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**Matter is anything that has mass (weight) and occupies space.**

Everything in the world is made of matter. Matter is anything that has mass (weight) and occupies space. All matter is made up of molecules that have a certain number of atoms. Atom is broken down even further into a nucleus, neutrons , protons and electrons. Molecule is a group of atoms. Compound is a group of molecules. Elements a single atom that still maintaining the properties of the original material called. Matter has three states: Solid, Liquid, and Vapor.

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MOLECULE A single molecule of water (H2O) which is made up of two hydrogen atoms and one oxygen atom. Not all materials are made up of molecules. Copper, for example, is made up of a single copper atom.

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THE ATOM A single atom consists of three basic components: a proton, a neutron, and an electron. Within the atom there is a Nucleus. The Nucleus contains the protons and neutrons. Orbiting around the nucleus are the electrons.

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ATOM CONSTRUCTION An atom is similar to a miniature solar system. As the sun is in the center of the solar system, so is the nucleus is in the center of the atom. Protons and neutrons are contained within the nucleus. Electrons orbit around the nucleus, which would be similar to planets orbiting around the sun.

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NUCLEUS The Nucleus is located in the center of the atom (shown in red). The Nucleus contains the protons and neutrons. Orbiting around the nucleus are the electrons.

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PROTONS Protons are located within the nucleus of the atom (shown in blue) . Protons are positively (+) charged. NEUTRONS Neutrons add atomic weight to an atom (shown in green).Neutrons have no electrical charge. ELECTRONS Electrons orbit around the nucleus of the atom (shown in yellow).Electrons are negatively (-) charged.

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Normally electrons are prevented from being pulled into the atom by the forward momentum of their rotation. Electrons are also prevented from flying away because of the magnetic attraction of the protons inside the nucleus, the same type of force that keeps the planets orbiting around the sun.

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ELECTRICAL CHARGES Remember: Unlike charges attract Like charges, repel Atoms always try to remain electrically balanced.

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BALANCED ATOMS Atoms normally have an equal number of electrons and protons. The negative charge of the electrons will cancel the positive charge of the protons, thus balancing the charge of the atom. This cancellation of charges creates a natural attraction or bonding

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ION PARTICLES When an atom loses or gains an electron, an imbalance occurs. The atom becomes either a positively or negatively charged particle called an ION. IONs will take or release an electron to become balanced again, this process is responsible for electron flow ( electricity ).

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ION CHARGE A positive (+) ION has one less electron than it has protons. A negative (-) ION has one more electron than it has protons. The positive ION attracts a negative ION to become balanced.

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ELECTRON ORBITS Electrons rotate around the atom at different orbits called Rings, Orbits, or Shells. BOUND ELECTRONS orbit the nucleus on the inner rings. Bound electrons have a strong magnetic attraction to the nucleus. FREE ELECTRONS orbit on the outermost ring which is known as the VALANCE RING.

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FREE ELECTRONS Only the FREE ELECTRONS in the outermost shell (Valance Ring) are free to move from atom to atom. This movement is called ELECTRON FLOW. Because of their distance from the nucleus, free electrons have a weak magnetic attraction. Since this attraction is not strong , the electrons move easily from atom to atom.

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INSULATORS An INSULATOR is any material that inhibits (stops) the flow of electrons (electricity). An insulator is any material with 5 to 8 free electrons in the outer ring. A toms with 5 to 8 electrons in the outer ring are held (bound) tightly to the atom, and make no room for more electrons. Insulator material includes glass, rubber, and plastic.

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CONDUCTORS A CONDUCTOR is any material that easily allows electrons (electricity) to flow. A CONDUCTOR has 1 to 3 free electrons in the outer ring. Because atoms with 1 to 3 electrons in the outer ring are held loosely to the atom, they can easily move to another atom or make room for more electrons. Conductor material includes copper and gold.

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SEMICONDUCTORS Any material with exactly 4 free electrons in the outer orbit is called SEMICONDUCTORS. A semiconductor is neither a conductor or insulator. semiconductor material includes carbon, silicon, and germanium. These materials are be used in the manufacturer of diodes, transistors, and integrated circuit chips.

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**Two Current Flow theories exist.**

The first is: ELECTRON THEORY The Electron Theory states that current flows from NEGATIVE to POSITIVE. Electrons move from atom to atom as they move through the conductor towards positive.

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**The second Current Flow theory is:**

CONVENTIONAL THEORY Conventional theory, also known as HOLE THEORY, states that current flows from POSITIVE to NEGATIVE. Protons or the lack of electrons (the holes) moves towards the negative. (Current flow direction in Hole Theory is the opposite of that in Electron Theory) .

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VOLTAGE Voltage is the electrical force that moves electrons through a conductor. Voltage is electrical pressure also known as EMF (Electro Motive Force) that pushes electrons. The greater the difference in electrical potential push (difference between positive and negative), the greater the voltage force

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Voltmeter The instrument used to measure voltage, difference potential or electromotive force is called voltmeter. A voltmeter is wired in parallel with the circuit to measure voltage. Safety instructions for measuring voltage: 1. choose a suitable voltmeter, each voltmeter is designed with a limit of voltage measurement. 2. Be sure that the connecting of positive terminal (+) and negative terminal (-) of voltmeter are correct.

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**Voltage can exist between two points without electron flow. **

The Voltmeter measures electrical pressure difference between two points being measured. Voltage can exist between two points without electron flow. Voltage is measured in units called VOLTS. Voltage measurements can use different value prefixes such as millivolt, volt, Kilovolt, and Megavolt. LARGER THAN BASE UNIT BASIC UNIT LESS THAN VOLTAGE kV V mV Symbol Kilovolt Volt millivolt Pronounced 1,000 1 0.001 Multiplier

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CURRENT (AMPERES) CURRENT is the quantity or flow rate of electrons moving past a point within one second. Current flow is also known as amperage, or amps for short. Higher voltage will produce higher current flow, and lower voltage will produce lower current flow.

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**Ammeter is the instrument used to measure current.**

Safety instructions for current measurement: 1. choose a suitable ammeter, since each ammeter has different limit of current measurement. 2. Be sure that the connection to positive terminal (+) and negative terminal (-) of ammeter are correct. 3. Do not directly connect ammeter terminals to dry cell terminals. Since it can damage the meter.

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**Current is measured in units called Amperes or AMP **

Ammeters are placed in series (inline) to count the electrons passing through it. Current is measured in units called Amperes or AMP Amperage measurements can use different value prefixes, such as micro amp, milliamp and Amp. BASIC UNIT LESS THAN BASE UNIT AMPERAGE A mA µA Symbol Amp milliamp Micro amp Pronounced 1 0.001 Multiplier

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**AFFECTS OF CURRENT FLOW **

Two common effects of current flow are Heat Generation – Electromagnetism HEAT: When current flows, heat will be generated. The higher the current flow the greater the heat generated. An example would be a light bulb. ELECTROMAGNETISM: When current flows, a small magnetic field is created. The higher the current flow, the stronger the magnetic field. An example: Electromagnetism principles are used in alternators, ignition systems, and other electronic devices.

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RESISTANCE Resistance is the force that reduces or stops the flow of electrons. It opposes voltage. Higher resistance will decrease the flow of electrons and lower resistance will allow more electrons to flow.

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**Ohmmeter is the instrument used to measure resistance.**

Multi meter is a meter combines the functions of ammeter, voltmeter and ohmmeter. Steps for resistance measurement: Turn the face dial to a position for required measuring, resistance, then touch both of terminals of multi meter (see figure 1) and adjust the meter range to 0 Ω. Touch both of terminals of meter to a resistance and take the reading (see figure 2).

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**An OHMMETER measures the resistance of an electrical circuit or component.**

No voltage can be applied while the ohmmeter is connected, or damage to the meter will occur. RESISTANCE UNITS Resistance is measured in units called OHMS. Resistance measurements can use different value prefixes, such as Kilo ohm and Mega ohms. More THAN BASE UNIT BASIC UNIT Resistance M K Ω Symbol Mega Ohm Kilo Ohm Ohm Pronounced 1000 1 Multiplier

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RESISTANCE FACTORS Various factors can affect the resistance. These include: :LENGTH The longer the conductor, the higher the resistance. DIAMETER : The narrower the conductor, the higher the resistance. TEMPERATURE: Depending on the material, most will increase resistance as temperature increases. PHYSICAL CONDITION (DAMAGE) Damage to the material. Any damage will increase resistance. TYPE of MATERIAL Various materials have a wide range of resistances.

