BASIC ELECTRICAL THEORY
Knowledge of key electrical terminology is necessary to fully understand principles in electrical science.
Conductors are materials with electrons that are loosely bound to their atoms, or materials that permit free motion of a large number of electrons. Atoms with only one valence electron, such as copper, silver, and gold, are examples of good conductors. Most metals are good conductors.
Insulators, or non-conductors, are materials with electrons that are tightly bound to their atoms and require large amounts of energy to free them from the influence of the nucleus. The atoms of good insulators have their valence shells filled with eight electrons, which means they are more than half filled. Any energy applied to such an atom will be distributed among a relatively large number of electrons. Examples of insulators are rubber, plastics, glass, and dry wood.
Resistors are made of materials that conduct electricity but also offer opposition to current flow. These types of materials are also called ''semiconductors'' because they are neither good conductors nor good insulators. Semiconductors have more than one or two electrons in their valence shells, but less than seven or eight. Examples of commonly used semiconductors are silicon and germanium. Each has four valence electrons.
The basic unit of measure for difference in electrical potential is the volt (symbol V or E). Because the volt unit is used, potential difference is called voltage. An object's electrical charge is determined by the number of electrons that the object has gained or lost. Because such a large number of electrons are involved, a unit called the coulomb is used to indicate the charge. One coulomb is equal to 6.24 x 1018 (billion, billion) electrons. For example, if an object gains one coulomb of negative charge, it has gained 6,240,000,000,000,000,000 extra electrons. A volt is defined as “a difference of potential causing one coulomb of current to do one joule of work.” A volt is also defined as “that amount of force required to force one ampere of current through one ohm of resistance.” The latter is the definition with which we will be most concerned in this manual.
What is electricity? Electricity is defined as the flow of electrons through simple materials and devices, or that force which moves electrons. Scientists think electricity is produced by very tiny particles called electrons and protons. These particles are too small to be seen, but they exist as subatomic particles in atoms. To understand them, you must first understand the structure of the atom.
Elements are the basic building blocks of all matter. The atom is the smallest particle to which an element can be reduced while still keeping the properties of that element. An atom consists of a positively charged nucleus surrounded by negatively charged electrons, so that the atom as a whole is electrically neutral. The nucleus is composed of two kinds of subatomic particles: protons and neutrons. These two particles exist in various combinations, depending upon the element involved.
Figure 1: Atomic Structure
The proton is the fundamental positive charge (+) of electricity and is located in the nucleus. The number of protons in the nucleus of any atom specifies the atomic number of that atom, or of that element. The proton carries a single unit positive charge equal in magnitude to the electron’s negative charge. The neutron is slightly heavier than the proton and is electrically neutral.
Figure 2: Carbon Atom
The electron is the fundamental negative charge (-) of electricity and revolves around the nucleus, or center, of the atom in concentric orbits, or shells.
In its natural state, an atom of any element contains an equal number of electrons and protons. The negative charge (-) of each electron is equal in magnitude to the positive charge (+) of each proton; therefore, the two opposite charges cancel, and the atom is said to be electrically neutral, or in balance.
One of the mysteries of the atom is that the electron and the nucleus attract each other. This attraction is called electrostatic force, and it is the force that holds the electron in orbit. Without this electrostatic force, the electron, which is traveling at high speeds, could not stay in its orbit. Bodies that attract each other in this way are called charged bodies. As mentioned previously, the electron has a negative charge and the nucleus (due to the proton) has a positive charge.
Figure 3: Electrostatic Force
The negative charge of the electron is equal, but opposite, to the positive charge of the proton. These charges are referred to as electrostatic charges. In nature, unlike charges (like electrons and protons) attract each other, and like charges repel each other. These facts together are known as the ''First Law of Electrostatics'' and are sometimes referred to as the ''Law of Electrical Charges''. This law should be remembered because it is one of the most vital concepts in electricity.
