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Direct Current Circuits

All naturally occurring matter (excluding artifically produced radioactive substances) is made up of 92 fundamental constituents called elements. These elements can exist either in the free state such as iron, oxygen, carbon, copper, tungsten, and aluminum, or in chemical unions commonly called compounds. The smallest unit which still retains all the original characteristics of an element is the atom.

Combinations of atoms, or subdivisions of compounds, result in another fundamental unit, the molecule. The molecule is the smallest unit of any compound. All reactive elements when in the gaseous state also exist in the molecular form, made up of two or more atoms. The nonreactive gaseous elements helium, neon, argon, krypton, xenon, and radon are the only gaseous elements that ever exist in a stable monatomic state at ordinary temperatures.

The Atom

An atom is an extremely small unit of matter - there are literally billions of them making up so small a piece of material as a speck of dust. To understand the basic theory of electricity and hence of radio, we must go further and divide the atom into its main components, a positively charged nucleus and a cloud of negatively charged particles that surround the nucleus. These particles, swirling around the nucleus in elliptical orbits at an incredible rate of speed, are called orbital electrons.

It is upon the behavior of these electrons when freed from the atom, that depends the study of electricity and radio, as well as allied sciences. Actually it is possible to subdivide the nucleus of the atom into a dozen or

so different particles, but this further subdivision can be left to quantum mechanics and atomic physics. As far as the study of electronics is concerned it is only necessary for the reader to think of the normal atom as being composed of a nucleus having a net positive charge that is exactly neutralized by the one or more orbital electrons surrounding it.

The atoms of different elements differ in respect to the charge on the positive nucleus and in the number of electrons revolving around this charge. They range all the way from hydrogen, having a net charge of one on the nucleus and one orbital electron, to uranium with a net charge of 92 on the nucleus and 92 orbital electrons. The number of orbital electrons is called the atomic number of the element.

Action of the From the above it must not be Electrons thought that the electrons re-

volve in a haphazard manner around the nucleus. Rather, the electrons in an element having a large atomic number are grouped into rings having a definite number of electrons. The only atoms in which these rings are completely filled are those of the inert gases mentioned before; all other elements have one or more uncompleted rings of electrons. If the uncompleted ring is nearly empty, the element is metallic in character, being most metallic when there is only one electron in the outer ring. If the incomplete ring lacks only one or two electrons, the element is usually non-metallic. Elements with a ring about half completed will exhibit both non-metallic and metallic characteristics; carbon, silicon, germanium, and arsenic are examples. Such elements are called semi-conductors.

In metallic elements these outer ring electrons are rather loosely held. Consequently,

there is a continuous helter-skelter movement of these electrons and a continual shifting from one atom to another. The electrons which move about in a substance are called free electrons, and it is the ability of these electrons to drift from atom to atom which makes possible the electric current.

Conductors and If the free electrons are nu-Insulatort merous- and loosely held, the

element is a good conductor. On the other hand, if there are few free electrons, as is the case when the electrons in an outer ring are tightly held, the element is a poor conductor. If there are virtually no free electrons, the element is a good insulator.

2-2 Fundamental Electrical

Units and Relationships

Electromotive Force: The free electrons in Potential Difference a conductor move constantly about and change their position in a haphazard manner. To produce a drift of electrons or electric current along a wire it is necessary that there be a difference in pressure or potential between the two ends of the wire. This potential difference can be produced by connecting a source of electrical potential to the ends of the wire.

As will be explained later, there is an excess of electrons at the negative terminal of a battery and a deficiency of electrons at the positive terminal, due to chemical action. When the battery is connected to the wire, the deficient atoms at the positive terminal attract free electrons from the wire in order for the positive terminal to become neutral. The attracting of electrons continues through the wire, and finally the excess electrons at the negative terminal of the battery are attracted by the positively charged atoms at the end of the wire. Other sources of electrical potential (in addition to a battery) are: an electrical generator (dynamo), a thermocouple, an electrostatic generator (static machine), a photoelectric cell, and a crystal or piezoelectric generator.

Thus it is seen that a potential difference is the result of a difference in the number of electrons between the two (or more) points in question. The force or pressure <hie to a potential difference is termed the electromotive force, usually abbreviated e.m.f. or E.M. F. It is expressed in units called volts.