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**There are two basic types of Electricity classifications:**

STATIC ELECTRICITY is electricity that is standing still. Voltage potential with NO electron flow. DYNAMIC ELECTRICITY is electricity that is in motion. Voltage potential WITH electron flow. Two types of Dynamic electricity exist: Direct Current (DC) Electron Flow is in only one direction. Alternating Current (AC) Electron flow alternates and flows in both directions (back and forth).

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**STATIC ELECTRICITY : Voltage potential with NO electron flow.**

Example: By rubbing a silk cloth on a glass rod, you physically remove electrons from the glass rod and place them on the cloth. The cloth now has a surplus of electrons (negatively charged), and the rod now has a deficiency of electrons (positively charged).

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DYNAMIC ELECTRICITY is electricity in motion, meaning you have electrons flowing, in other words voltage potential WITH electron flow. Two types of dynamic electricity exists: Direct Current (DC) Alternating Current (AC)

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DIRECT CURRENT (DC) Electricity with electrons flowing in only one direction is called Direct Current or DC. DC electrical systems are used in cars.

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**ALTERNATING CURRENT (AC)**

Electricity with electrons flowing back and forth, negative -positive- negative, is called Alternating Current, or AC. The electrical appliances in your home use AC power.

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**SOURCES OF ELECTRICITY**

Electricity can be created by several means: Friction creates static electricity. Heat can act upon a device called a thermo couple to create DC. Light applied to photoelectric materials will produce DC electricity. Pressure applied to a piezoelectric material produce DC electricity. Chemical Action – battery produce DC electricity. – Alternator produce AC electricity. magnetic action

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AN ELECTRICAL CIRCUIT The circuit shown below has a power source, fuse, switch, two lamps and wires connecting each into a loop or circle.

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**ELECTRICAL CIRCUIT REQUIREMENTS**

A complete Electrical Circuit is required in order to make electricity practical. Electrons must flow from and return to the power source. There are three different circuit types, all require the same basic components: 1. Power Source is needed to supply the flow of electrons (electricity). 2. Protection Device prevents damage to the circuit. 3. Load Device converts the electricity into work. 4. Control Device allows the user control to turn the circuit on or off 5. Conductors provide an electrical path to and from the power source.

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**BASIC CIRCUIT CONSTRUCTION**

1. Power Source (Battery, Alternator, Generator, etc.) 2. Protection Device (Fuse, Fusible Link, or Circuit Breaker) 3. Load Device (Lamp, Motor, Winding, Resistor, etc.) 4. Control (Switch, Relay, or Transistor) 5. Conductors (A Return Path, Wiring to Ground)

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LOADS Any device such as a lamp or horn that consumes electricity is called a load. In an electrical circuit, all loads are regarded as resistance. Loads with high resistance cause less current to flow while those with lower resistance allow high current rates to flow.

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Ohm’s Law V = IR The voltage change [V] (volts) across any resistive load is equal to the product of the current [I] (amps) and the resistance [R] (Ohms). Two of the most basic laws of electricity that you will use are Ohm’s Law and the Power Law Ohm’s law deals with the relationship between voltage across, current flow through and impedance, or in our simple cases resistance for, a single device, part of a circuit or complete circuit. Defining terms: Voltage could be thought of as the electrical pressure needed to move electrons, measured in volts Current is the flow of elections, measured in amperes Resistance is the restriction to flow, measured in ohms Electrical Circuits and Controls - 1

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WHAT IS OHM'S LAW? A simple relationship exists between voltage, current, and resistance in electrical circuits. OHM'S LAW Ohm's Law says: The current in a circuit is directly proportional to the applied voltage and inversely proportional to the amount of resistance. CURRENT is affected by either voltage or resistance. VOLTAGE is not affected by either current or resistance. RESISTANCE is not affected by either voltage or current.

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**Voltage = Current x Resistance**

OHM'S LAW FORMULA E = I R Voltage = Current x Resistance E Voltage applied to the circuit, in volts (V) I Current flowing in the circuit, in amperes (A) R Resistance in the circuit, in ohms

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**Example 1 – Instructor Example**

120 V R = 12 ohms i = ? Current I = V/R = 120 V/12 Ohms = 10 amps This simple example is just to demonstrate the relationships of Ohm’s Law and the Power Law. Electrical Circuits and Controls - 1

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**Example 2 – Student Example**

R = 24 Ohms 240 V I = ? I = Students should work in groups to confirm they have the correct answer and understand the process. Power formula can be used to get the current of a device knowing its wattage and voltage Light 60 W bulb at 120 V implies I = P/V = 60W / 120 V = 0.5 A Additional Student Problem What is the current flow for your 960 W toaster plugged into 120 V outlet? Electrical Circuits and Controls - 1

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**APPLICATIONS OF OHM'S LAW**

In the following circuit, assume that resistance R is 2 and voltage V that is applied to it is 12 V. Then, current I flowing in the circuit can be determined as follows:

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**V = I x R APPLICATIONS OF OHM'S LAW**

In the following circuit, assume that resistance R is 4 ohms. The voltage V that is necessary to permit a current I of 3 A to pass through the resistance can be determined as follows:

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**APPLICATIONS OF OHM'S LAW**

In the following circuit, assume that a voltage V of 12 V is applied to the circuit and current I of 4 A flows in it. Then, the resistance value R of the resistance or load can be determined as follows:

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Kirchhoff’s Laws Voltage Law: The sum of the voltage rises around a closed loop in a circuit must equal the sum of the voltage drops. Current Law: The sum of all currents into a junction (node) must equal the sum of all currents flowing away from the junction. Kirchhoff’s Laws are two relationships we can use to solve for values in a circuit or electrical system. Crudely the Voltage Law says that pressure drop around a loop must equal the pressure developed by the pump (source) The second law simply says that you cannot accumulate electrons at a point. Electrical Circuits and Controls - 2

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**Resistors in Series V = I R1 + I R2 + I R3**

Applying Kirchhoff’s voltage law gives us: V = I R1 + I R2 + I R3 Note V or E for source is equal to sum of IR1 (voltage drop across R1) plus IR2 and IR3. Note voltage drop on any one R will be proportional to the relative size of that resistor compared to total resistance We can also use this to derive a relationship to be used later. If we want to show the sum of all resistors as one equivalent resistance: Divide through by I. Let E/I or V/I equal Req get Req = R1 + R2 + R3 Electrical Circuits and Controls - 2

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TYPES OF CIRCUITS - SERIES CIRCUITS A Series Circuit has only one path to ground Therefore: 1. An open in the circuit will disable the entire circuit. 2. The voltage divides between the loads. 3. The current flow is the same . 4. The resistance of each load is different. Vt = V1 + V2 + V3 + V4 It = I1 = I2 = I3 = I4 Rt = R1 + R2 + R3 + R4

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**Equivalent Resistance**

If desired, several resistors can sometimes be replaced by a single “equivalent” resistor: Req = R1 + R2 + R3 + … For resistors in series: R1 R3 R2 Req Do a simple example: Each each resistor is 1 ohm, what is the total equivalent resistance. Student Example: Assume R1 = 1 ohms , R2 = 2 ohms and R3 =3 ohms, what is the total equivalent resistance? (6 ohms) Note since the same current flows through each resistor, the voltage drop across each will be different (directly proportional to size of the resistor.) Electrical Circuits and Controls - 2

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**SERIES CIRCUIT CALCULATIONS**

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**In this example, the circuit includes 4 series resistors. **

Rt = R1 + R2 + R3 + R4 Rt = Rt = 10 Ω > > I = 1.2 Amps

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VOLTAGE DROP A voltage drop is the amount of voltage or electrical pressure that is used or given up as electrons pass through a resistance (load). All voltage will be used up in the circuit. The sum of the voltage drops will equal source voltage. A voltage drop measurement is done by measuring the voltage before entering the load and the voltage as it leaves the load.

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VOLTAGE DROP TOTAL When more than one load exists in a circuit: the voltage divides and will be shared among the loads. The sum of the voltage drops equal source voltage. The higher the resistance the higher the voltage drop. Depending on the resistance, each load will have a different voltage drop.

