRECTION OF

b'lG. 5.—Illustrating the movement of electrons from the negative to the positive terminal of a battery. In practice it is customary to think of an electric current as flowing from the positive to the negative. The reason for this contradiction is due to the fact that the early electrical experimenters assumed the direction of current to be from the positive to the negative, which is now known to be opposite as far as analyzing a circuit is concerned. It causes considerable misunderstanding to those not duly informed.

b'lG. 5.—Illustrating the movement of electrons from the negative to the positive terminal of a battery. In practice it is customary to think of an electric current as flowing from the positive to the negative. The reason for this contradiction is due to the fact that the early electrical experimenters assumed the direction of current to be from the positive to the negative, which is now known to be opposite as far as analyzing a circuit is concerned. It causes considerable misunderstanding to those not duly informed.

Resistance to the Movement of Electrons.—The progressive motion of electrons in a conductor are retarded by the collisions of the atoms of the substance, and it is this hindrance to their movement which constitutes the electrical resistance in a conductor.

This resistance varies in different metals, and also with the temperature of the conductor. When the temperature increases, the higher will be the velocity of the atoms and electrons, which in turn causes more frequent collisions and as a result, there is a greater hindrance to their progress.

The frequency of collisions between the atoms and electrons is also increased when a greater number of electrons are present. It is on account of this fact that the heating in a current carrying conductor increases with the size of the current.

Electric Pressure.—It has been previously mentioned that the directed motion of free electrons in a conductor constitutes an electric current. To understand how a flow of current may be established, it is well to consider the analogy of, for example, a water pump in a hydraulic system. See fig. 6.

In this case, by virtue of the pump piston the water enters the pump at the intake end at low pressure and leaves the discharge end at high pressure. The difference in pressure at the two ends of the pump causes water to flow through the pipe.

The action of the electrical system is similar. In any electrical circuit a generator or battery may be used to supply an electromotive force in a similar manner as the pump in the hydraulic system supplies mechanical force. Here the positive and the negative binding posts of the generator correspond to the discharge and the intake end of pump respectively. See fig. 7.

Similarly in case of the generator it is said that the pressure is higher at the positive end and lower at the negative, corresponding to the discharge and intake ends of the pump in the hydraulic system.

It is this difference in pressure between the generator terminals which causes an electric current to flow in the circuit, in much the same way as the water is forced through a pipe in the hydraulic system.

Electrical pressure variously called "difference in potential" and "electromotive force" is measured in terms of a unit called the volt.

Electric Current.—Again using the circuit (water pipes) in the hydraulic system, the rate at which water is flowing through the pipe may be measured in gallons per second. Similarly in the electric circuit the amount of current flowing is measured in a unit called "coulomb" which expresses the rate of flow.

When the current in a circuit flows at the rate of one coulomb per second the name of one ampere is used. This term facilitates the expression of current flow in that it makes it unnecessary to say "per second" each time, as second is already a part of the unit "ampere."

Thus one coulomb per second is one ampere, and ten coulombs per second is ten amperes, etc.

The relation between coulombs and amperes may be expressed as follows:

where I is the current in amperes; Q is the amount of electricity in coulombs; and t is the time of flow in seconds.

Thus for example if a battery sends a current of 5 amperes through a circuit for one hour, the number of coulombs of electricity that will flow through the circuit will be 5x60x60 = 18,000 coulombs.

Resistance to Current Flow.—All conductors of electricity oppose the flow of current through them, i.e., they have elec-' trical resistance. The unit of resistance is called the ohm. A conductor may be said to have one ohm's resistance if the ratio of the electrical pressure in volts to the current flowing through it, is unity.

Thus, for example, if the current flowing through a circuit is found to be 10 amperes, and the electrical pressure 10 volts the resistance of the circuit will be = 1 ohm.

Ohm's Law.—When considering the flow of electrons in a conductor it is evident that the greater the e.m.f. (electromotive force) is, the more electrons will flow in the circuit, and also the greater the resistance of a conductor, the less number of electrons will flow through.

It has been found that there is a definite mathematical relationship between the e.m.f. applied to a circuit having a definite resistance, and the current flow. This relationship is known as the ohm's law. This law states that the current flowing through a resistance under a given e.m.f. is inversely-proportional to the resistance and directly proportional to the

voltage. Thus 7 = ^ in which 7, is the current in amperes; E, the e.m.f. in volts and R, the resistance in ohms.

Series Circuits.—If there be several resistances in series, as shown in fig. 8, the equation becomes

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BATTERY

t'V;. 8.—Simple circuit with three resistances connected in seriep.

The sum of the difference of potential across the various parts of the circuit is equal to the total voltage impressed on the circuit. Thus, E=E1+E2+E3.

