1. Electrical Quantities and Basic Circuits
Chapter 1
Electrical Quantities and Basic Circuits
Section 1-1 Electrical Theory
Section 1-2 Circuits
Section 1-3 Magnetism
Section 1-4 Power

2. Objectives Section 1-1 Electrical Theory
State the three fundamental parts of an atom and identify their states of charge.
Define and describe conductors, insulators, and semiconductors.
State the operating function of a diode in a circuit.
State the two forms of energy and give examples of each.
Define voltage and state its unit of measure and common abbreviation.
Define current and state its unit of measure and common abbreviation.
Define resistance and state its unit of measure and common abbreviation.
Determine an unknown voltage, current, and resistance with Ohm’s law.

3. In an atom, electrons orbit the nucleus in shells that can hold a specific number of electrons.
All matter consists of an organized collection of atoms. An atom is the smallest particle that an element can be reduced to and still keep the properties of that element. The three fundamental particles contained in atoms are protons, neutrons, and electrons. Protons and neutrons make up the nucleus, and electrons whirl about the nucleus in orbits of shells. See Figure 1-1. The number of electrons in a shell determines many of the characteristics of the atom.

4. A conductor allows free electrons to pass readily through it.
A conductor is a material that has very little resistance and permits electrons to move through it easily. Conductors offer very little resistance to electron flow and conduct electricity very well. By applying a negative charge to one side of the conductor and a positive charge to the other side of the conductor, electrons are forced to move through the conductor. This movement is called current and is expressed in amperes (A). See Figure 1-2.

5. Electrons in a conductor atom are held to the atom with minimal force.
If the outer shell of electrons in an atom is less than half complete, that material is a conductor. For example, if the outer shell contains one, two, or three electrons, those electrons are held to the atom with minimal force. See Figure 1-3. These electrons can be moved easily from atom to atom. Some examples of conductors are metals such as silver, copper, gold, and aluminum.

6. Electrons in an insulator atom are held to the atom with a relatively strong force and cannot be moved very easily.
An insulator is a material with an atomic structure that allows few free electrons to pass through it. Insulators offer high resistance to electron flow and do not conduct electricity very well. If there are more than four electrons in the outer shell of an atom, those electrons are held to the atom with a relatively strong force and cannot be moved very easily. See Figure 1-4. Some examples of insulators are rubber, plastic, glass, and paper.

7. Nonmetallic-sheathed cable is manufactured in various wire sizes and with a specified number of conductors. Printed circuit boards have conductors laminated on an insulated material that makes up the board.
The electrical term used to describe the opposition to electron flow is resistance. Resistance is expressed in ohms (Ω). The letter R may also be used to represent resistance. Nonmetallic-sheathed cable contains conductors and insulators that are used in common electrical circuits. See Figure 1-5. Printed circuit boards, on the other hand, have conductors laminated on an insulated material that makes up the board.

8. Semiconductors are made from materials that have four valence electrons.
Semiconductor materials fall between the low resistance offered by a conductor and the high resistance offered by an insulator. Semiconductors are made from atoms that have only four valence electrons. See Figure 1-6.

9. Current flows from negative potential to positive potential and is assisted by free electrons when voltage is applied to N-type material.
N-type material is material created by doping a region of a crystal with atoms of a material that have more electrons in their outer shells than the crystal. Adding these atoms to the crystal results in more free electrons. Free electrons (carriers) support current flow. Current flows from negative to positive through the crystal when voltage is applied to N-type material. The material is N-type material because electrons have a negative charge. See Figure 1-7.

10. When voltage is applied to P-type material, the holes are filled with free electrons that move from the negative potential to the positive potential through the crystal.
In P-type material, holes act as carriers. The holes are filled with free electrons when voltage is applied, and the free electrons move from negative potential to positive potential through the crystal. See Figure 1-8. Movement of the electrons from one hole to the next makes the holes appear to move in the opposite direction. Hole flow is equal to and opposite of electron flow. Typical materials used for doping a crystal to create P-type material are gallium, boron, and indium.