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**VOLTAGE DROP CALCULATION**

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**𝟏 𝑹𝒕 = 𝟏 𝑹𝟏 + 𝟏 𝑹𝟐 + 𝟏 𝑹𝟑 + 𝟏 𝑹𝟒 TYPES OF CIRCUITS - PARALLEL CIRCUITS**

A Parallel Circuit has multiple paths or branches to ground. Therefore: In the event of an open in the circuit in one of the branches, current will continue to flow through the remaining. Voltage is the same in each branch. Current flow through each branch is different. Resistance of each branch is different. Vt = V1 = V2 = V3 = V4 It = I1 + I2 + I3 + I4 𝟏 𝑹𝒕 = 𝟏 𝑹𝟏 + 𝟏 𝑹𝟐 + 𝟏 𝑹𝟑 + 𝟏 𝑹𝟒

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**Applying Kirchhoff’s voltage law gives us:**

Resistors in Parallel Applying Kirchhoff’s voltage law gives us: Note you could think of R’s a banks of lights. All light bulbs see the same voltage. They are all in parallel. The voltage for each light is the same: V = I1R1 = I2R2 = I3R3 For resistors connected in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3 In this case if each Resistor is 1 ohm, what is Req ? (ans. 1/3 ohm) Keep in mind as Req goes down, Ix from source goes up (fixed voltage) Add more lights, current goes up, equivalent resistance goes down. voltage law: V = I1R1 = I2R2 = I3R3 current law: Ix = I1 + Iy and Iy = I2 + I3 Electrical Circuits and Controls - 2

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**Equivalent Resistors For Resistors in Parallel Req R1 R2 R3**

Do a simple example - assume all resistors are equal to 1 ohm, what is the equivalent total resistance. Ans. 1/3 ohm Note that for a parallel circuit total resistance is smaller than each component. . Req Electrical Circuits and Controls - 2

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Example Problem: If each of the R’s were (R =240 ohm), what would be the equivalent resistance for all three resistances . Req = 80 ohms I = V/R = 1.5 amp P = V I = 120 V x 1.5 Amp = 180 W (or 60W x 3 checks) Note: Total Req is smaller than individuals, power use goes up as add more bulbs in parallel, but each bulb sees same voltage R1 R3 R2 Req = Electrical Circuits and Controls - 2

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**PARALLEL CIRCUIT CALCULATIONS**

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To determine the total resistance when resistors are of equal value in a parallel circuit, use the following illustration , there are three 15 W resistors. The total resistance is: Value of any one Resistor Number of Resistors Rt = Rt= 𝟏𝟓 𝟑 Rt =3 Ω

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**The second formula is used when there are only two resistors.**

𝐑𝐭= 𝑹𝟏×𝑹𝟐 𝑹𝟏+ 𝑹𝟐 𝑹𝒕= 𝟓×𝟏𝟎 𝟓+𝟏𝟎 𝑹𝒕= 𝟓𝟎 𝟏𝟓 𝑹𝒕=𝟑.𝟑𝟑 Ω

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When unequal value resistors are placed in a parallel circuit, opposition to current flow is not the same in every circuit branch. Current is greater through the path of least resistance. In the following circuit R1 is 40 W and R2 is 20 W. Small values of resistance means less opposition to current flow. More current will flow through R2 than R1.

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**Using Ohm’s Law, the total current for each circuit can be calculated.**

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Or

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**SERIES PARALLEL CIRCUIT**

A series-parallel circuit has some components in series and others in parallel. The power source and control or protection devices are usually in series; the loads are usually in parallel.

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First, use the formula to determine total resistance of parallel circuit to find the total resistance of R1 and R2. When the resistors in a parallel circuit are equal , the following formula is used: 𝐑𝐭′= 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂𝒏𝒚 𝒐𝒏𝒆 𝑹𝒆𝒔𝒊𝒔𝒕𝒆𝒓 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒓𝒆𝒔𝒊𝒔𝒕𝒆𝒓𝒔 𝐑𝐭′= 𝟏𝟎 𝟐 𝐑𝐭′=𝟓 Ω

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**Second, redraw the circuit showing the equivalent values**

Second, redraw the circuit showing the equivalent values. The result is a simple series circuit which uses already learned equations and methods of problem solving. 𝐑𝐭=𝟓+𝟏𝟎=𝟏𝟓 Ω

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**In the following illustration R1 and R2 are in series with each other**

In the following illustration R1 and R2 are in series with each other. R3 is in parallel with the series circuit of R1 and R2. First, use the formula to determine total resistance of a series circuit to find the total resistance of R1 and R2. The following formula is used: Rt' = R1 + R2 Rt' = 10 Ω + 10 Ω Rt' = 20 Ω

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**Second, redraw the circuit showing the equivalent values**

Second, redraw the circuit showing the equivalent values. The result is a simple parallel circuit which uses already learned equations and methods of problem solving

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Power Work Whenever a force of any kind causes motion, work is accomplished. In the illustration below work is done when a mechanical force is used to lift a weight. If a force were exerted without causing motion, then no work is done.

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**Basic Relationship – Power Law**

P = IV Power dissipated [P] (watts) is equal to product of the current [I] (amps) and voltage [V] (volts) Power is actually the time rate of expending energy or doing work. Electrically we define this in terms of watts (joule per second). Horsepower is another unit of power 1 hp = 746 W In relatively simple resistive circuits Power is simply the product of current and voltage, and is measured in units of watts. Electrical Circuits and Controls - 1

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Electric Power In an electrical circuit, voltage applied to a conductor will cause electrons to flow. Voltage is the force and electron flow is the motion. The rate at which work is done is called power and is represented by the symbol “P” Power is measured in watts, represented by the symbol “W” In a direct current circuit. One watt is the rate work is done in a circuit when 1 amp flows with 1 volt applied.

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Power Formulas In a DC circuit, power is the product of voltage times current. Later in this course, you will learn a slightly different version of this relationship for an alternating current (AC) circuit. 𝐏=𝐄 x 𝐈 or 𝐏=𝐄𝐈 Two other power equations can be derived from this formula by substituting other components of Ohm’s Law. 𝐏=𝐈𝟐x 𝐑 And 𝐏= E2 𝐑

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**Example P = V I = 120 V * 10 Amps = 1200 Watts R = 12 ohms 120 V i = ?**

This simple example is just to demonstrate the relationships of Ohm’s Law and the Power Law. Electrical Circuits and Controls - 1

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Example 2 R = 24 Ohms 240 V I = ? Students should work in groups to confirm they have the correct answer and understand the process. Power formula can be used to get the current of a device knowing its wattage and voltage Light 60 W bulb at 120 V implies I = P/V = 60W / 120 V = 0.5 A Additional Student Problem What is the current flow for your 960 W toaster plugged into 120 V outlet? P = Electrical Circuits and Controls - 1

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Example 3 Without doing any calculations, which light bulb has the lowest resistance? 75 W bulb at 120 V 150 W bulb at 120 V Electrical Circuits and Controls - 1

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**In the following illustration, power can be calculated using any of the power formulas.**

P = EI P = 12 Volts x 2 Amps P = 24 Watts or P = I2R P = (2 Amps)2 x 6 Ω P= E2 R P= ( 12 Volts )2 6 Ω P= I = 2 Amps 12 Volts + R = 6 Ω _

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**Additional Calculations**

For example, a common household lamp may be rated for 120 volts and 100 watts. Using Ohm’s Law, the rated value of resistance of the lamp can be calculated. P= E2 R → R= E2 P → R= ( 120 Volts )2 100 watts → R=𝟏𝟒𝟒 Ω Using the basic Ohm’s Law formula, the amount of current flow for the 120 volt, 100 watt lamp can be calculated. I= E R → I= Volts 𝟏𝟒𝟒 Ω → I=𝟎.𝟖𝟑𝟑 𝐀𝐦𝐩𝐬 By comparison, a lamp rated for 120 volts and 75 watts has a resistance of 192 W and a current of amps would flow if the lamp had the rated voltage applied to it. R= E2 P → R= E2 P → R= ( 120 Volts )2 75 watts → R=𝟏𝟗𝟐Ω I= E R → I= ( 120 Volts )2 𝟏𝟗𝟐Ω → I=𝟎.𝟔𝟐𝟓 𝐀𝐦𝐩𝐬

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Magnetism The principles of magnetism are an integral part of electricity. In fact, magnetism can be used to produce electric current and vice versa. Types of Magnets Permanent magnets come in many shapes. Magnets have two characteristics: They attract iron and. If free to move a magnet will assume a north-south orientation.