It should be noted that for there to be a potential difference between two bodies or points it is not necessary that one have a positive charge and die other a negative charge. If two bodies each have a negative

charge, but one more negative than the other, the one with the lesser negative charge will act as though it were positively charged with respect to the other body. It is the algebraic potential difference diat determines die force with which electrons are attracted or repulsed, the potential of the earth being taken as die zero reference point.

The Electric The flow of electrons along a Current conductor due to the application

of an electromotive force constitutes an electric current. This drift is in addition to the irregular movements of the electrons. However, it must not be thought that each free electron travels from one end of the circuit to the other. On the contrary, each free electron travels only a short distance before colliding with an atom; this collision generally knocking off one or more electrons from the atom, which in turn move a short distance and collide with other atoms, knocking off other electrons. Thus, in the general drift of electrons along a wire carrying an electric current, each electron travels only a short distance and the excess of electrons at one end and the deficiency at the other are balanced by the source of the e.m.f. When this source is removed the state of normalcy returns; there is still the rapid interchange of free electrons between atoms, but there is no general trend or net movement in either one direction or the other.

Ampere and There are two units of measure-Coulomb ment associated with current, and they are often confused. The rate of flow of electricity is stated in amperes. The unit of quantity is the coulomb. A coulomb is equal to 6.28 x 10 electrons, and when this quantity of electrons flows by a given point in every second, a current of one ampere is said to be flowing. An ampere is equal to one coulomb per second; a coulomb is, conversely, equal to one ampere-second. Thus we see that coulomb indicates amount, and ampere indicates rate of flow of electric current.

Older textbooks speak of current flow as being from the positive terminal of the e.m.f. source through the conductor to the negative terminal. Nevertheless, it has long been an established fact that the current flow in a metallic conductor is the electronic flow from the negative terminal of the source of voltage through the conductor to the positive terminal. The only exceptions to the electronic direction of flow occur in gaseous and electrolytic conductors where the flow of positive ions toward the cathode or negative electrode constitutes a positive flow in the opposite direction to the electronic flow. (An ion is an atom, molecule.



or particle which either lacks one or mote electrons, or else has an excess of one or more electrons.)

In radio work the terms electron flow and current are becoming accepted as being synonymous, but the older terminology is still accepted in the electrical (industrial) field. Because of the confusion this sometimes causes, it is often safer to refer to the direction of electron flow rather than to the direction of the current. Since electron flow consists actually of a passage of negative charges, current flow and algebraic electron flow do pass in the same direction.

Resistance The flow of current in a material depends upon the ease with which electrons can be detached from the atoms of the material and upon its molecular structure. In other words, the easier it is to detach electrons from the atoms the more free electrons there will be to contribute to the flow of current, and the fewer collisions that occur between free electrons and atoms the greater will be the total electron flow.

The opposition to a steady electron flow is called the resistance of a material, and is one of its physical properties.

The unit of resistance is the ohm. Every substance has a specific resistance, usually expressed as ohms per mil-foot, which is determined by the materials molecular structure and temperature. A mil-foot is a piece of material one circular mil in area and one foot long. Another measure of resistivity frequently used is expressed in the units microhms per centimeter cube. The resistance of a uniform length of a given substance is directly proportional to its length and specific resistance, and inversely proportional to its cross-sectional area. A wire with a certain resistance for a given length will have twice as much resistance if the length of the wife is doubled. For a given length, doubling the cross-sectional area of the wire will halve the resistance, while doubling the diameter will reduce the resistance to one fourth. This is true since the cross-sectional area of a wire varies as the square of the diameter. The relationship between the resistance and the linear dimensions of a conductor may be expressed by the following equation:

R = - A


R = resistance in ohms

r= resistivity in Ohms per nil-foot

I = length of conductor in feet A = cross-sectional area in circular mils


Resistivity in

Temp. Coeft. of

Ohms per


resistance per °C



at 20° C.