11. In a diode, P-type and N-type materials exchange carriers at the junction of the two materials, creating a thin depletion region.
A diode is an electronic component that allows current to pass through it in only one direction. This is made possible by the doping process, which creates N-type material and P-type material in the same component. The P-type and N-type materials exchange carriers at the junction of the two materials, creating a thin depletion region. See Figure 1-9.

12. In forward bias, electrons flow from cathode to anode, but in reverse bias, electrons do not flow.
A diode has a relatively low resistance in the forward-bias direction and a high resistance in the reverse-bias direction. The anode (depicted by a triangle) represents the P-type material, and the cathode (depicted by a straight line) represents the N-type material. Electrons flow from the cathode to the anode, or against the triangle, when the diode is in forward bias. When a negative polarity is applied to the anode and a positive polarity is applied to the cathode, the diode is in reverse bias and there is no electron flow. See Figure 1-10.

13. Manufacturers use a variety of methods to indicate the cathode end of a diode.
Manufacturers mark diodes in different ways to indicate the cathode and the anode. See Figure Diodes may be marked with the schematic symbol, or there may be a band at one end to indicate the cathode. Some manufacturers use the shape of the diode package to indicate the cathode end. Typically the cathode end is marked or enlarged to ensure proper installation and connection into a circuit.

14. The forms of energy used to produce electricity include coal, nuclear power, natural gas, and oil.
The sources of energy used to produce electricity are coal, nuclear power, natural gas, and oil. Wind, solar power, and water also provide energy. These energy sources are used for producing work when converted to electricity. Some energy sources, such as coal, oil, and natural gas, are consumed during use. Energy sources such as wind, solar power, and water are not consumed during use. See Figure 1-12.

15. Electrical energy is used to produce motion, light, heat, sound, and visual outputs.
Electricity is converted into motion, light, heat, sound, and visual outputs. See Figure Approximately 62% of all electricity is converted into rotary motion by electric motors. Three-phase motors use the largest amount of electricity in commercial and industrial applications. Three-phase motors are used because they are the most energy-efficient motors.

16. Voltage is produced by electromagnetism, heat, light, chemical reaction, pressure, and friction.
Voltage may be produced when electrons are freed from atoms by electromagnetism (generators), heat (thermocouples), light (photocells), chemical reaction (batteries/fuel cells), pressure (piezoelectricity in strain gauges), and friction (static electricity). See Figure 1-14.

17. DC voltage is produced from batteries, photovoltaic cells, and rectified AC voltage supplies and can vary from almost pure DC voltage to half-wave DC voltage.
The most common power sources that directly produce DC voltage are batteries, fuel cells, and photovoltaic cells. In addition to obtaining DC voltage directly from batteries and photovoltaic cells, DC voltage is also obtained from a rectified AC voltage supply. See Figure DC voltage is obtained any time an AC voltage is passed through a diode. Diodes convert AC voltage to DC voltage by allowing the voltage and current to flow in only one direction. DC voltage obtained from a rectified AC voltage supply can vary from almost pure DC voltage to half-wave DC voltage. Common DC voltage levels include 1.5 V, 6 V, 9 V, 12 V, 24 V, 36 V, and 125 V.

18. AC voltage has one positive alternation and one negative alternation per cycle and is either single-phase (1ϕ) or three-phase (3ϕ).
A cycle is one complete positive and negative alternation of a wave form. An alternation is half of a cycle. A sine wave has one positive alternation and one negative alternation per cycle. See Figure 1-16.

19. The amount of current a cell or battery can supply depends on the cell or battery size.
Different voltage sources produce different amounts of current. For example, standard AAA, AA, A, C, and D size batteries all produce 1.5 V, but each size is capable of delivering a different amount of current. Size AAA batteries are capable of delivering the smallest amount of current, and size D batteries are capable of delivering the highest amount of current. For this reason, a load connected to a size D battery operates longer than the same load connected to a size AAA battery. See Figure 1-17.