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Magnetic Lines of Flux Every magnet has two poles, one north pole and one south pole. Magnetic Lines of Flux follow these rules : Magnetic lines are Invisible . flux leave the north pole and enter the south pole. The magnetic lines of flux always form closed loops. lines of flux never cross each other.

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**Interaction between Two Magnets**

When two magnets are brought together, the magnetic flux field around the magnets causes some form of interaction. Two unlike poles brought together cause the magnets to attract. Two like poles brought together cause the magnets to repel.

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Electromagnetism Left-Hand Rule for Conductors Every electric current generates a magnetic field. A relationship exists between the direction of current flow and the direction of the magnetic field. The left-hand rule for conductors demonstrates this relationship. If a current-carrying conductor is grasped with the left hand with the thumb pointing in the direction of electron flow, the fingers will point in the direction of the magnetic lines of flux.

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**Current-Carrying Coil**

A coil of wire carrying a current, acts like a magnet. Individual loops of wire act as small magnets. The strength of the field can be increased by Adding more turns to the coil Increasing the amount of current

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**Left-Hand Rule for Coils**

A left-hand rule exists for coils to determine the direction of the magnetic field. The fingers of the left hand are wrapped around the coil in the direction of electron flow. The thumb points to the north pole of the coil.

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Electromagnets An electromagnet is composed of a coil of wire wound around a core made of soft iron or some other material that easily conducts magnetic lines of force. When current is passed through the coil, the core becomes magnetized. The ability to control the strength and direction of the magnetic force makes electromagnets useful. A large variety of electrical devices such as motors, circuit breakers, contactors, relays and motor starters use electromagnetic principles.

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**The supply of current for electrical devices may come from**

Direct current (DC) , source electrons flow continuously in one direction from the source of power through a conductor to a load and back to the source of power. Alternating current (AC) , source electrons flow first in one direction then in another. AC generator reverses its terminal polarities many times a second.

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AC Sine Wave A sine wave is The graphic representation of current or voltage of AC. There are two axes of the graphic representation : The vertical axis represents the direction and magnitude of current or voltage. The horizontal axis represents time.

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When the waveform is above the time axis, current is flowing in one direction. This is referred to as the positive direction. When the waveform is below the time axis, current is flowing in the opposite direction. This is referred to as the negative direction. A sine wave moves through a complete rotation of 360 degrees, which is referred to as one cycle. Alternating current goes through many of these cycles each second.

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**Single-Phase and Three-Phase AC Power**

Alternating current is divided into 2 types single-phase - small electrical demands (home) Three-Three-Phase – large electrical demands (commercial ) Illustration bellow show three overlapping AC cycles, offset by 120 electrical degrees.

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AC Generators A basic generator consists of a magnetic field, an armature, slip rings, brushes and a resistive load. The magnetic field is created by an electromagnet. An armature is any number of conductive wires wound in loops which rotates through the magnetic field.

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**Basic Generator Operation**

Initial position of zero degrees An armature rotates through the magnetic field. At an initial position of zero degrees, the armature conductors are moving parallel to the magnetic field and not cutting through any magnetic lines of flux. No voltage is induced.

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**Operation from Zero to 90 Degrees**

As the armature rotates from zero to 90 degrees, the conductors cut through more and more lines of flux, building up to a maximum induced voltage in the positive direction.

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**Operation from 90 to 180 Degrees**

The armature continues to rotate from 90 to 180 degrees, cutting fewer lines of flux. The induced voltage decreases from a maximum positive value to zero.

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**Operation from 180 to 270 Degrees**

As the armature continues to rotate from 180 degrees to 270 degrees, the conductors cut more lines of flux, but in the opposite direction, and voltage is induced in the negative direction, building up to a maximum at 270 degrees.

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**Operation from 270 to 360 Degrees**

As the armature continues to rotate from 270 to 360 degrees, induced voltage decreases from a maximum negative value to zero. This completes one cycle.

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**Four-Pole AC Generator**

An increase in the number of poles, would cause an increase in the number of cycles completed in a revolution. A two-pole generator would complete one cycle per revolution . A four-pole generator would complete two cycles per revolution. An AC generator produces one cycle per revolution for each pair of poles.

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Frequency Frequency is the number of cycles per second of voltage induced in the armature. If the armature rotates at a speed of 60 revolutions per second, the generated voltage will be 60 cycles per second. The unit for frequency is hertz(Hz) 1 Hz is equal to 1 cycle per second. The standard power line frequency in the Kuwait is 50 Hz.

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**The following illustration shows 15 cycles in 1/4 second which is equivalent to 60 Hz.**

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Voltage and Current Peak Value Voltage and current in an AC circuit rise and fall over time in a pattern referred to as a sine wave. The peak value of a sine wave occurs twice each cycle, once at the positive maximum value and once at the negative maximum value.

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Peak-to-Peak Value The value of the voltage or current between the peak positive and peak negative values is called the peak-to-peak value.

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Instantaneous Value The instantaneous value is the value at any one point in the sine wave.

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**e = Epeak x sin θ Calculating Instantaneous Voltage**

The voltage waveform produced as the armature rotates through 360 degrees rotation is called a sine wave because the instantaneous voltage (e) is related to the sine trigonometric function. The sine of an angle is represented symbolically as sin θ, where the Greek letter theta (θ) represents the angle. The sine curve is a graph of the following equation for values of θ from 0 to 360 degrees: Instantaneous voltage is equal to the peak voltage times the sine of the angle of the generator armature. e = Epeak x sin θ

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The following example illustrates instantaneous values at 90,150, and 240 degrees. The peak voltage is equal to 100 volts. By substituting the sine at the instantaneous angle value, the instantaneous voltage can be calculated. Any instantaneous value can be calculated. For example theta θ =240° e = Epeak x sin θ e = 100 x e = volts

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**RMS= Epeak x 0.707 Epeak = RMS x 1.41**

Effective Value of an AC Sine Wave Translating the varying values into an equivalent constant value, referred to at the effective value of voltage or current. This is also known as the RMS value ( root-mean-square ). RMS value is equal to the peak value times RMS= Epeak x 0.707 Epeak = RMS x 1.41

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Inductance The circuits studied to this point have been resistive. Resistance and voltage are not the only circuit properties that effect current flow, however inductance is the property of an electric circuit that opposes change in electric current. Resistance opposes current flow Inductance opposes change in current flow. Inductance is designated by the letter ( L ) . The unit of measurement for inductance is the henry (h).

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**Current Flow and magnetic Field Strength**

Current flow produces a magnetic field in a conductor. The amount of current determines the strength of the magnetic field. As current flow increases, field strength increases, and as current flow decreases, field strength decreases.

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**Any change in current causes a corresponding change in the magnetic field surrounding the conductor.**

A change in the magnetic field surrounding the conductor induces a voltage in the conductor, this self-induced voltage opposes the change in current. This self-induced voltage known as counter EMF . This opposition causes a delay in the time it takes current to attain its new steady value. If current increases, inductance tries to hold it down. If current decreases, inductance tries to hold it up. Inductance is somewhat like mechanical inertia * get object moving * stop a mechanical object from moving. Example: A vehicle takes few moments to accelerate to a desired speed, or decelerate to a stop.

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Inductors All conductors have inductance. inductors are coils of wire wound for a specific inductance, or wound around a metal core to concentrate the inductance. The inductance of a coil is determined by : number of turns in the coil coil diameter Length core material. An inductor is usually indicated symbolically on drawing as

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**Simple Inductive Circuit**

In a resistive circuit, current change is considered instantaneous. If an inductor is used, the current does not change as quickly. The electrical wire used in the circuit has some resistance and inductance. Inductors also have resistance. However, to simplify examples in this book, the resistance and inductance of the wiring and the resistance of inductors are not considered.

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In the following circuit, initially the switch is in position 2, and there is no current flowing through the ammeter (A). When the switch is moved to position 1, current will rise rapidly at first, then more slowly as the maximum value is approached.