0.003 to 0.007























The resistance also depends upon temperature, increasing with increases in temperature for most substances (including most metals), due to increased electron acceleration and hence a greater number of impacts between electrons and atoms. However, in the case of some substances such as carbon and glass the temperature coefficient is negative and the resistance decreases as the temperature increases. This is also true of electrolytes. The temperature may be raised by the external application of heat. of by the flow of the current itself. In the latter case, the temperature is raised by the heat generated when the electrons and atoms collide.

Conductors and In the molecular structure of insulators many materials such as glass,

porcelain, and mica all electrons are tightly held within their orbits and there are comparatively few free electrons. This type of substance will conduct an electric current only with great difficulty and is known as an insulator. An insulator is said to have a high electrical resistance.

On the other hand, materials that have a large number of free electrons are known as conductors. Most metals, those elements which have only one or two electrons in their outer ring, are good conductors. Silver, copper, and aluminum, in that order, are the best of the common metals used as conductors and are said to have the greatest conductivity, or lowest resistance to the flow of an electric current.

Fundamental These units are the volt,

Electrical Units the ampere, and the ohm.

They were mentioned in the preceding paragraphs, but were not completely defined in terms of fixed, known quantities.

The fundamental unit of current, от rate of flow of electricity is the ampere. A current of one ampere will deposit silver from a specified solution of silver nitrate at a rate of 1.118 milligrams per second.

Figure 2


Shown above arc various types al resistors used in electronic circuits. The larger units are power resistors. On the left Is a variable power resistor. Three precision-type resistors are shown in the center with two small composition resistors beneath fhem. At the right Is a eompasltion-type potentiometer, used for audio circuit*).

The international standard for the ohm is the resistance offered by a uniform column of mercury at 0°C., 14.4521 grams in mass, of constant cross-sectional area and 106.300 centimeters in length. The expression megohm (1,000,000 ohms) is also sometimes used when speaking of very large values of resistance.

A volt is the e.m.f. that will produce a current of one ampere through a resistance of one ohm. The standard of electromotive force is the Weston cell which at 20° C. has a potential of 1.0183 volts across its terminals. This cell is used only for reference purposes in a bridge circuit, since only an infinitesimal




rl -- Rz I-Wi--n



At (A) the battery is in series with a single resistor. At (B) the battery is in series with two resistors, the resistors themselves being in series. The arrows Indicate the direction of electron flow.

amount of current may be drawn from it without disturbing its characteristics.

Ohms Law The relationship between the electromotive force (voltage), the flow of current (amperes), and the resistance which impedes the flow of current (ohms), is very clearly expressed in a simple but highly valuable law known as Ohms law. This law states that the current in amperes is equal to the voltage in volts divided by the resistance in ohms. Expressed as an equation:

I =-R

If the voltage (E) and resistance (R) are known, the current (I) can be readily found. If the voltage and current are known, and the resistance is unknown, the resistance (R) is

equal to - . When the voltage is the unknown quantity, it can be found by multiplying I x R. These three equations are all secured from the original by simple transposition. The expressions are here repeated for quick reference:

I=- R=~ E=IR R I


Resistive Circuits 25



The two res/stors Rj one R2 are said to be in parollel sinea the flaw af currant is offered two parollal paths. An elaetran leaving paint A will pass e/t/ier throug/i R or R2, but not througti borb, to reacb fbe positive terminal of the battery. If a large number of electrons are considered, the greafer number will pass through whichever of the two resistors bos rhe lower resistance.

where I is the current in amperes, R is the resistance in ohms, E is the electromotive force in volts.

Application of All electrical circuits fall in-Ohms Low to one of three classes: series

circuits, parallel circuits, and series-parallel circuits. A series circuit is one in which the current flows in a single continuous path and is of the same value at every point in the circuit (figure 3). In a parallel circuit there are two or more current paths between two points in the circuit, as shown in figure 4. Here the current divides at A, part going through Rj and part through Rj, and combines at В to return to the battery. Figure 5 shows a series-parallel circuit. There are two paths between points A and В as in the parallel circuit, and in addition there are two resistances in series in each branch of the parallel combination. Two other examples of series-parallel arrangements appear in figure 6. The way in which the current splits to flow through the parallel branches is shown by the arrows.