20. The smaller the AWG number, the greater the cross-sectional area and the heavier the wire.
A conductor with a large cross-sectional area has less resistance than a conductor with a small cross-sectional area. See Figure A large conductor may also carry more current. The longer the conductor, the greater the resistance is as well. Short conductors have less resistance than long conductors of the same size. Copper (Cu) is a better conductor (less resistance) than aluminum (Al) and may carry more current for a given size. Temperature also affects resistance. For metals, the higher the temperature, the greater the resistance.

21. Abbreviations are used to simplify the expression of common electrical terms and quantities.
Electrical abbreviations are used to simplify the expression of common electrical terms and quantities. An abbreviation is a letter or combination of letters that represents a word. The exact abbreviation used normally depends on the use of the electrical unit. For example, voltage may be abbreviated using a capital letter E or V. A capital letter V is used to indicate voltage quantity because voltage is measured in volts (V). These abbreviations are often interchanged and both can be used to represent voltage. See Figure 1-19.

22. Ohm’s law is the relationship between voltage (E), current (I), and resistance (R) in a circuit.
Ohm’s law is the relationship between voltage, current, and resistance in a circuit. Ohm’s law states that current in a circuit is proportional to the voltage and inversely proportional to the resistance. Any value in this relationship can be found when the other two values are known. The relationship between voltage, current, and resistance may be visualized by presenting Ohm’s law in pie chart form. See Figure 1-20.

23. 1-1 Checkpoint
1. What are the three fundamental particles contained in atoms?
2. Which particle has a negative charge?
3. What unit is used to measure resistance?
4. What device allows current to flow in only one direction?
5. What type of fuel is used to produce the most amount of electricity?
6. What electrical devices consume the largest share of produced electricity?
7. Voltage is measured in volts (V), but what letter is used to represent voltage?
8. What device converts AC voltage to DC voltage?
9. What are the two types of AC voltage?
10. Current is measured in amperes (A), but what letter is used to represent current?
11. What are the two types of current?
12. Resistance is measured in ohms (Ω), but what letter is used to represent resistance?
13. If resistance is increased in a circuit, does current increase or decrease?
14. If 12 V is applied to a circuit that has a resistance of 500 Ω, how many milliamperes (mA) will flow through the circuit?
15. If 230 V and 6.25 A are measured in a heating element, how much resistance (in Ω) does the heating element have?

24. Objectives Section 1-2 Circuits
Calculate resistance at any point in a series or parallel circuit.
Calculate voltages at any point in a series or parallel circuit.
Calculate current at any point in a series or parallel circuit.

25. A series connection has two or more components connected so there is only one path for current flow.
Fuses, switches, loads, and other electrical components can be connected in series. A series connection is a connection that has two or more components connected so there is only one path for current flow. Opening the circuit at any point stops the flow of current. Current stops flowing any time a fuse blows, a circuit breaker trips, or a switch or load opens. An example of a series connection is a DC series motor. See Figure A DC series motor is a DC motor that has the series field coils connected in series with the armature. The armature wires are marked A1 and A2. The series coil wires are marked S1 and S2.

26. A parallel connection has two or more components connected so there is more than one path for current flow.
Fuses, switches, loads, and other components can be connected in parallel. A parallel connection is a connection that has two or more components connected so there is more than one path for current flow. An example of a parallel connection is a DC shunt motor. See Figure A DC shunt motor is a DC motor that has the field connected in parallel (shunt) with the armature. The armature wires are marked A1 and A2. The parallel (shunt) coil wires are marked F1 and F2.

27. A series/parallel connection is a combination of series- and parallel-connected components.
Fuses, switches, loads, and other components can be connected in a series/parallel connection. A series/parallel connection is a combination of series- and parallel-connected components. An example of a series/parallel connection is a DC compound motor. See Figure A DC compound motor is a DC motor with the field connected in both series and parallel (shunt) with the armature. The armature wires are marked A1 and A2. The parallel (shunt) coil wires are marked F1 and F2. The series coil is marked S1 and S2.