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**Inductive Time Constant**

In an inductive circuit , time constant is the ratio of inductance (in henrys) to resistance (in ohms). During the first time constant current rises to 63.2% of its maximum value. During the second time constant, current rises to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for current to reach its maximum value.

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Similarly, when the switch in the previous circuit is returned to position 2, the magnetic field around the inductor will begin to collapse, returning stored energy to the circuit, and it will take about five time constants for current to reach zero.

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**Calculating the Time Constant of an Inductive Circuit**

The time constant is designated by the symbol “t” To determine the time constant of an inductive circuit use one of the following formulas:

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**In the following illustration, L1 is equal to 15 millihenrys and R1 is equal to 5 W.**

When the switch is closed, it will take 3 milliseconds for current to rise from zero to 63.2% of its maximum value and approximately 15 milliseconds for full current to be reached.

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**Formula for Series Inductors**

The same rules for calculating total resistance can be applied to calculating total inductance. In the following circuit, an AC generator is used to supply electrical power to four inductors. Total inductance of series inductors is calculated using the following formula:

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**Formula for Parallel Inductors**

In the following circuit, an AC generator is used to supply electrical power to three inductors. Total inductance of parallel inductors is calculated using the following formula:

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Capacitance Capacitance and Capacitors Capacitance is a measure of a circuit’s ability to store an electrical charge. A device manufactured to have a specific amount of capacitance is called a capacitor. A capacitor is made up of a pair of conductive plates separated by a thin layer of insulating material. Another name for the insulating material is dielectric material.

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When a voltage is applied to the plates, electrons are forced onto one plate. That plate has an excess of electrons while the other plate has a deficiency of electrons. The plate with an excess of electrons is negatively charged. The plate with a deficiency of electrons is positively charged.

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Direct current cannot flow through the dielectric material because it is an insulator; however, the electric field created when the capacitor is charged is felt through the dielectric. Capacitors are rated for the amount of charge they can hold. The capacitance of a capacitor depends on: Area of the plates Distance between the plates Type of dielectric material used. The unit of measurement for capacitance is farads (F). Farad is a large unit and capacitors are often rated in microfarads (mF) or picofarads (pF).

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**Capacitor Circuit Symbols**

Capacitance is usually indicated symbolically on an electrical drawing by a combination of a straight line with a curved line, or two straight lines.

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**Simple Capacitive Circuit**

In a resistive circuit, voltage change is instantaneous. In a circuit with a resistor and capacitor in series, the voltage across the capacitor does not change as quickly. In the following circuit, initially the switch is in position 2 and no voltage is measured by the voltmeter (V). When the switch is moved to position 1, voltage across the capacitor will rise rapidly at first, then more slowly as the maximum value is approached.

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**Capacitive Time Constant**

time constant of a capacitive circuit is the product of capacitance, in farads, times resistance, in ohms. The time constant gives the time in seconds required for voltage across the capacitor to reach 63.2% of its maximum value. During the first time constant, voltage will rise to 63.2% of its maximum value. During the second time constant, voltage will rise to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for voltage across the capacitor to reach its maximum.

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When the switch in the previous circuit is returned to position 2, the capacitor will retain its charge because there is no path for current flow. When the switch is moved to position 3, the capacitor will begin to discharge, and it will take about five time constants for the voltage across the capacitor and the current through the resistor to reach zero.

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**τ (in seconds) = R (megohms) x C (microfarads) **

Calculating the Time Constant of a Capacitive Circuit To determine the time constant of a capacitive circuit, use one of the following formulas: τ (in seconds) = R (megohms) x C (microfarads) τ (in microseconds) = R (megahms) x C (picofarads) τ (in microseconds) = R (ohms) x C (microfarads)

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**τ = RC τ = 2µF x 10 Ω τ = 20 microseconds**

In the following illustration, C1 is equal to 2 mF, and R1 is equal to 10 Ω. When the switch is closed, it will take 20 microseconds for voltage across the capacitor to rise from zero to 63.2% of its maximum value. It will take about five time constants, 100 microseconds, for this voltage to rise to its maximum value. τ = RC τ = 2µF x 10 Ω τ = 20 microseconds

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**Formula for Series Capacitors**

Connecting capacitors in series decreases total capacitance. The formula for series capacitors is similar to the formula for parallel resistors. In the following circuit, an AC generator supplies electrical power to three capacitors. Total capacitance is calculated using the following formula:

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**Formula for Parallel Capacitors**

Adding capacitors in parallel increases circuit capacitance. In the following circuit, an AC generator is used to supply electrical power to three capacitors. Total capacitance is calculated usingthe following formula:

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**circuit with only inductance, capacitance, or both, but no**

resistance, opposition to current flow is called Reactance, designated by the symbol “X”. Total opposition to current flow in an AC circuit that contains both reactance and resistance is called Impedance, designated by the symbol “Z”. resistance, reactance and impedance are expressed in ohms AC circuit only has inductance and resistance Z= 𝑹𝟐+ 𝑿𝑳 𝟐 AC circuit only has capacitance and resistance Z= 𝑹𝟐+ 𝑿𝑪 𝟐

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Inductive Reactance Inductance only affects current flow when the current is changing. Inductance produces a self-induced voltage (counter emf) that opposes changes in current. This opposition to current flow is called inductive reactance and is designated by the symbol “XL. Inductive reactance is proportional to both the inductance and the frequency applied. The formula for inductive reactance is: XL = 2πfL XL = 2 x 3.14 x frequency x inductance For a 60 hertz circuit containing a 10 mh inductor, the inductive reactance is: XL = 2 x 3.14 x 60 x 0.010 XL = Ω

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**XL = 2πfL XL = 2 x 3.14 x frequency x inductance**

The formula for inductive reactance is: XL = 2πfL Where: XL = inductive reactance measured in ohms 2π = a constant (2 x = 6.28) f = the AC frequency of the electrical supply in hertz L = the inductance value of the coil in henries. XL = 2 x 3.14 x frequency x inductance

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**For a 60 hertz circuit containing a 10 mh inductor, the inductive reactance is:**

XL = 2πfL XL = 2 x 3.14 x 60 x 0.010 XL = Ω For this example, the resistance is zero so the impedance is equal to the reactance. If the voltage is known, Ohm’s Law can be used to calculate the current. If, for example, the voltage is 10 volts, the current is calculated as follows; 𝐈= 𝐄 𝐙 𝐈= 𝟏𝟎 𝟑.𝟕𝟔𝟖 𝐈=𝟐.𝟔𝟓 𝐀𝐦𝐩𝐬

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In the following illustration, resistance and inductive reactance are equal. Current lags voltage by 45 degrees. Z= 𝑹𝟐+ 𝑿𝑳 𝟐 Z= 𝟏𝟎𝟐+ 𝟏𝟎 𝟐 Z= 𝟐𝟎𝟎 Z=𝟏𝟒.𝟏𝟒𝟐𝟏Ω

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Capacitive Reactance Capacitance also opposes AC current flow. Capacitive reactance is designated by the symbol XC. The larger the capacitor, the smaller the capacitive reactance. Current flow in a capacitive AC circuit is also dependent on frequency. The following formula is used to calculate capacitive reactance: Xc= 1 2πfc Where: XL = Capacitive reactance measured in ohms 2π = a constant (2 x = 6.28) f = the AC frequency of the electrical supply in hertz C = the capacitance value of the capacitor in microfarads.