Some atoms can lose electrons, while others can gain electrons; thus, it is possible to transfer electrons from one object to another. When this occurs, the equal distribution of negative and positive charges no longer exists. One object will contain an excess of electrons and become negatively charged, and the other will become deficient in electrons and become positively charged. These objects, which can contain billions of atoms, will then follow the same law of electrostatics as the electron and proton in the example shown above. The electrons that can move around within an object are said to be free of electrons and will be discussed in more detail in a later section. The greater the number of these free electrons an objective contains, the greater its negative electric charge. Thus, something's electric charge can be used as a measure of its electrons.
A special force acts between the charged objects discussed above. Forces of this type are the results of an electrostatic field that exists around each charged particle or object. This electrostatic field, and the force it creates, can be illustrated with lines called lines of force, as shown below.
Figure 4: Electrostatic Field
As previously stated, charged objects repel or attract each other because of the way these fields act together. This force is present with every charged object. When two objects of opposite charges are brought near one another, the electrostatic field is concentrated in the area between them, as shown in the following figure. The direction of the small arrows shows the direction of the force as it would act upon an electron if it were released into the electric field.
Figure 5: Electrostatic Field Between Opposite Polarity
When two objects of like charge are brought near one another, the lines of force repel each other, as shown in the figure below.
Figure 6: Electrostatic Field Between Like Polarity
The strength of the attraction or of the repulsion depends upon two factors: (1) the amount of charge on each object, and (2) the distance between the objects. The greater the charge on the objects, the greater the electrostatic field between them. The greater the distance between the objects, the weaker the electrostatic field between them, and vice versa. This leads us to the Law of Electrostatic Attraction, commonly referred to as Coulomb's law of electrostatic charges, which states that the force of electrostatic attraction or repulsion is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them, as shown in the following equation:
F = force of electrostatic attraction or repulsion (Newtons)
K = constant of proportionality (Coulomb2/N∙m2) q1 = charge of first particle (Coulombs) q2 = charge of second particle (Coulombs) d = distance between two particles (meters)
If q1 and q2 are both either positively or negatively charged, the force is repulsive. If q1 and q2 are of opposite polarity or charge, the force is attractive.
Potential difference is the term used to describe the magnitude of the electrostatic force between two charged objects. If a charged body is placed between two objects with a potential difference, the charged body will try to move in one direction, depending upon the polarity of the object. If an electron is placed between a negatively charged body and a positively charged body, the potential difference pushes the electron toward the positively charged object. The electron, being negatively charged, will be repelled from the negatively charged object and attracted by the positively charged object.
Figure 7: Potential Difference Between Two Charged Objects
Due to the force of the electrostatic field, these electrical charges have the ability to do work by moving charged particles by attraction and/or repulsion. This ability to do work is called ''potential;'' therefore, if one charge is different from another, there is a potential difference between them. The sum of the potential differences of all charged particles in the electrostatic field is referred to as ''electromotive force'' (EMF).
The basic unit of measure of potential difference is the ''volt''. The symbol for potential difference is ''V'', indicating the ability to do the work of forcing electrons to move. Because the volt unit is used, potential difference is also called ''voltage''.
Potential difference, or voltage, can be measured at any two points in an electrical circuit. For example, the potential difference across a power supply may be several hundred volts, while the potential difference across a load on the same power supply may only be a few volts. The magnitude of the potential difference depends upon both the power supply and the location in the circuit where the potential is measured. This does not mean that the circuit in question does not still contain a high voltage, only that the difference between those two points in the circuit is only a few volts.
Electrons are in rapid motion around the nucleus. While the electrostatic force is trying to pull the nucleus and the electron together, the electron is in motion and trying to pull away. These two effects balance out, keeping the electron in orbit. The electrons in an atom exist in different energy levels. The energy level of an electron is proportional to its distance from the nucleus. Higher energy level electrons exist in orbits, or shells, that are farther away from the nucleus. These shells nest inside one another and surround the nucleus. The nucleus is the center of all the shells. The shells are lettered beginning with the shell nearest the nucleus: K, L, M, N, O, P, and Q. Each shell has a maximum number of electrons it can hold. For example, the K shell will hold a maximum of two electrons, while the L shell will hold a maximum of eight electrons. As shown below, each shell has a specific number of electrons that it will hold for a particular atom.
