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Table of Contents
- Introduction ..............................................................................
- Electron Theory........................................................................
- Conductors, Insulators and Semiconductors.........................
- Electric Charges .......................................................................
- Current ......................................................................................
- Voltage ....................................................................................
- Resistance ..............................................................................
- Simple Electric Circuit ...........................................................
- Ohmís Law ..............................................................................
- DC Series Circuit ....................................................................
- DC Parallel Circuit ..................................................................
- Series-Parallel Circuits ...........................................................
- Power ......................................................................................
- Magnetism .............................................................................
- Electromagnetism ..................................................................
- Introduction to AC .................................................................
- AC Generators ........................................................................
- Frequency...............................................................................
- Voltage and Current ...............................................................
- Inductance ..............................................................................
- Capacitance ............................................................................
- Inductive and Capacitive Reactance
- Series R-L-C Circuit ................................................................
- Parallel R-L-C Circuit ..............................................................
- Power and Power Factor in an AC Circuit
- Transformers ..........................................................................
- Three-Phase Transformers ....................................................
- Review Answers ....................................................................
- Final Exam ..............................................................................
Welcome to the first course in the STEP 2000 series, Siemens Technical Education Program designed to prepare our distributors for the year 2000 and beyond. This course covers Basics of Electricity and is designed to prepare you for subsequent courses on Siemens Energy & Automation products.
Upon completion of Basics of Electricity you will be able to:
ï Explain the difference between conductors and
insulators
ï Use Ohmís Law to calculate current, voltage, and
resistance
ï Calculate equivalent resistance for series, parallel, or
series-parallel circuits
ï Calculate voltage drop across a resistor
ï Calculate power given other basic values
ï Identify factors that determine the strength and polarity
of a current-carrying coilís magnetic field
ï Determine peak, instantaneous, and effective values of
an AC sine wave
ï Identify factors that effect inductive reactance and ca-
pacitive reactance in an AC circuit
ï Calculate total impedance of an AC circuit
ï Explain the difference between real power and apparent
power in an AC circuit
Introduction
Elements of an atom
Electron Theory
All matter is composed of molecules which are made up of a combination of atoms. Atoms have a nucleus with electrons orbiting around it. The nucleus is composed of protons and neutrons (not shown). Most atoms have an equal number of electrons and protons. Electrons have a negative charge (-). Protons have a positive charge (+). Neutrons are neutral. The negative charge of the electrons is balanced by the positive charge of the protons. Electrons are bound in their orbit by the attraction of the protons. These are referred to as bound electrons.
Electrons in the outer band can become free of their orbit by the application of some external force such as movement through a magnetic field, friction, or chemical action. These are referred to as free electrons. A free electron leaves a void which can be filled by an electron forced out of orbit from another atom. As free electrons move from one atom to the next an electron flow is produced. This is the basis of electricity.
Free electrons
Conductors
Conductors, Insulators and Semiconductors
An electric current is produced when free electrons move from one atom to the next. Materials that permit many elec- trons to move freely are called conductors. Copper, silver, aluminum, zinc, brass, and iron are considered good conduc- tors. Copper is the most common material used for conduc- tors and is relatively inexpensive.
Materials that allow few free electrons are called insulators. Materials such as plastic, rubber, glass, mica, and ceramic are good insulators.
An electric cable is one example of how conductors and insulators are used. Electrons flow along a copper conductor to provide energy to an electric device such as a radio, lamp, or a motor. An insulator around the outside of the copper conductor is provided to keep electrons in the conductor.
Insulators
Elements are often identified by the number of electrons in orbit around the nucleus of the atoms making up the element and by the number of protons in the nucleus. A hydrogen atom, for example, has only one electron and one proton. An aluminum atom (illustrated) has 13 electrons and 13 protons. An atom with an equal number of electrons and protons is said to be electrically neutral.
Electrons in the outer band of an atom are easily displaced by the application of some external force. Electrons which are forced out of their orbits can result in a lack of electrons where they leave and an excess of electrons where they come to rest. The lack of electrons is called a positive charge because there are more protons than electrons. The excess of electrons has a negative charge. A positive or negative charge is caused by an absence or excess of electrons. The number of protons remains constant.
Neutral state of an atom
Electric Charges
Positive and negative charges
Attraction and repulsion of electric charges
The old saying, ìopposites attract,î is true when dealing with electric charges. Charged bodies have an invisible electric field around them. When two like-charged bodies are brought together, their electric field will work to repel them. When two unlike-charged bodies are brought together, their electric field will work to attract them. The electric field around a charged body is represented by invisible lines of force. The invisible lines of force represent an invisible elec- trical field that causes the attraction and repulsion. Lines of force are shown leaving a body with a positive charge and entering a body with a negative charge.
During the 18th century a French scientist, Charles A. Coulomb, studied fields of force that surround charged bodies. Coulomb discovered that charged bodies attract or repel each other with a force that is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them. Today we call this Coulombís Law of Charges. Simply put, the force of attraction or repulsion depends on the strength of the charged bodies, and the distance between them.
Coulombís Law
Direction of current flow Some authorities distinguish between electron flow and current flow. Conventional current flow theory ignores the flow of electrons and states that current flows from positive to negative. To avoid confusion, this book will use the electron flow concept which states that electrons flow from negative to positive.
Electricity can be compared with water flowing through a pipe. A force is required to get water to flow through a pipe. This force comes from either a water pump or gravity. Voltage is the force that is applied to a conductor that causes electric current to flow.