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The capacitive reactance for a 60 hertz circuit with a 10 microfarad capacitor is calculated as follows: 𝑿𝒄= 𝟏 𝟐×𝟑.𝟏𝟒×𝟔𝟎×𝟎.𝟎𝟎𝟎𝟎𝟏𝟎 𝑿𝒄= Ω For this example, the resistance is zero so the impedance is equal to the capacitance. If the voltage is known, Ohm’s Law can be used to calculate the current. If, for example, the voltage is 10 volts, the current is calculated as follows; 𝐈= 𝐄 𝐙 𝐈= 𝟏𝟎 𝟐𝟔𝟓.𝟑𝟗 𝐈=𝟎.𝟎𝟑𝟕𝟔 𝐀𝐦𝐩𝐬

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In the following illustration, resistance and capacitive reactance are equal. Current lags voltage by 45 degrees. Z= 𝑹𝟐+ 𝑿𝑪 𝟐 Z= 𝟏𝟎𝟐+ 𝟏𝟎 𝟐 Z= 𝟐𝟎𝟎 Z=𝟏𝟒.𝟏𝟒𝟐𝟏Ω

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Series R-L-C Circuit Circuits often contain resistance, inductance, and capacitance. In an inductive AC circuit, current lags voltage by 90 degrees. In a capacitive AC circuit, current leads voltage by 90 degrees. In vector form, inductive and capacitive reactance are 180 degrees apart. net reactance is determined by taking the difference between the two quantities. • Resistive if XL and XC are equal • Inductive if XL is greater than XC • Capacitive if XC is greater than XL

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**Z= 𝑹𝟐+ (𝑿𝑳−𝑿𝑪) 𝟐 Calculating Total Impedance in a Series R-L-C circuit**

The following formula is used to calculate total impedance of a circuit containing resistance, capacitance, and inductance: Z= 𝑹𝟐+ (𝑿𝑳−𝑿𝑪) 𝟐 Where: Z = total impedance in ohms R = resistance of the circuit in ohms XC = Capacitive reactance of circuit in ohms XL= Inductive reactance of circuit in ohms

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In the case inductive reactance is greater than capacitive reactance, subtracting XC from XL results in a positive number , indicating : circuit reactance is inductive current lags voltage. In the case capacitive reactance is greater than inductive reactance, subtracting XC from XL results in a negative number , indicating: circuit reactance is capacitive. current leads voltage. In either case, the value squared will result in a positive number.

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**Calculating Reactance and Impedance**

in a Series R-L-C circuit In the following 120 volt, 60 hertz circuit, resistance is 1000 W, inductance is 5 mh, and capacitance is 2 mF , calculate impedance for this circuit.

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𝑋 𝐿 =2 𝜋𝑓𝐿 𝑋 𝐿 =6.28×60 ×0.005 𝑋 𝐿 =1.884 Ω 𝑋 𝑐 = 1 2𝜋𝑓𝐶 𝑋 𝑐 = ×60 × 𝑋 𝑐 =1327 Ω 𝑍= 𝑅 2 + 𝑋𝐿 −𝑋𝐶 2 𝑍= − 𝑍= − 𝑍= 𝑍= 𝑍= Ω Given that the applied voltage is 120 volts, current can be calculated as follows: 𝐈= 𝐄 𝐙 𝐈= 𝟏𝟐𝟎 𝟏𝟔𝟔𝟎.𝟏 𝐈=𝟎.𝟎𝟕𝟐𝟑 𝐀𝐦𝐩𝐬

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**Calculating Impedance in a Parallel R-L-c circuit**

In the following 120 volt, 60 hertz circuit, capacitive reactance is 25 Ω, inductive reactance is 50 Ω, and resistance is 1000 Ω. A simple application of Ohm’s Law will find the branch currents.

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𝐈𝐑= 𝐄 𝐑 𝐈𝐑= 𝟏𝟐𝟎 𝟏𝟎𝟎𝟎 𝐈𝐑= .𝟏𝟐𝟎 𝐀𝐦𝐩𝐬 𝐈𝐋= 𝐄 𝐗𝐋 𝐈𝐋= 𝟏𝟐𝟎 𝟓𝟎 𝐈𝐋=𝟐.𝟒 𝐀𝐦𝐩𝐬 𝐈𝐂= 𝐄 𝐗𝐂 𝐈𝐂 = 𝟏𝟐𝟎 𝟐𝟓 𝐈𝐂=𝟒.𝟖 𝐀𝐦𝐩𝐬

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**Total current can be calculated :**

IT= IR2+ IC−IL 2 IT= −2.4 2 IT= IT= IT=2.403 Amps Impedance can then be calculated as follows: 𝐙𝐓= 𝑬 𝐈𝑻 𝐙𝐓= 𝟏𝟐𝟎 𝟐.𝟒𝟎𝟑 𝐙𝐓=𝟒𝟗.𝟒𝟗 Ω

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**Voltage Drop – Definition**

Voltage drop is defined as the amount of voltage loss that occurs through all or part of a circuit due to impedance. Excessive voltage drop in a circuit can cause lights to flicker or burn dimly, heaters to heat poorly, and motors to run hotter than normal and burn out. This condition causes the load to work harder with less voltage pushing the current. The National Electrical Code recommends limiting the voltage drop from the breaker box to the farthest outlet for power, heating, or lighting to 3 percent of the circuit voltage. This is done by selecting the right size of wire

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**If the circuit voltage is 120 volts, then 3 percent of 120 volts is 3**

If the circuit voltage is 120 volts, then 3 percent of 120 volts is 3.6 volts. This means that voltage lost from the wires in the circuit should not exceed 3.6 volts and the outlet should still have 120 or volts to supply.

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Causes Resistance in the conductor causes voltage drop. There are four fundamental causes of voltage drop: Material - Copper is a better conductor than aluminum and will have less voltage drop than aluminum for a given length and wire size. 2. Wire Size - Larger wire sizes (diameter) will have less voltage drop than smaller wire sizes (diameters) of the same length. 3. Wire Length - Shorter wires will have less voltage drop than longer wires for the same wire size (diameter). 4. Current Being Carried - Voltage drop increases on a wire with an increase in the current flowing through the wire.

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Voltage Drop Formulas Mathematical formulas are used to calculate the voltage drop for given wires sizes, lengths, and types under load. These formulas may be used to determine any one of the four factors affecting voltage drop if the other three factors are known. Keep in mind there are separate formulas for single and three phase.

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**𝐂𝐌= 𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭×𝐀×𝐋 𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩**

Formulas For Copper Single Phase Circuits: 𝐂𝐌= 𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭×𝐀×𝐋 𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩 Where: CM = Area of conductor in circular mills A = Single Phase line current in Amperes L = Length (one-way) of circuit in feet V = Voltage Drop (Volts)

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Example 1 Find the size of copper ( constant 25 ) wire to carry a load of 40 amperes at 240 volts a distance of 500 feet with 2% voltage drop. Use the formula: 𝐂𝐌= 𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭×𝐀×𝐋 𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩 𝐂𝐌= 𝟐𝟓×𝟒𝟎 𝐚𝐦𝐩𝐬×𝟓𝟎𝟎 𝐟𝐞𝐞𝐭 𝟒.𝟖 𝐯𝐨𝐥𝐭𝐬 𝐂𝐌=𝟏𝟎𝟒𝟏𝟔𝟕 𝐜𝐢𝐫𝐜𝐮𝐥𝐚𝐫 𝐦𝐢𝐥𝐬

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Example 2 How far can No. 6 copper wire be used to carry a load of 30 amperes at 240 volts and keep within 1% voltage drop? 𝐋= 𝐂𝐌×𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩 𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭×𝐀 𝐋= 𝟐𝟔𝟐𝟓𝟎 𝐜𝐢𝐫𝐜𝐮𝐥𝐚𝐫 𝐦𝐢𝐥𝐬×𝟐.𝟒 𝐯𝐨𝐥𝐭𝐬 𝟐𝟓×𝟑𝟎 𝐚𝐦𝐩𝐬 𝐋=𝟖𝟒 𝐟𝐞𝐞𝐭

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**P = EI P = EI cos θ True Power and Apparent Power Formulas**

The formula for apparent power is: P = EI The formula for true power is: P = EI cos θ

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**Calculating Apparent Power in a simple R-L-C**

In the following 120 volt circuit, current is equal to 84.9 mA. Inductive reactance is 100 Ω and capacitive reactance is 1100 Ω. The phase angle is -45 degrees. By referring to a trigonometric table, the cosine of -45 degrees is found to be

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**The apparent power consumed by the circuit is:**

P = EI P = 120 x P = 10.2 VA The true power consumed by the circuit is: P = EI cos θ P = 120 x x P = 7.2 Watts Another formula for true power is: P = I2R P = x 1000

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Power Factor Power factor is the ratio of true power to apparent power in an AC circuit. Power factor is expressed in the following formula: 𝐏𝐨𝐰𝐞𝐫 𝐅𝐚𝐜𝐭𝐨𝐫= 𝐓𝐫𝐮𝐞 𝐏𝐨𝐰𝐞𝐫 𝐀𝐩𝐩𝐚𝐫𝐞𝐧𝐭 𝐏𝐨𝐰𝐞𝐫 𝐏𝐅= EI cos θ EI 𝐏𝐅=cos θ

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In a purely resistive circuit, where current and voltage are in phase, there is no angle of displacement between current and voltage. The cosine of a zero degree angle is one. The power factor is one. This means that all energy delivered by the source is consumed by the circuit and dissipated in the form of heat.