28. Principles of series and parallel circuits can be used to produce several different heat outputs in heating element circuits.
By varying the total resistance of a heating element, the heat output of the heating element can be varied. The total resistance can be varied by using several individual heating elements that can be connected in series, in parallel, or in a series/parallel combination. See Figure 1-24.

29. Photovoltaic cells are placed in series to increase the voltage output from a set of photovoltaic cells.
Photovoltaic cells are rated by the amount of energy they convert. Most manufacturers rate photovoltaic cell output in terms of voltage (V) and current (mA). Photovoltaic cells produce a limited amount of voltage and current. For example, each photovoltaic cell may produce up to 0.6 V. To increase the voltage output, cells are connected in series. See Figure 1-25.

30. Photovoltaic cells are placed in parallel to increase the current output from a set of photovoltaic cells.
In addition to the maximum voltage, each photovoltaic cell can produce up to 40 mA of current. To increase the current output, cells are connected in parallel. See Figure To increase both voltage and current, the individual cells are connected in both series and parallel.

31. 1-2 Checkpoint
What is the total voltage of six 1.5 V batteries connected in series?
If 200 mA total is measured at the 60 V power supply that includes three 100 Ω resistors connected in series, how much current is flowing through each resistor?
What is the total voltage of six 1.5 V/10 mA-rated batteries connected in parallel?
In a circuit that contains a 100 Ω, a 200 Ω, and a 300 Ω resistor connected in parallel, which resistor would have the largest amount of current flowing through it?
If six 3 V/200 mA-rated photovoltaic cells that are connected in series and six more 3 V/200 mA-rated photovoltaic cells also connected in series and then placed in parallel with the first set of six, what is the total voltage of the combination of photovoltaic cells?
If six 3 V/200 mA-rated photovoltaic cells that are connected in series and six more 3 V/200 mA-rated photovoltaic cells also connected in series and then placed in parallel with the first set of six, what is the total available current of the combination of photovoltaic cells?

32. Objectives Section 1-3 Magnetism
Define the molecular theory of magnetism and electromagnetism.
Define inductance and state how it affects an AC circuit.
Define capacitance and state how it affects an AC circuit.

33. The molecular theory of magnetism states that all substances are made up of a number of molecular magnets that can be arranged in either an organized or disorganized manner.
The molecular theory of magnetism is the theory that states that all substances are made up of a number of molecular magnets that can be arranged in either an organized or disorganized manner. See Figure A material is demagnetized if it has disorganized molecular magnets. A material is magnetized if it has organized molecular magnets.

34. In 1819, the Danish physicist Hans C
In 1819, the Danish physicist Hans C. Oersted discovered that a magnetic field is created around an electrical conductor when electric current flows through the conductor.
In 1819, the Danish physicist Hans C. Oersted discovered that a magnetic field is created around an electrical conductor when electric current flows through the conductor. Electromagnetism is the magnetism produced when electric current passes through a conductor. See Figure 1-28.

35. The lines of force (lines of induction) are present along the full length of a conductor.
The direction in which current flows through a conductor determines the direction of the magnetic field around it. Lines of force (lines of induction) are present all along the full length of the conductor. See Figure 1-29.

36. The total number of lines of force (maxwells) in a one sq cm section of a magnetic field equals the flux density of the field (gauss).
One line of force is called a maxwell, and the total number of lines is called flux. The total number of lines of force in a space of 1 square centimeter (sq cm) equals the flux density (in gauss) of the field. For example, 16 lines of force in 1 sq cm equal 16 gauss. See Figure 1-30.

37. If a conductor is formed into a coil, the lines of force combine, forming a stronger field than the lines of force from a single loop.
If a conductor is wound into multiple loops (a coil), the magnetic lines of force combine. Thus, the magnetic force of a coil with multiple turns is stronger than the magnetic force of a coil with a single loop. See Figure 1-31.