Figure 8: Energy Shells and Electrons
An important point to remember is that when the outer shell of an atom contains eight electrons, the atom becomes very stable, or very resistant to changes in its structure. This also means that atoms with one or two electrons in their outer shell can lose electrons much more easily than atoms with full outer shells. The electrons in the outermost shell are called valence electrons. When external energy, such as heat, light, or electrical energy, is applied to certain materials, the electrons gain energy, become excited, and may move to a higher energy level. If enough energy is applied to the atom, some of the valence electrons will leave the atom. These electrons are called free electrons. It is the movement of free electrons that provides electric current in a metal conductor.
An atom that has lost or gained one or more electrons is said to be ionized, or to have had an ion change. If an atom loses one or more electrons, it becomes positively charged and is referred to as a positive ion. If an atom gains one or more electrons, it becomes negatively charged and is referred to as a negative ion.
The density of the atoms in copper wire is such that the valence orbits of the individual atoms overlap, causing the electrons to move easily from one atom to the next. Free electrons can drift from one orbit to another in a random direction. When a potential difference is applied, the direction of their movement is controlled. The strength of the potential difference applied at each end of the wire determines how many electrons change from their random motion to a more directional path through the wire. The movement, or flow, of these electrons is called electron current flow, or just current.
To produce current, the electrons must be moved by a potential difference. The symbol for current is I. The basic measurement for current is the ampere (A). One ampere of current is defined as “the movement of one coulomb of charge past any given point of a conductor during one second of time.”
If a copper wire is placed between two charged objects that have a potential difference, all of the negatively charged free electrons will be pushed from the negative charge to the positive charge. This force opposite to the conventional direction of the electrostatic lines of force is shown in the following figure.
Figure 9: Electron Flow Through a Copper Wire with a Potential Difference
The direction of electron flow in the next figure is from the negative (-) side of the battery, through the wire, and back to the positive (+) side of the battery.
Figure 10: Potential Difference Across a Conductor Causes a Current to Flow
The direction of electron flow is from a point of negative potential to a point of positive potential. The solid arrow shown in Figure 10 indicates the direction of electron flow. As electrons vacate their atoms during electron current flow, positively charged atoms (holes) result. The flow of electrons in one direction causes a flow of positive charges. The direction of the positive charges is in the opposite direction of the electron flow. This flow of positive charges is known as ''conventional current'' and is shown in the figure above as a dashed arrow. All of the electrical effects of electron flow from negative to positive, or from a higher potential to a lower potential, are the same as those that would be created by a flow of positive charges in the opposite direction. Therefore, it is important to realize that both conventions are in use and that they are essentially equivalent; that is, all effects predicted are the same.
Generally, electric current flow can be classified as one of two general types: direct current (DC) or alternating current (AC). A direct current flows continuously in the same direction. An alternating current periodically reverses direction. An example of DC current is the current obtained from a battery. An example of AC current is common household current.
Electrical units of measurement are based on the International (metric) System, also known as the SI System. Units of electrical measurement in the SI System include the following:
Voltage, or electromotive force (EMF) or potential difference, is the pressure or force that causes electrons to move in a conductor. Voltage is similar to differential pressure in a piping system that has the potential to cause fluid to flow. In electrical formulas and equations, voltage is symbolized with a capital E, while on laboratory equipment or schematic diagrams, voltage is often represented with a capital V.
Electron current, or amperage, is described as the movement of free electrons through a conductor. In electrical formulas, current is symbolized with a capital I, while in the laboratory or on schematic diagrams, it is common to use a capital A to indicate amperage (amps).