In a circuit as shown in fig. 8, the current I, is the same in each part of the circuit, but the voltage across each resistance depends directly upon the size of that resistance.

Example:—What voltage must be furnished by the battery in fig. 8, in order to force 0.25 ampere through the circuit if Ru R2 and R3 are 5,15 and 20 ohms respectively?

The total resistance i? = 5 + 15+2Q = 40 ohms. The total voltage is 40 X0.25 = 10 volts.

The voltage required for each part may be conveniently used as a check. Thus

= 0.25X5 = 1.25 volts Ei = 0.25 X15 = 3.75 volts Ez = 0.25 X 20 = 5 volts. Hence 1.25 +3.75 +5 = 10 volts, as before.

Parallel Circuits.—In parallel circuits, see fig. 9, the voltage across the various resistances is the same and the current flowing through each resistance varies inversely with the value of it. The sum of all the currents, however, is equal to the main current leaving the battery. Thus

When Ohm's law is applied to the individual resistances, the following is obtained:

u r E ,E ..E ■ T ■ p/l , 1 ■ 1 Y Hence / = K+Y+RS or \r+R+rJ '

and since -j =R, the equivalent resistances of the several resistances connected in parallel is =

Example:—If the resistances in previous example be connected in parallel as shown in fig. 9, what will be the total current and the current flowing through each resistance if the voltage remains unchanged or 10 volts?

The total resistance (R) for the combination will be found as follows:

1 1.11 19 _ D 60 _ , ^=5"+l5+20 = 60 Then ^ = ^=3.16 ohm.

The total current =3^ = 3.17 amperes.

The current in the 5 ohms resistance is ^ = 2 amperes.

The current through each resistance may conveniently be added as a check. Thus 2+0.67+0.5 = 3.17 amperes as before.

Power in Electrical Circuits.—As previously stated, the electrons in their movement through a circuit do not have a clear path, but are in constant collision with atoms of the metals causing the metal to heat up. The heat so developed, varies with the number of collision and increases with the increase in current flow, due to a higher potential. It has been found that this developed heat or power loss varies directly as the resistance and as the square of the current, which relation may be written

in which IF is the power in watts; E, I and R being the voltage current and resistances of the circuit. Thus to determine the power consumed in a device, multiply the voltage across it by the current flowing through it.

Example:—If certain heating elements take 25 amperes at a potential of 110 volt, what is the power consumption?

As the watt is a small unit of electrical power, the kilowatt (k.w.) which is a unit 1,000 times larger is more convenient, when it is desired to express larger amounts of power.

Therefore to change watts to kilowatts di vide by 1,000 and to change kilowatts to watts multiply by 1,000.

1 000

Thus one kilowatt is =—or 1.34 horse power.

To obtain the horse power consumption in the above heating 2 750

Example.—A certain carbon resistor is marked 1 watt and has 3 code colors as follows: yellow body, black tip and orangecoloreddot. What is the maximum current that may safely be sent through it?

Solution.—In this case it is first necessary to find the resistance value in ohms. With reference to page 182 the Radio Manufacturer's Association's Code colors indicate that the resistor has a resistance of 40,000 ohms, which may be checked as follows: yellow body means (4); black tip means (0) and orange dot means (000) or 40,000. Now the value of power dissipation in watts is equal to (PR) from which it follows that

I=amperes or 5 milli-amperes.

With an increase in current above the derived value, the heating of the resistor may become excessive and may even damage or change the accuracy of the resistance in question.

The solution of circuit shown on opposite page is in reality very simple if it be kept in mind that any number of resistances connected in series may be replaced by a single resistor with a value equal to the arithmetical sum of the individual resistors, or that any number of resistors in parallel can be replaced by an equivalent whose value is equal to the reciprocal of the sum of the reciprocals of the individual units.

Circuit A-l consists of resistors R„ and Rb in series, and the two also in parallel with Rd. This group is connected in series with R0 and the whole combination is again connected in parallel with Rf.

The simplest way to solve a resistance combination of this type is to remember the foregoing and to go through the problem step by step, combining each series and each parallel group and to replace them with their equivalent resistance.

Hence, to solve this circuit first replace Ra and Rb by their equivalent Rg.

The next step is to combine Rg and Rd replacing them by their equivalent Rh. By replacing Rc and Rh by their equivalent Rj, the original circuit now being reduced to the form as shown in fig. A-4.

In the manner similar to that already described Rj and Rf in parallel is replaced by a resistance Rk obtaining the result as shown in fig. A-5. Finally as a result of these calculations a resistance is obtained having the same current limiting* effect as that shown in fig. A-l. '

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