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**In a purely reactive circuit, voltage and current are 90 degrees apart**

In a purely reactive circuit, voltage and current are 90 degrees apart. The cosine of a 90 degree angle is zero. The power factor is zero. This means the circuit returns all energy it receives from the source to the source.

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In a circuit where reactance and resistance are equal, voltage and current are displaced by 45 degrees. The cosine of a 45 degree angle is The power factor is This means the circuit uses approximately 70% of the energy supplied by the source and returns approximately 30%.

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Transformers are electromagnetic devices that transfer electrical energy from one circuit to another by mutual induction. A single-phase transformer has two coils, a primary and a secondary. Mutual induction is the transfer of electrical energy from the primary to the secondary through magnetic fields .

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**Transformers are used to step a voltage up to a higher level, or down to a lower level.**

The following discussion of step-up and step-down transformers applies to transformers with an iron core.

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**It is the number of turns which determine if a transformer is a**

step up or step down transformer. The following “rules-of-thumb” apply to transformers: 1. If the primary coil has fewer turns than the secondary coil, the transformer is a step-up transformer. 2. If the primary coil has more turns than the secondary coil, the transformer is a step-down transformer. 3. When the number of turns on the primary and secondary coils of a transformer are equal, input voltage, impedance, and current are equal to output voltage, impedance, and current.

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Step-Up Transformer The primary coil has fewer turns than the secondary coil. Voltage and impedance are stepped up. Secondary has twice as many turns as the primary Voltage is stepped up from 120 VAC to 240 VAC. Because impedance is also stepped up, current is stepped down from 10 amps to 5 amps.

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**Step-Down Transformer**

The following circuit illustrates a step-down transformer. The primary coil has more turns than the secondary coil. The step-down ratio is 2:1 Voltage and impedance are stepped down, current is stepped up

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**Formulas for Calculating the**

Number of Primary and Secondary Turns of a Transformer There are a number of useful formulas for calculating, voltage, current, and the number of turns between the primary and secondary of a transformer. These formulas can be used with either step-up or step-down transformers. The following legend applies to the transformer formulas: ES = secondary voltage EP = primary voltage IS = secondary current IP = primary current NS = turns in the secondary coil NP = turns in the primary coil

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To find voltage: 𝐄𝐬= 𝐄𝐩×𝐈𝐩 𝐈𝐬 𝐄𝐩= 𝐄𝐬×𝐈𝐬 𝐈𝐩 To find current: 𝐈𝐬= 𝐄𝐩×𝐈𝐩 𝐄𝐬 𝐈𝐩= 𝐄𝐬×𝐈𝐬 𝐄𝐩 To find number of turns: 𝐍𝐬= 𝐄𝐬×𝐍𝐩 𝐄𝐩 𝐍𝐩= 𝐄𝐩×𝐍𝐬 𝐄𝐬

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**Optional equipment that can be included in a circuit is of two kinds:**

Control devices Protective devices

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**A control device is something that allows us to determine where and when electricity flows.**

Most control devices either open or close the path of the circuit. Switches, thermostats, and time clocks are examples of common control devices found in circuits. A protective device is used to protect either the load or the path from: excessive heat overcurrent Overvoltage Most protective devices open the circuit path if excessive current is flowing in the circuit. Common examples of protective devices include fuses and circuit breakers

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**Control devices are needed to start, stop, or redirect current flow in an electrical circuit.**

Control devices include : 1. Switches • Single Pole Single Throw (SPST) • Single Pole Double Throw (SPDT) • Momentary Contact • Multiple Pole Multiple Throw (MPMT or Gang Switch) • Mercury • Temperature (Bimetal) • Time Delay • Flasher 2. Relays 3. solenoids

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**Most switches require physical movement for operation**

Relays and Solenoids are operated with electromagnetism.

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SWITCHES A switch is the most common circuit control device. Switches usually have two or more sets of contacts. Opening these contacts is called "break" or "open" the circuit, Closing the contacts is called "make" or "completing" the circuit. Switches are described by the number of Poles and Throws they have. "Poles" refer to the number of input circuit terminals "Throws" refer to the number of output circuit terminal. Switches are referred to as: • SPST (single-pole, single-throw) • SPDT (single-pole, double-throw) • MPMT (multiple-pole, multiple-throw)

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**SINGLE POLE SINGLE THROW (SPST)**

The simplest type of switch. It either "completes" (turn on) or "break" (turn off) the circuit in a single circuit. This switch has a single input pole and a single output throw.

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**SINGLE POLE DOUBLE THROW (SPDT)**

A single-pole input, double-throw output switch has one wire going it and two wires coming out.

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**MULTIPLE POLE MULTIPLE THROW (MPMT)**

Multiple-Pole input, Multiple-Throw output switches, have movable contacts wired in parallel. These switches move together to supply different sets of output contacts with current. The dotted line between the switches indicates they move together; one will not move without the other moving as well.

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MOMENTARY CONTACT The momentary contact switch has a spring-loaded contact that keeps it from making the circuit except when pressure is applied to the button. This is a "normally open" type (shown below). START switch A variation of this type is the normally closed (not shown) which works the opposite as described above. STOP switch The spring holds the contacts closed except when the button is pressed. In other words the circuit is "ON" until the button is pushed to break the circuit.

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MERCURY A mercury switch is made of a sealed capsule that is partially filled with mercury. In one end of the capsule are two electrical contacts. As the switch is rotated (moved from true vertical) the mercury flows to the opposite end of the capsule with the contacts, completing the circuit.. Mercury is a hazardous waste and should be handled with care.

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BI-METALLIC A temperature-sensitive switch, also known as a "bi-metallic" switch, usually contains a bimetal element that bends when heated to make contact completing a circuit or to break contact opening a circuit.

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TIME DELAY SWITCH The time delay switch contains a bimetal strip, contacts, and a heating element. The time delay switch is normally closed. As current flows through the switch, current flows through the heating element causing it to heat, which causes the bimetal strip to bend and open the contacts. As current continues to flows through the heating element, the bimetal strip is kept hot, keeping the switch contacts open. The amount of time delay before the contacts open is determined by the characteristics of the bimetal strip amount of heat produced by the heating element

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RELAYS A relay is simply a remote-control switch, which uses a small amount of current to control a large amount of current. A typical relay has both a: • Control circuit • Power circuit. Relay construction contains : • iron core • electromagnetic coil • An armature (moveable contact set).

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**There are two types of relays:**

• normally open. • normally closed. A Normally open (N.O.) relay has contacts that are "open" until the relay is energized A normally closed (N.C.) relay has contacts that are "closed" until the relay is energized.

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**SOLENOIDS - PULLING TYPE**

A solenoid is an electromagnetic switch that converts current flow into mechanical movement. As current flows through the winding, a magnetic field is created. The magnetic field will pull the moveable iron core into the center of the winding. This type of solenoid is called a "pulling" type solenoid, as the magnetic field pulls the moveable iron core into the coil.

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CIRCUIT PROTECTION Circuit protection devices are used to protect wires and connectors from being damaged by excess current flow either caused by an over current or short-circuit. Excess current causes excess heat, which causes circuit protection to "open circuit".

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**CIRCUIT PROTECTION DEVICES**

Fuses and circuit breakers are used as circuit protection devices. Circuit protection devices are available in a variety of types, shapes, and specific current ratings.

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FUSES A fuse is the most common protection device. A fuse is placed in an electrical circuit, so that when current flow exceeds the rating of the fuse it "blows" or "blows out". The element in the fuse melts, opening the circuit and preventing other components of the circuit from being damaged by the overcurrent. The size of the metal fuse element determines its rating. Remember, excessive current causes excess heat, and it's the heat and not the current that causes the circuit protector to open. Once a fuse "blows" it must be replaced with a new one.