38. The strength of a magnetic field produced by a conductor may be increased by increasing the voltage, increasing the number of coils, or inserting an iron core through the coil.
Oersted attempted several other experiments to increase the strength of the magnetic field. He found three ways to increase the strength of the magnetic field in a coil: increase the amount of current by increasing the voltage, increase the number of turns in the coil, and insert an iron core through the coil. See Figure These early experiments led to the development of a huge control industry, which depends on magnetic coils to convert electrical energy into usable magnetic energy.

39. A conductor formed into a coil produces a strong magnetic field around the coil when current flows through the coil.
An inductive circuit is a circuit in which current lags voltage. In a DC circuit, a magnetic field is created and remains at maximum potential until the circuit (switch) is opened. At this point the inductor is storing energy in the circuit. Once the circuit is opened, the magnetic field collapses. At this point the inductor is releasing energy back into the circuit. In an AC circuit, the magnetic field is continuously building and collapsing until the circuit is opened. The magnetic field also changes direction with each change in sine wave alternation. See Figure 1-33.

40. Phase shift occurs when voltage and current in an AC circuit do not reach their maximum amplitude and zero level simultaneously.
In an inductive circuit, the current lags the voltage. When current and voltage are not synchronized, they are said to be out of phase with each other. The greater the inductance in a circuit, the larger the phase shift. See Figure In-phase AC sine waves occur in resistive circuits. Phase shifts in AC sine waves occur in inductive circuits.

41. Capacitors are available in different shapes and sizes.
A capacitive circuit is a circuit in which current leads voltage (voltage lags current). Capacitance (C) is the ability of a component or circuit to store energy in the form of an electrical charge. A capacitor is an electric device that stores electrical energy by means of an electrostatic field. Small capacitors may be manufactured in several shapes and sizes for use in electronic control boards. See Figure Larger capacitors are manufactured for use in bigger devices like electrical motors.

42. With a charged capacitor, the electron orbits become stretched toward the positively charged plate.
When the charging voltage is removed and the shorting switch S2 is closed, the excess electrons on the left plate will move through the switch to the right plate. Now the capacitor acts as a voltage source with the left plate as the negative terminal and the right plate as the positive terminal. At this point the capacitor is releasing energy into the circuit. The supply of electricity is limited to the electrical energy stored in the dielectric. The movement of electrons off the left plate reduces the negative charge, and their arrival at the right plate reduces the positive charge. See Figure 1-36.

43. Current leads voltage in AC capacitive circuits.
The motion of electrons will continue until there is no charge on either plate and the difference of potential is zero. At this point, all of the energy originally stored in the dielectric material will have been used to move the electrons from the left plate to the right plate. No electrostatic field exists between the plates at that time. When capacitance is created in an electrical circuit, a phase shift occurs between the voltage and the current in the circuit. See Figure 1-37.

44. An elastic diaphragm and water can be used to represent the internal action of a capacitor.
An elastic diaphragm represents the internal action of a capacitor. The diaphragm insulates one side of the water supply from the other. Since it is elastic, it can move and stretch to allow the water to push it back and forth. The elastic diaphragm opposes the flow of the water in one direction but flexes back and helps water flow in the reverse direction. This reverse action is faster than the pressure developed when using a pump. The water (current) “leads” the pressure (voltage). This results in a phase shift where current leads voltage. See Figure 1-38.

45. The current flowing in an inductive AC circuit is directly proportional to the applied voltage and inversely proportional to the inductive reactance.
Ohm’s law applies equally to inductive AC circuits as it does to a resistive circuit. The current (I) flowing in an inductive AC circuit is directly proportional to the applied voltage (E) and inversely proportional to the inductive reactance (XL). See Figure The relationship is represented mathematically by the following expression:
In this expression, the current is in amperes (A), the applied voltage is in volts (V), and the reactance is in ohms (Ω). Increasing the voltage or decreasing the reactance will cause an increase in the current. Decreasing the applied voltage or increasing the reactance will cause a decrease in the current.