In every circuit, each of the parts has some resistance; the batteries or generator, the connecting conductors, and the apparatus itself. Thus, if each part has some resistance, no matter how little, and a current is flowing through it, there will be a voltage drop across it. In other words, there will be a potential difference between the two ends of the circuit element in question. This drop in voltage is equal to the product of the current and the resistance, hence it is called the IR drop.

The source of voltage has an internal resistance, and when connected into a circuit so that current flows, there will be an IR drop in the source just as in every other part of the circuit. Thus, if the terminal voltage of the source could be measured in a way that would cause no current to flow, it would be found to be more than the voltage measured when a current flows by the amount of the IR drop

In this type af circuit the resistors are arranged in series groups, and these serlesed groups are then placed In parallel.

in the source. The voltage measured with no current flowing is termed the no load voltage; that measured with current flowing is the load voltage. It is apparent that a voltage source having a low internal resistance is most desirable.

Resistances The current flowing in a series in Series circuit is equal to the voltage

impressed divided by the total resistance across which the voltage is impressed. Since the same current flows through every part of the circuit, it is merely necessary to add all the individual resistances to obtain the total resistance. Expressed as a formula;


= R, + Rj + Rj + . . . + Rn

Of course, if the resistances happened to be all the same value, the total resistance would be the resistance of one multiplied by the number of resistors in the circuit.

Resistances Consider two resistors, one of in Parallel 100 ohms and one of 10 ohms, connected in parallel as in figure 4, with a voltage of 10 volts applied across each resistor, so the current through each can be easily calculated.

I = - R

E = 10 volts R = 100 ohms

E = 10 volts R = 10 ohms

10 100

0.1 ampere

I, = - = 1.0 ampere 10

Total current = I + Ij = 1.1 ampere

Until it divides at A, the entire current of 1.1 amperes is flowing through the conductor from the battery to A, and again from В through the conductor to the battery. Since this is more current than flows through the smaller resistor it is evident that the resistance of the parallel combination must be less than 10 ohms, the resistance of the smaller resistor. We can find this value by applying Ohms law.

E = 10 volts I = 1.1 amperes

10 1Л

= 9-09 ohms

The resistance of the parallel combination is 9.09 ohms.

Mathematically, we can derive a simple formula for finding the effective resistance of two resistors connected in parallel. This formula is:

Rl x Rj


where R is the unknown resistance,

Rl is the resistance of the first resistor, Rl is the resistance of the second resistor.

If the effective value required is known, and it is desired to connect one unknown resistor in parallel with one of known value, the following transposition of the above formula will simplify the problem of obtaining the unknown value:

Rl xR Rl -R

tt;*ere R is the effective value required, Rj is the known resistor, Rj is the value of the unknown resistance necessary to give R when in parallel with R,.

The resultant value of placing a number of unlike resistors in parallel is equal to the reciprocal of the sum of the reciprocals of the various resistors. This can be expressed as:

111 1

- + - + - + . ... - Rl Rj R3 Rn

The effective value of placing any number of unlike resistors in parallel can be determined from the above formula. However, it is commonly used only when there are three or more resistors under consideration, since the simplified formula given before is more convenient when only two resistors are being used.

From the above, it also follows that when two or more resistors of the same value are placed in parallel, the effective resistance of the paralleled resistors is equal to the value of one of the resistors divided by the number of resistors in parallel.

The effective value of resistance of two or



Figure 6


more resistors connected in parallel is always less than the value of the lowest resistance in the combination. It is well to bear this simple rule in mind, as it will assist greatly in proximating the value of paralleled resistors.

Resistors in To find the total resistance of Series Parallel several resistors connected in series-parallel, it is usually easiest to apply either the formula for series resistors or the parallel resistor formula first, in order to reduce the original arrangement to a simpler one. For instance, in figure 5 the series resistors should be added in each branch, then there will be but two resistors in parallel to be calculated. Similarly in figure 7, although here there will be three parallel resistors after adding the series resistors in each branch. In figure 6В the paralleled resistors should be reduced to the equivalent series value, and then the series resistance values can be added.

Resistances in series-parallel can be solved by combining the series and parallel formulas into one similar to the following (refer to figure 7):

Rl -I- R, Rj + R4 Rs + Re + R7

Voltage Dividers A voltage divider is exactly what its name implies: a resistor or a series of resistors connected across a source of voltage from which various lesser values of voltage may be obtained by connection to various points along the resistor.