''Resistance'' is “the opposition to current flow.” The amount of opposition to current flow produced by a material depends upon the number of available free electrons it contains and the types of obstacles the electrons encounter as they attempt to move through the material. Resistance is measured in ohms and is represented by the symbol R in equations. One ohm is defined as “the amount of resistance that will limit the current in a conductor to one ampere when the potential difference (voltage) applied to the conductor is one volt.” The symbol for ohm is the Greek letter capital omega (Ω). If a voltage is applied to a conductor, current flows. The amount of current flow depends upon the resistance of the conductor. The lower the resistance, the higher the current flow for a given amount of voltage. The higher the resistance, the lower the current flow.
In 1827, Georg Simon Ohm discovered that there was a definite relationship between the voltage, current, and resistance in an electrical circuit. Ohm's law defines this relationship and can be stated in three ways:
E = IxR or E = IR
If any two of the component values are known, the third can be calculated.
Example 1: Given that I = 2 A and E = 12 V, find the circuit resistance.
Solution: Since applied voltage and circuit current are known, use Ohm's law to solve for resistance.
Example 2: Given E = 260 V and R = 240 Ώ, solve for the current flow through a circuit.
Solution: Since applied voltage and resistance are known, use Ohm's law to solve for current.
Example 3:Find the applied voltage when given a circuit resistance of 100 Ώ and circuit current of 0.5 amps.
Solution: Since circuit resistance and circuit current are known, use Ohm's law to solve for applied voltage.
Electricity is used to do work, such as turning a motor or generating heat. Specifically, ''power'' is “the rate at which work is done,” or “the rate at which heat is generated.” The unit commonly used to specify electric power is the watt. In equations, you will find power abbreviated with the capital letter P, and the watt, the unit of measure for power, is abbreviated with the capital letter W. Power is also described as the current (I) in a circuit times the voltage (E) across the circuit. The following equation is a mathematical representation of this concept.
Using Ohm's law for the value of voltage (E),
and using substitution laws,
power can be described as the current (I) in a circuit squared times the resistance (R) of the circuit. The following equation is the mathematical representation of this concept.
P = I2R
To understand electricity and one of its major means of generation you must first understand the basic principles of magnetism. '''Magnetism''' is a property of matter which responds to a magnetic field. All matter responds to a magnetic field to some degree on the atomic or subatomic level, although some materials such as glass or plastic are affected to such a small degree that it is essentially negligible. Because electricity is basically the movement of charged particles (electrons) along a conductor, magnetism has a profound effect on electrical currents in a material.
Figure 11: Basic Magnetic Field
Figure 11 shows a basic permanent bar magnet and its magnetic field. The north and south "poles" are labeled as such. The lines of flux are illustrated, and represent the direction of force the magnetic field will have on other objects.
Now look what happens as an electrical conductor is passed through this field (Figure 12). For this example we will use a copper wire. As the wire passes through the field, the electrons in the wire are forced to move in one direction along the wire.
Figure 12: Conductor Through a Magnetic Field
If the wire was kept still and instead the magnet itself was rotated in a circle, causing the north and south poles to alternatively pass by the wire, the electrons would move first in one direction (as seen in Figure 12), and then in the opposite direction for the opposite pole.? This back and forth movement of electrons in a conductor is the basis for alternating current (AC) power. Figure 13 demonstrates what happens when you do this with a load in a closed circuit.
Figure 13: Magnetic Field with a Load
Just as a moving magnetic field can generate electrical current, a conductor with an electrical current moving though it (I) generates its own magnetic field (B)(Figure 14).
Figure 14: Magnetic Field generated by a Current
The magnetic properties of electrical conductors can be utilized in many different ways to achieve specific goals. Coils, transformers, generators and electric motors are just a few examples of the technology you use every day, all thanks to the relationship between electricity and magnetism.
There are several types of electrical circuits. Each type has distinct characteristics related to how voltage and current behave within the circuit.
Each electrical circuit has at least four basic parts:
In the next figure, the source of electromotive force or EMF is the battery, the conductors are wires that connect the various component parts, the resistor is the load, and a switch is used as the circuit control device.
A closed circuit (shown below) is an uninterrupted, or unbroken, path for current from the source (EMF), through the load, and back to the source.