46. Capacitive reactance is inversely proportional to the capacitance and the frequency.
Capacitive reactance (XC) is the opposition to current flow by a capacitor. Capacitive reactance is measured in ohms (Ω). In an AC circuit, the capacitor is constantly charging and discharging. The voltage across the capacitor is in constant opposition to the applied voltage. This constant opposition to changes in the applied voltage creates an opposition to current flow in the circuit. The amount of opposition offered to current flow in an AC circuit by a capacitor is a function of the capacitance and the frequency of the voltage. The capacitive reactance is inversely proportional to the capacitance and the frequency. This means that increasing the capacitance or frequency causes the reactance to decrease. See Figure 1-40.

47. 1-3 Checkpoint
Does increasing the number of loops in a coil increase or decrease the electromagnetic field when current passes through the coil?
Inductance is measured in henrys (H), but what letter is used to represent inductance?
Capacitance is measured in farads (F), but what letter is used to represent capacitance?
Inductive reactance and capacitive reactance oppose a flow of current in a circuit and are stated or measured in what electrical unit?
In an AC circuit that includes a coil (inductance), is the voltage and current in phase or out of phase?

48. Objectives Section 1-4 Power
Define true power and state its unit of measure and common abbreviation.
Determine an unknown power, voltage, and current with the power formula.
Calculate power at any point in a series or parallel circuit.
Define reactive power and state its unit of measure and common abbreviation.
Define apparent power and state its unit of measure and common abbreviation.
Define power factor and explain its relationship to efficiency.

49. The power formula is the relationship between power (P), voltage (E), and current (I) in an electrical circuit.
The power formula is the relationship between power (P), voltage (E), and current (I) in an electrical circuit. Any value in this relationship may be found using the power formula when the other two values are known. The relationship between power, voltage, and current may be visualized by presenting the power formula in pie chart form. See Figure 1-41.

50. True power is always less than apparent power in a circuit with a phase shift between voltage and current.
The nameplate information on a 1/4 HP inductive motor shows the difference between true power and apparent power. See Figure The 1/4 HP AC motor (resistive/reactive load) is required to lift a 60 lb load 30′ in 15 sec. To lift the load, the motor must deliver W (true power). The motor nameplate lists motor current at 5 A and voltage at 115 V. The rated current (5 A) multiplied by the rated voltage (115 V) equals 575 VA. The difference between true power and apparent power exists because the coil in the motor must produce a rotating magnetic field for the motor to perform the work. Reactive power and true power are required from the power source because the motor coil is a reactive load. In small 1ϕ AC motor circuits, apparent power is much higher than true power.

51. A running capacitor can be added to a motor to achieve a power factor of 1.0 and 100% efficiency.
An example of power factor and efficiency can be shown with a small 60 Hz 1ϕ AC induction motor. The motor may be operated alone or a running capacitor can be added. When the motor is operated on its own, it has a lagging power factor of 37.5% efficiency. This is due to the effect of inductive reaction within the motor. When capacitors and capacitive reaction are introduced into the circuit, the current draw by the motor drops 2.5 A. The drop in current draw results from the corrected power factor. This results in less line voltage drop from the power source and a higher efficiency of the power source. The motor still uses 180 W of power to do its work but the overall efficiency of the system is significantly improved. See Figure 1-43.

52. Ohm’s law can be used on circuits with impedance by substituting Z (impedance) for R (resistance) in the formula.
Ohm’s law is used in circuits that contain impedance. However, the letter Z is substituted for the letter R in the formula. The letter Z represents the total resistive force (resistance and reactance) opposing current flow. The relationship between voltage (E), current (I), and impedance (Z) may be visualized by presenting the relationship in pie chart form where the known variables can be used to calculate the unknown variable. See Figure 1-44.

53. 1-4 Checkpoint
If 8 A are measured in a 120 V circuit, how much power (in W) is the circuit using?
If two 25 W and four 60 W lamps are connected into a parallel circuit, what is the total power (in W) used by the circuit?
If a string of sixty 2 W holiday lights are connected in series, what is the total power (in W) of all the lights?
What electrical unit is reactive power measured in?
What electrical unit is apparent power measured in?
What is the ratio between true power and apparent power called?