A voltage divider serves a most useful purpose in a radio receiver, transmitter or amplifier, because it offers a simple means of obtaining plate, screen, and bias voltages of different values from a common power supply


Voltage Divider 27

Rs R6


source. It may also be used to obtain very low voltages of the order of .01 to .001 volt with a high degree of accuracy, even though a means of measuring such voltages is lacking. The procedure for making these measurements can best be given in the following example.

Assume that an accurately calibrated voltmeter reading from 0 to 150 volts is available, and that the source of voltage is exactly 100 volts. This 100 volts is then impressed through a resistance of exactly 1,000 ohms. It will, then, be found that the voltage along various points on the resistor, with respect to the grounded end, is exactly proportional to the resistance at that point. From Ohms law, the current would be 0.1 ampere; this current remains unchanged since the original value of resistance (1,000 ohms) and the voltage source (100 volts) are unchanged. Thus, at a 500-ohm point on the resistor (half its entire resistance), the voltage will likewise be halved or reduced to 50 volts.

The equation (E = I x R) gives the proof: E = 500 X 0.1 = 50. At the point of 250 ohms on the resistor, the voltage will be one-fourth thetotal value, or 25 volts (E = 250 x 0.1 = 25). Continuing with this process, a point can be found where the resistance measures exactly 1 ohm and where the voltage equals 0.1 volt. It is, therefore, obvious that if the original source of voltage and the resistance can be measured, it is a simple matter to predetermine the voltage at any point along the resistor, provided that the current remains constant, and provided that no current is taken from the tap-on point unless this current is taken into consideration.

Voltage Divider Proper design of a voltage Calculations divider for any type of radio equipment is a relatively simple matter. The first consideration is the amount of bleeder current to be drawn. In addition, it is also necessary that the desired voltage and the exact current at each tap on the voltage divider be known.

Figure 8 illustrates the flow of current in a simple voltage divider and load circuit. The light arrows indicate the flow of bleeder current, while the heavy arrows indicate the flow of the load current. The design of a combined




The arroWM Indleofa the manner In wh/ch the currant flow dlyldoM between the voltage divider lt*eH and the external load circuit.

bleeder resistor and voltage divider, such as is commonly used in radio equipment, is illustrated in the following example:

A power supply delivers 300 volts and is conservatively rated to supply all needed current for the receiver and still allow a bleeder current of 10 milliamperes. The following voltages are wanted: 75 volts at 2 milliamperes for the detector tube, 100 volts at 5 milliamperes for the screens of the tubes, and 250 volts at 20 milliamperes for the plates of the tubes. The required voltage drop across Rj is 75 volts, across Rj 25 volts, across R, 150 volts, and across R it is 50 volts. These values are shown in the diagram of figure 9. The respective current values are also indicated. Apply Ohms law:

R, R4




= 8,823 ohms.

= 1,351 ohms.

Rro*a/ = 7,500+ 2,083 + 8,823 + 1,351 = 19,757 ohms.

A 20,000-ohm resistor with three sliding taps will be of the approximately correct size, and would ordinarily be used because of the difficulty in securing four separate resistors of the exact odd values indicated, and because no adjustment would be possible to compensate for any slight error in estimating the probable

currents through the various taps.

When the sliders on the resistor once are set to the proper point, as in the above ex-

Figure 9


The method hr computing the values of the resistors Is discussed In the aceompanylng text.

ample, the voltages will remain constant at the values shown as long as the current remains a constant value.

Disadvantages of One of the serious disadvan-Voltage Dividers tages of the voltage divider becomes evident when the the current drawn fromone of the taps changes. It is obvious that the voltage drops are interdependent and, in turn, the individual drops are in proportion to the current which flows through the respective sections of the divider resistor. The only remedy lies in providing a heavy steady bleeder current in order to make the individual currents so small a part of the total current that any change in current will result in only a slight-change in voltage. This can seldom be realized in practice because of the excessive values of bleeder current which would be required.

