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**Basic Electrical Theory**

S. Christian Mariger Ph.D. Biological Systems Engineering Virginia Tech

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Objectives Identify and describe the scientific principles related to electricity. Explain the electron theory and it’s relationship to electricity. Describe electrical terminology. Define Ohm’s law. Explain electrical power and energy relationships.

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**Objectives continued Perform electrical calculations.**

List and describe the basic types of electrical circuits.

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**Electron Theory Each element has its own unique structure.**

All matter is made up of atoms. Atoms are made up of: Electrons Protons Neutrons Each element has its own unique structure.

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Electron Theory Atoms Nucleus Protons: positive charge Neutrons: neutral charge Orbits Electrons: negative charges circle the nucleus in orbits Neutrons Electricity is the flow of electrons from atom to atom in a conductor.

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Electron Theory Electrons are in orbits at different distances from the nucleus. Electrons in the orbit the greatest distance from the nucleus are in the valence shell. The outer orbit contains between 1 and 8 electrons. Conductors contain < 4 e in the outer orbit. Insulators contain > 4 e in the outer orbit. Semiconductors contain exactly 4 e.

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**Electron Theory Valence shell electrons**

Some elements have atoms with valence shell electrons that have a strong magnetic attraction with the + charges in the nucleus. These electrons will not easily move from atom to atom. These elements are poor conductors of electricity and are called insulators. Insulators include: glass, paraffin, rubber, porcelain, wood, and most plastics.

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**Electron Theory Valence shell electrons:**

Some elements have valence shell electrons that have a weak magnetic attraction with the + charges in the nucleus and will move easily from atom to atom. These materials are good electrical conductors. Silver, Gold, Copper and Aluminum are examples of conductors.

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The Copper Atom The copper atom has 29 electrons in four orbits or shells. The lone electron in the outer shell can easily be knocked out of it’s orbit by a free electron from a generator or battery. The electron once free will collide with another nearby atom in a chain reaction. e- e- e- e- Elements with fewer than four electrons in their outer shell are good conductors. Almost all metals have fewer than four electrons in their outer shell and thus are good conductors. e- e- e- e- e- e- e- e- e- e- Cu e- e- e- e- e- e- e- e- e- e- e- e- e- e- e-

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**Electrical Current Current: the flow of electrons in a conductor**

Free electron from generator e- e- Cu e- Cu e- e- Cu Cu e- e- e- e- e- Copper Atom Note that the flow of electrons (e-) is from negative to positive!

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**Electron vs. Conventional Theory**

In reality we know that electrons flow from negative to positive (Electron Theory). However most electrical diagrams are based on the idea that electricity flows from positive to negative (Conventional Theory). This seldom causes problems unless we are working with a DC circuit.

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**Two Theories of Current Flow**

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Electrical Circuit Circuit: a continuous conductor that provides a path for the flow of electrons away from and back to the generator or source of current. Note the “conventional flow” of this diagram. + Battery -

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Electrical Voltage An electrical generator (or battery) forces electrons to move from atom to atom. This push or force is like the pressure created by a pump in a water system. In an electrical circuit this pressure (electromotive force) is called voltage. The volt (V) is the unit by which electrical pressure is measured.

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**Electrical Current (Amperage)**

While voltage refers to the electrical pressure of a circuit, current or amperage refers to the electrical flow of a circuit. Current or amperage is the amount of electric charges (or electrons) flowing past a point in a circuit every second. One ampere (amp or A) is equal to 6.28 billion billion (or 6.28 x 1018) electrons per second.

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Resistance Opposition to flow in electrical circuits is called resistance (or impedance). Measured in Ohms by using an ohmmeter. One ohm, or R is the amount of electrical resistance overcome by one volt to cause one amp of current to flow. Electrical current follows the path of least resistance. Electricity can encounter resistance by the type of conductor, the size of conductor and even corrosion on the connections.

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Resistance Resistance is proportional to the length and the diameter of the wire being used in the circuit. Thick wires (having larger diameter) have less resistance than thin wires (smaller diameter). Longer wires have more resistance than short wires. If the length of wire is doubled, the resistance is doubled. If the size or cross-sectional area of the wire is reduced to half, the resistance is doubled. Wire Gage (AWG): As wire gage ↑ wire size (diameter) ↓ .

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**Resistance Temperature also affects resistance.**

As a conductor gets hotter, the amount of resistance increases. Resistance can be good as well as bad. In a controlled setting such as electric heat or a cooking stove, electrical resistance is beneficial. Too much friction or resistance in a wire can result in the insulation melting and increased potential for a fire hazard.