Electrons are negative and are attracted by positive charges. They will always be attracted from a source having an excess of electrons, thus having a negative charge, to a source having a deficiency of electrons which has a positive charge. The force required to make electricity flow through a conduc- tor is called a difference in potential, electromotive force (emf), or more simply referred to as voltage. Voltage is desig- nated by the letter ìEî, or the letter ìVî. The unit of measure- ment for voltage is volts which is designated by the letter ìVî.
Voltage
A third factor that plays a role in an electrical circuit is resistance. All material impedes the flow of electrical current to some extent. The amount of resistance depends upon composition, length, cross-section and temperature of the resistive material. As a rule of thumb, resistance of a conduc- tor increases with an increase of length or a decrease of cross-section. Resistance is designated by the symbol ìRî. The unit of measurement for resistance is ohms (W).
Resistance is usually indicated symbolically on an electrical drawing by one of two ways. An unfilled rectangle is com- monly used. A zigzag line may also be used.
Resistance can be in the form of various components. A resistor may be placed in the circuit, or the circuit might contain other devices that have resistance.
The following chart reflects special prefixes that are com- monly used when dealing with values of resistance:
Prefix Symbol Decimal
1 kilohm 1 kW 1000 W 1 megohm 1 MW 1,000,000 W
Resistance
Resistance circuit symbols
Units of measurement for resistance
- Elements are identified by the number of ____________ in orbit around the nucleus.
- A material that has an excess of electrons is said to have a ____________ charge.
- A material that has a deficiency of electrons is said to have a ____________ charge.
- Like charges ____________ and unlike charges ____________.
- The force that is applied to a conductor to cause current flow is ____________.
- Electrons move from
a. positive to negative b. negative to positive
- With an increase of length or a decrease of cross- section of a conductor, resistance will
a. increase b. decrease
Review 2
Ohmís Law
George Simon Ohm and Ohmís Law
The relationship between current, voltage and resistance was studied by the 19th century German mathematician, George Simon Ohm. Ohm formulated a law which states that current varies directly with voltage and inversely with resis- tance. From this law the following formula is derived:
I E
R
= or Current = Voltage Resistance
Ohmís Law is the basic formula used in all electrical circuits. Electrical designers must decide how much voltage is needed for a given load, such as computers, clocks, lamps and motors. Decisions must be made concerning the rela- tionship of current, voltage and resistance. All electrical design and analysis begins with Ohmís Law. There are three mathematical ways to express Ohmís Law. Which of the formulas is used depends on what facts are known before starting and what facts need to be known.
I E R
E I R R E
I
= = × =
There is an easy way to remember which formula to use. By arranging current, voltage and resistance in a triangle, one can quickly determine the correct formula.
Ohmís Law triangle
To use the triangle, cover the value you want to calculate. The remaining letters make up the formula.
R E
I
I E E = I ×R^ =
R
Using the triangle
Ohmís Law can only give the correct answer when the correct values are used. Remember the following three rules:
ï Current is always expressed in Amperes or Amps
ï Voltage is always expressed in Volts
ï Resistance is always expressed in Ohms
Using the simple circuit below, assume that the voltage sup- plied by the battery is 10 volts, and the resistance is 5 W.
To find how much current is flowing through the circuit, cover the ìIî in the triangle and use the resulting equation.
I E
R
= → I =^10 volts^ → I= amps 5
Ω
Using the same circuit, assume the ammeter reads 200 mA and the resistance is known to be 10 W. To solve for voltage, cover the ìEî in the triangle and use the resulting equation.
E = I × R → E =. 2 × 10 → E = 2 volts
Remember to use the correct decimal equivalent when deal- ing with numbers that are preceded with milli (m), micro (m) or kilo (k). In this example had 200 been used instead of converting the value to .2, the wrong answer of 2000 volts would have been calculated.
Examples of solving Ohmís Law
The equation for total resistance in a series circuit allows us to simplify a circuit. Using Ohmís Law, the value of current can be calculated. Current is the same anywhere it is mea- sured in a series circuit.
I E
R
I
I amps
=
=
=
Ω Ω Ω Ω Ω
Voltage can be measured across each of the resistors in a circuit. The voltage across a resistor is referred to as a voltage drop. A German physicist, Kirchhoff, formulated a law which states the sum of the voltage drops across the resis- tances of a closed circuit equals the total voltage applied to the circuit. In the following illustration, four equal value resistors of 1.5 Weach have been placed in series with a 12 volt battery. Ohmís Law can be applied to show that each resistor will ìdropî an equal amount of voltage.
Ω Ω Ω Ω
Current in a series circuit
Voltage in a series circuit
First, solve for total resistance:
Rt R R R R Rt Rt
= + + + = + + + =
Ω
Second, solve for current:
I E
R
I
I amps
=
=
=
Third, solve for voltage across any resistor:
E I R
E
E volts
= ×
= ×
If voltage were measured across any single resistor, the meter would read three volts. If voltage were read across a combination of R3 and R4 the meter would read six volts. If voltage were read across a combination of R2, R3, and R the meter would read nine volts. If the voltage drops of all four resistors were added together the sum would be 12 volts, the original supply voltage of the battery.
It is often desirable to use a voltage potential that is lower than the supply voltage. To do this, a voltage divider, similar to the one illustrated, can be used. The battery represents Ein which in this case is 50 volts. The desired voltage is represented by Eout which mathematically works out to be 40 volts. To calculate this voltage, first solve for total resistance.
Rt R R Rt Rt
= + = + =
Voltage division in a series circuit