Kirchhoff s Laws Ohms law is all that is necessary to calculate the values in simple circuits, such as the preceding examples; but in more complex problems, involving several loops or more than one voltage in the same closed circuit, the use of Kirchhoff s laws wHl greatly simplify the calculations. These laws are merely rules for applying Ohms law.

Kirchhoffs first law is concerned with net current to a point in a circuit and states that:

At any point in a circuit the current flowing toward the point is equal to the current flowing away from the point.

Stated in another way: if currents flowing to the point are considered positive, and those flowing from the point are considered nega-




The current flowing toward point A Is equal to the current flowing away from point A.

tive, the sum of all currents flowing toward and away from the point - taking signs into account - is equal to zero. Such a sum is known as an algebraic sum; such that the law can be stated thus: The algebraic sum of all currents entering and leaving a point is zero.

Figure 10 illustrates this first law. Since the effective resistance of the network of resistors is 5 ohms, it can be seen that 4 amperes flow toward point A, and 2 amperes flow away through the two 5-ohm resistors in series. The remaining 2 amperes flow away through the 10-ohm resistor. Thus, there are 4 amperes flowing to point A and 4 amperes flowing away from the point. If R is the effective resistance of the network (5 ohms), Rj = 10 ohms, Rj = 5 ohms, R3 = 5 ohms, and E = 20 volts, we can set up the following equation:


R Rl Rj -t- R3

20 5

20 10

5 + 5


Kirchhoffs second law is concerned with net voltage drop around a closed loop in a circuit and states that:

In any closed path or loop in a circuit the sum of the IR drops must equal the sum of the applied e.m.f.s.

The second law also may be conveniently stated in terms of an algebraic sum as: The algebraic sum of all voltage drops around a closed path of loop in a circuit is zero. The applied e.m.f.s (voltages) are considered positive, while IR drops taken in the direction of current flow (including the internal drop of the sources of voltage) are considered negative.

Figure 11 shows an example of the application of Kirchhoffs laws to a comparatively simple circuit consisting of three resistors and


Kirchoffs Laws


3 volts

set voltage drops around each loop equal to zero.

Ii 2ц5 з) + г(1-1-1г)+3= 0 (first loop) -6 +г (l2 +3 l2= 0 (second loop)


2Ii + 2Ii -212+3 = 0

4II + 3 ,

-=.-= l2

2l2- 2Ii +312-6= 0 5 I 2-2 [1-6 = 0

equate 411 + 3

2 Il + 6


20 ll + 15 = 4 If + 12

I i =-ampere


1 .g- ampere


The voftage drop around any closed loop In a network Is equal to zero.

two batteries. First assume an arbitrary direction of current flow in each closed loop of the circuit, drawing an arrow to indicate the assumed direction of current flow. Then equate the sum of all IR drops plus battery drops around each loop to zero. You will need one equation for each unknown to be determined. Then solve the equations for the unknown currents in the general manner indicated in figure 11. If the answer comes out positive the direction of current flow you originally assumed was correct. If the answer comes out negative, the current flow is in the opposite direction to the arrow which was drawn originally. This is illustrated in the example of figure II where the direction of flow of I, is opposite to the direction assumed in the sketch.

Pov/er in In order to cause electrons

Resistive Circuits to flow through a conductor, constituting a current flow, it is necessary to apply an electromotive force (voltage) across the circuit. Less power is expended in creating a small current flow through a given resistance than in creating a large one; so it is necessary to have a unit of power as a reference.

The unit of electrical power is the watt, which is the rate of energy consumption when

an e.m.f. of 1 volt forces a current of 1 ampere through a circuit. The power in a resistive circuit is equal to the product of the voltage applied across, and the current flowing in, a given circuit. Hence: P (watts) = E (volts) X I (amperes).

Since it is often convenient to express power in terms of the resistance of the circuit and the current flowing through it, a substitution of IR for E (E =r: IR) in the above formula gives: P = IR x I or P = IR. In terms of voltage and resistance, P = E/R. Here, I = E/R and when this is substituted for I the original formula becomes P = E x E/R, or P = EVR. To repeat these three expressions:

P = EI, P = IR, and P = EVR,

where P is the power in watts,

E is the electromotive force in volts, and

I is the current in amperes.