Figure 15: Closed Circuit
An open circuit, or incomplete circuit (Figure 16), exists if a break in the circuit occurs; this removes the complete path for current flow.
Figure 16: Open Circuit
A short circuit is a circuit that offers very little resistance to current flow and can cause dangerously high current flow through a circuit. Short circuits usually are caused by an inadvertent connection between two points in a circuit that offers little or no resistance to current flow. Shorting around resistor R in the figure below will probably cause the fuse to blow.
Figure 17: Short Circuit
A series circuit is a circuit where there is only one path for current flow. In a series circuit, the current is the same throughout the circuit. This means that the current flow through R1 is the same as the current flow through R2 and R3. In a series circuit, current is the same, while the voltage throughout the circuit is different.
Figure 18: Series Circuit
Example: A series circuit has three resistors with resistances of 60Ω, 100Ω, and 150Ω in series (shown below). What is the total resistance of the circuit?
Figure 19: Resistance in a Series Circuit
The total voltage across a series circuit is equal to the sum of the voltages across each resistor in the circuit (Figure 20), as shown in the following equation:
Figure 20: Voltage Drops in a Series Circuit
Ohm's law may now be applied to either the entire series circuit or to individual component parts of the circuit. When used on individual component parts, the voltage across that part is equal to the current times the resistance of that part. For the circuit shown in the following figure, the voltage can be determined as shown below:
Figure 21: Voltage Total in a Series Circuit
To find the total voltage across a series circuit, multiply the current by the total resistance, as shown in the following equation:
Example 1: A series circuit has three resistors with resistances of 50Ω, 75Ω, and 100Ω in series (Figure 22). Find the voltage necessary to produce a current of 0.5 amps.
Figure 22: Example 1 Series Circuit
Step 1: Find circuit current. As we already know, current is the same throughout a series circuit. In this case, it is already given as 0.5 amps.
Step 2: Find RT.
Step 3: Find VT. Use Ohm's law.
Example 2: A 120 V battery is connected in series with three resistors with resistances of 40Ω, 60Ω, and 100Ω. Find the voltage across each resistor.
Figure 23: Example 2 Series Circuit
Step 1: Find total resistance.
Step 2: Find circuit current (I).
Solving for I:
Step 3: Find the voltage across each component.
The voltages of V1, V2, and V3 in Example 2 are known as voltage drops or IR drops. Their effect is to reduce the available voltage to be applied across the other circuit components. The sum of the voltage drops in any series circuit is always equal to the applied voltage. We can verify our answer in Example 2 by using the following equation:
Parallel circuits are those circuits that have two or more components connected across the same voltage source as shown below. Resistors R1, R2, and R3 are in parallel with each other and the source. Each parallel path is a branch with its own individual current. When the current leaves the source V, part I1 of IT will flow through R1, part I2 will flow through R2, and part I3 will flow through R3. Current through each branch can be different, but voltage is the same.
Figure 24: Parallel Circuit
The sum of the currents flowing through each branch of a parallel circuit is equal to the total current flow in the circuit. Using Ohm's law, the branch current for a three-branch circuit equals the applied voltage divided by the resistance, as shown in the following equations:
Example 1: Two resistors, each drawing 3 A, and a third resistor drawing 2 A are connected in parallel across a 115 V source (Figure 25). What is the total current?
Figure 25: Parallel Circuit
Example 2: Two branches, R1 and R2, are across a 120 V power source. The total current flow is 30 A. Branch R1 takes 22 A. What is the current flow in Branch R2?
Figure 26: Example 2 Parallel Circuit
Example 3: In a parallel circuit, R1= 15 Ω, R2 = 20 Ω, and R3 = 10 Ω, with an applied voltage of 120 V. What current will flow through each branch?
Figure 27: Example 3 Parallel Circuit
Example: Find the total resistance of the circuit shown in the figure below if the line voltage is 120 V and total current is 26 A.