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**Resistance in a Conductor**

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**R = ρ L / A Resistance Where R = Resistance (Ω)**

ρ = Resistivity of wire – a function of Temperature L= Length of wire A= Cross-sectional area of wire As wire gage ↑ wire size (diameter) ↓

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Resistivity (ρ) When selecting wire it is critical to consider: the length of the run, the gauge of the voltage of the circuit, the amp draw and the temperature.

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Ohm’s Law Identifies the relationship between voltage, amperage (current) and resistance. States that the current (amperage) in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance in a circuit. The greater the voltage, the greater the current. If the resistance is doubled, the current will be half.

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Ohm’s Law

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**Possible results E = IR or I = E/R or R= E/I**

When voltage drops, the amperage drops in the same proportion if the resistance remains the same. If the voltage is cut in half, the amperage is cut in half. When voltage increases, amperage increases in the same proportion if the resistance remains the same. If voltage is doubled, amperage is doubled. When resistance increases, amperage decreases in the inverse proportion as long as the voltage remains the same. If resistance doubles, the amperage is cut in half. When resistance decreases, the amperage goes up in inverse proportion if the voltage remains the same. If resistance is cut in half, the amperage is doubled. E = IR or I = E/R or R= E/I

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Electrical Power Electrical power P is the work done per time by a current I (amperage) under pressure (voltage) V or E. The unit of measure for electrical power is the watt (W). Watts (P) = volts (E) X amperes (I)

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**Electrical Power Relationships**

Volts = watts / amperes Amperes = watts / volts Kilowatts = watts / 1000 Horsepower (theoretical) = 746 watts Horsepower (practical) = 1000 watts Electric motor < 1 HP = 1200 watts/HP

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Electrical Energy Electrical Energy is Electrical Power P multiplied by the time of use t. Electrical Energy = P t (in W or kW) Electrical Energy is what you pay for! Electric Energy Cost ($) = (Pt)($/kWh)

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AC Power Alternating current: current that reverses it’s direction at a given frequency (60 Hz). Single-phase AC changes direction 120 times every second. This is called 60 cycle current, one cycle for each transition from straight to reverse and back to straight polarity.

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AC Phases Phase: is a timed source of electricity through a conductor (60 cycles/second.) Single Phase: is current from one source with three wires. One hot wire One neutral wire One ground wire Three Phase: is actually three single phases combined (180 cycles/second.)

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DC Power In Direct current systems electrons (current) flows in only one direction. DC is used in all automotive and mobile equipment electrical systems. Direct current is also used power electric motors in many “AC” appliances such as the cooling fan in your computer. AC can be “rectified” DC with the use of diodes (devices that allow current to pass in only one direction)

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Conductors

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**A simple circuit often contains**

The source with the necessary potential difference to start the flow of electrons (battery or generator). A conductor for the electrons to flow from the source. A resistive load (light bulb, electric motor, etc.) to use the flow of electrons. A conductor to connect the load back to the source. Often devices such as switches, fuses/circuit breakers are also added.

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**Types Of Circuits There are three basic types of circuits**

Series circuits Parallel circuits Series-Parallel circuits - Some circuits combine elements of both types

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**Series Circuits Series Circuits**

Designed so that the current or electricity must flow through each device or resistor (light bulb for example) in the circuit. If one of the devices such as a lamp for example burns out, the flow of electricity is stopped. This system would not work well for lighting or most applications. The series principle is used in fuses and circuit breakers, where it is necessary to stop the flow of current for safety purposes.

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**Series Circuits Rs = R1 + R2 + R3 +….**

Resistors connected in series have the same current flow through them. Rs = R1 + R2 + R3 +…. Resistors connected in series have different voltage drops across them (unless they have the same resistance); in other words, the voltage drop across the resistor depends on the resistance of the resistor.

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Series Circuits

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**Parallel Circuits Parallel Circuits**

Each device (light bulb for example) has an independent path for the flow of electricity. If one device or “bulb” burns out, the remaining bulbs in the circuit are not affected.

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**Parallel Circuits 1/Rp = 1/R1 + 1/R2 + 1/R3 +….**

Resistors connected in parallel have the same voltage across them. 1/Rp = 1/R1 + 1/R2 + 1/R3 +…. Resistors connected in parallel have different current flows through them (unless they have the same resistance); in other words, the current flow through the resistor depends on the resistance of the resistor.

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Parallel Circuit

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**Series-Parallel Circuit**

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Branch Circuits A circuit may have many branches, but in each branch, the delivery wire and the return wire are attached to the corresponding wire on the main circuit. The main circuit and branch circuits meet at a breaker/fuse box or distribution panel.

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