To apply the above equations to a typical problem: The voltage drop across a cathode resistor in a power amplifier stage is 50 volts; the plate current flowing through the resistor is 150 milliamperes. The number of watts the resistor will be required to dissipate is found from the formula: P = EI, or 50 X.150 = 7.5 watts (.150 amperes is equal to 150 milliamperes). From the foregoing it is seen that a 7.5-watt resistor will safely carry the required current, yet a 10- or 20-watt resistor would ordinarily be used to provide a safety factor.

In another problem, the conditions being similar to those above, but with the resistance (R = 3334 ohms), and current being the known factors, the solution is obtained as follows: P = IR = .0225 X 333.33 = 7.5. If only the voltage and resistance are known, P = E/R = 2500/333.33 = 7.5 watts. It is seen that all three equations give the same results; the selection of the particular equation depends only upon the known factors.

Power, Energy and Work

It is important to remember that power (expressed in watts, horsepower, etc.), represents the rate of energy consumption or the rate of doing work. But when we pay our electric bill


To deliver the greatest amount of power to the load, the load resistance should be equal to the Internal resistance af the battery Rj.


The ttvo targe unit* ore high valua filter сарос/. *er . Shown beneath fhe*e are various types of by.pass capocltars for r-f md audio applicaHon.

to the power company we have purchased a specific amount of energy or work expressed in the common units of kilowatt-hours. Thus rate of energy consumption (watts or kilowatts) multiplied by time (seconds, minutes or hours) gives us total energy or work. Other units of energy are the watt-second, BTU, calorie, erg, and joule.

Heating Effect Heat is generated when a source of voltage causes a current to flow through a resistor (or, for that matter, through any conductor). As explained earlier, this is due to the fact that heat is given off when free electrons collide with the atoms of the material. More heat is generated in high resistance materials than in those of low resistance, since the free electrons must strike the atoms harder to knock off other electrons. As the heating effect is a function of the current flowing and the resistance of the circuit, the power expended in heat is given by the second formula: P = IR.

2-3 Electrostatics - Capacitors

Electrical energy can be stored in an electrostatic field. A device capable of storing energy in such a field is called capacitor (in earlier usage the term condenser was frequently used but the IRE standards call for the use of capacitor instead of condenser) and

is said to have a certain capacitance. The

energy stored in an electrostatic field is expressed in joules (watt seconds) and is equal to CEV2, where С is the capacitance in farads (a unit of capacitance to be discussed) and E is the potential in volts. The charge is equal to CE, the charge being expressed in coulombs.

Capacitance and Two metallic plates sep-Capacitors arated from each other by

a thin layer of insulating material (called a dielectric, in this case), becomes a capacitor. When a source of d-c potential is momentarily applied across these plates, they may be said to become charged. If the same two plates are then joined together momentarily by means of a switch, the capacitor will discharge.

When the potential was first applied, electrons immediately flowed from one plate to the other through the battery or such source of d-c potential as was applied to the capacitor plates. However, the circuit from plate to plate in the capacitor was incomplete (the two plates being separated by an insulator) and thus the electron flow ceased, meanwhile establishing a shortage of electrons on one plate and a surplus of electrons on the other.

Remember that when a deficiency of electrons exists at one end of a conductor, there is always a tendency for the electrons to move about in such a manner as to re-establish a state of balance. In the case of the capacitor herein discussed, the suфlus quantity of electrons on one of the capacitor plates cannot move to the other plate because the circuit has been broken; that is, the battery or d-c potential was removed. This leaves the capacitor in a charged condition; the capacitor plate with the electron deficiency is positively charged, the other plate being negative.

In this condition, a considerable stress exists in the insulating material (dielectric) which separates the two capacitor plates, due to the mutual attraction of two unlike potentials on the plates. This stress is known as electrostatic energy, as contrasted with electromagnetic energy in the case of an inductor. This charge can also be called potential energy because it is capable of performing work when the charge is released through an external circuit. The charge is proportional to the voltage but the energy is proportional to the voltage squared, as shown in the following analogy.

The charge represents a definite amount of electricity, or a given number of electrons. The potential energy possessed by these electrons depends not only upon their number, but also upon their potential or voltage.

Compare the electrons to water, and two capacitors to standpipes, a 1 [lid. capacitor to

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