Figure 28: Equivalent Resistance in a Parallel Circuit
The total load connected to a 120 V source is the same as the single equivalent resistance of 4.62 Ω connected across the source (Figure 28). Equivalent resistance is the total resistance, or a combination of the loads present in a circuit.
The total resistance in a parallel circuit can also be found by using the following equation:
Example 1: Find the total resistance of a 4Ω, an 8Ω, and a 16Ω resistor in parallel (Figure 29).
Figure 29: Total Resistance in a Parallel Circuit
NOTE: Whenever resistors are in parallel, the total resistance is always smaller than in any single branch.
Example 2: Now add a fourth resistance of 4Ω in parallel to the circuit in Figure 29 above. What is the new total resistance of the circuit?
Example: Five lamps, each with a resistance of 40Ω, are connected in parallel. Find the total resistance.
When any two resistors are unequal in a parallel circuit, it is easier to calculate RT by multiplying the two resistances and then dividing the product by the sum, as shown in the following equation. (This is only valid when there are only two resistors in parallel.)
Example: Find the total resistance of a parallel circuit that has one 12 Ω resistor and one 4 Ω resistor.
In certain cases involving two resistors in parallel, it is useful to find an unknown resistor, Rx, to obtain a certain RT. To find the appropriate formula, we start with the equation for total resistance and let the known resistor be R and the unknown resistor be Rx.
Example: What value of resistance must be added, in parallel, with an 8Ω resistor to provide a total resistance of 6 Ω (shown below)?
Figure 30: Example Parallel Circuit
Faults within a DC circuit will cause various effects, depending upon the nature of the fault. An understanding of the effects of these faults is necessary to fully understand DC circuit operation.
A circuit must have a complete path for current flow; that is, it must be connected from the negative side to the positive side of a power source without interruption. A series circuit has only one path for current to flow. If this path is broken, no current flows, and the circuit becomes an open circuit (Figure 31), and the resistance across the broken circuit is infinite (∞).
Figure 31: Open Series Circuit
Circuits can be opened deliberately, such as by the use of a switch, or they may be opened by a defect, such as a broken wire or a burned-out resistor.
Since no current flows in an open series circuit, there are no voltage drops across the loads. No power is consumed by the loads, and total power consumed by the circuit is zero.
A parallel circuit has more than one path for current to flow.? If one of the paths is opened, current will continue to flow as long as a complete path is provided by one or more of the remaining paths (Figure 32). It does not mean that you cannot stop current flow through a parallel circuit by opening it at one point; it means that the behavior of a parallel circuit depends on where the opening occurs.
Figure 32: Open Parallel Circuit (Total)
If a parallel circuit is opened at a point where only a branch current flows, then only that branch is open, and current continues to flow in the rest of the circuit (Figure 33).
Figure 33: Open Parallel Circuit (Branch)
In a DC circuit, the only current limit is the circuit resistance. If there is no resistance in a circuit, or if the resistance suddenly becomes zero, a very large current will flow. This condition of very low resistance and high current flow is known as a ''short circuit'' (Figure 34).
Figure 34: Shorted DC Circuit
A short circuit is said to exist if the circuit resistance is so low that current increases to a point where damage can occur to circuit components. With an increase in circuit current flow, the terminal voltage of the energy source will decrease. This occurs due to the internal resistance of the energy source causing an increased voltage drop within the energy source. The increased current flow resulting from a short circuit can damage power sources, burn insulation, and start fires. Fuses are provided in circuits to protect against short circuits.
When a parallel circuit becomes short circuited, the same effect occurs as in a series circuit; there is a sudden and very large increase in circuit current (Figure 35).
Figure 35: Shorted Parallel Circuit
Parallel circuits are more likely than series circuits to develop damaging short circuits. This is because each load is connected directly across the power source. If any of the load becomes shorted, the resistance between the power source terminals is practically zero. If a series load becomes shorted, the resistance of the other loads keeps the circuit resistance from dropping to zero (Figure 36).
Figure 36: Shorted Resistor in a Series Circuit