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FUSE TYPES Fuses are classified into basic categories: blade type fuses cartridge type fuses

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BASIC CONSTRUCTION The blade type fuse is a compact design with a metal element and transparent insulating housing which is color-coded for each current rating. (Standard Auto shown below; however construction of both the mini and maxi fuses are the same.)

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CIRCUIT BREAKERS Circuit breakers are used in place of fuses for the protection of complicated power circuits such as the power windows, sunroofs and heater circuits. Three types of circuit breakers exists: The manual reset type - mechanical, the automatic resetting type - mechanical, and the automatically reset solid state type - PTC. Circuit breakers are usually located in relay/fuse boxes; however, some components like power window motors have circuit breakers built in.

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**CIRCUIT BREAKER CONSTRUCTION**

(MANUAL TYPE) A circuit breaker basically consists of a bimetal strip connected to two terminals and to a contact in between. Manual circuit breaker when tripped (current flow beyond its rating) will open and must be reset manually. These manual circuit breakers are called "non-cycling" circuit breakers.

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**CIRCUIT BREAKER OPERATION (MANUAL TYPE)**

The circuit breaker contains a metal strip made of two different metals bonded together called a bimetal strip. This strip is in the shape of a disc and is concaved downward. When heat from the excessive current is higher than the circuit breaker current rating, the two metals change shape unevenly. The strip bends or warps upwards and the contacts open to stop current flow. The circuit breaker can be reset after it is tripped.

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**AUTOMATIC RESETTING TYPE – MECHANICAL**

Circuit breakers that automatically reset are called "cycling" circuit breakers. This type of circuit breaker is used to protect high current circuits, such as power door locks, power windows, air conditioning, etc. The automatically resetting circuit breaker contains a bimetal strip. The bimetal strip will overheat and open from the excess current by an overcurrent condition and is automatically reset when the temperature of the bimetal strip cools.

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**AUTO RESET CONSTRUCTION AND OPERATION**

A cycling circuit breaker contains a metal strip made of two different metals bonded together called a bimetal strip. When heat from the excessive current is higher than the circuit breaker current rating the two metals change shape unevenly. The strip bends upwards and a set of contacts open to stop current flow. With no current flowing the bimetal strip cools and returns to its normal shape, closing the contacts, and resuming the current flow. Automatically resetting circuit breakers are said to "cycle "because they cycle open and closed until the current returns to a normal level.

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RESISTORS All electrical circuits require resistance to operate correctly. Resistors are sometimes added to an electrical circuit to limit current flow, create voltage drops, or provide different operating modes. All resistors are rated in both a fixed ohm value of resistance and a power rating in watts. (Watt = Volts X Amps) Basic categories of resistors are : 1. Fixed 2. Variable Each has different characteristics and usage.

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FIXED RESISTORS Fixed-value resistors are divided into two category types of resistors: Carbon / Metal Oxide Wire-Wound. Carbon and Metal Oxide Film Fixed Resistor Electrical Symbol

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CARBON RESISTORS Carbon resistors are commonly used in electronic systems. Carbon is mixed with binder; the more carbon, the lower the resistance. Carbon resistors have a fixed resistance value and are used to limit current flow. They are rated in watts and most have color-code bands to show the resistance value. A typical resistor has a watt rating from 0.125W to 2.0 W. Note: Metal-Oxide Film is sometimes used instead of carbon. While carbon is commonly used for ratings up to 0.5 watt , Metal-Oxide Film provide, better high-temperature satiability and is often used for watt resistors. Metal Oxide Film Carbon

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**RESISTOR RATING COLOR BANDS**

The first two bands set the digit or number value of the resistor. The third band, also known as the multiplier band, is the number of zeros added to the number value. The last band is the Tolerance band. Example: +/- 10%

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**RESISTOR COLOR BAND CHART**

The chart below is used to interpret the color bands on the carbon resistor. Another chart is used to show the value of tolerance band colors (not shown).

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**READING COLOR BANDS - RATING VALUE**

Using the illustration below: The first color band is Green with a value of "5". The second color band is Red with a value of "2". The third band is Black with a value of "0" zero. (No zeros are added) So the resistor has a base value of 52 ohms.

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**READING COLOR BANDS - TOLERANCE VALUE**

Resistors vary in tolerance (accuracy). Common tolerance values are 20%, 10%, 5%, 2%, or 1%, simply meaning the maximum percent allowable difference the resistor value actually is from the designed value rating. A 1% resistor is a higher quality resistor than one with a 20% rating. The tolerance band (last band) is silver with a value of 10%. So, the resistance value is "52 ohms plus or minus 5.2 ohms" (46.8 to 57.2 ohms)

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VARIABLE RESISTORS Variable resistors provide an infinite amount of resistance values. Variable resistors are used by electrical circuits to provide information on temperature, position, or light source. Variable Resistors are used in the headlamp switch to dim or brighten dash panel lighting. Variable Resistors have two connections, one to the fixed end of a resistor and the other to a sliding contact on the resistor. Turning the control moves the sliding contact away from or toward the fixed end, increasing or decreasing the resistance. Variable Resistors control resistance, thus controlling current flow. Generic Variable Resistor Electrical Symbol

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**Variable Resistors OPERATION**

As the wiper moves along the Variable Resistors it exposes more or less of the resistor. Moving the wiper towards the high places a small portion of the resistor in series with the light, causing the light to glow bright. Moving the wiper toward the low, places a larger portion of the resistor in series with the lamp; this increased resistance causes less current to flow lowering the intensity of the light.

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Lockout procedures There are nine steps involved in the lockout procedures. Think, plan and check. Think through the entire procedure and identify all parts of any systems that need to be shutdown. Communicate. Let other employees working on the equipment know when and why you are shutting down the system. Locate all power sources. Locate all switches and other electrical sources that need to be locked out. Neutralize all power at its sources. Lower any suspended parts, block any moveable parts,and disconnect the electricity. Lockout all power sources. Used a lock designed for only this purpose and a lockout tag that includes your name, and the time, the date and department. Test operating controls. Test the operating controls to make certain the power has been removed. Turn the controls back off. Be sure to check each and every control is in the "OFF" position before beginning any necessary maintenance or repairs. Perform any maintenance or repairs. Remove locks and restore energy. Tools should be removed from equipment and machine guards put back in place. Notify other workers that the machines are working and back on. Restart equipment only after all workers are at a safe distance.

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What is Voltage ? Voltage is the electrical force that causes free electrons to move from one atom to another. "Volts" is the measure of "electrical pressure" that causes current flow. Voltage is sometimes referred to as a potential difference between two points along a conductor. Voltage is typically supplied by either a generator or battery. The scientific symbol for voltage is an "E", for "Electromotive force” or "V" as the voltage symbol.

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What is Current ? Current is a measure of the rate of electron flow through a material. Electrical current is measured in units of amperes or "amps" for short. This flow of electrical current develops when electrons are forced from one atom to another. One amp is defined as 6.28 x electrons per second. When current flows in a conductor, heat is produced. This happens because every conductor offers some resistance to current flowing. The scientific symbol for amperage is an "I", or "A" as the amperage symbol.

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What is Power ? The ability to do work. Watt is the standard unit in the metric system. 746 watts equals one horsepower in the English system of units. AC power is represented graphically by a sinusoidal or sine waveform. -- called sine wave for short. There are five characteristics of AC power; Amplitude, Cycles, Frequency, Peak to Peak, and RMS.

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What is the Amplitude ? Amplitude is the maximum value of current or voltage. It is represented by either of the two peaks of the since wave. This voltage level is also referred to as the peak voltage, and can be either positive or negative. Positive and negative refer only to the direction of current flow.

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What is RMS ? Is the actual useful voltage that is available and is called RMS. This stands for Root Mean Square and it is the standard way of measuring and reporting alternating current and voltage. It is not the peak; it is the average. The RMS is found by dividing the peak amplitude by the square root of 2 (approximately 1.414). It is typically represented by a dotted line drawn across each peak near the 70 percent point.

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What is a Cycle ? A cycle is one complete repetition of the sine wave pattern. It is produced by one complete revolution (360 degrees) of the AC generator. Since the sine wave begins at zero, goes positive through the positive peak, then negative through zero and reaches the negative peak, and to zero, we say a full cycle has been completed.

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What is Frequency ? Frequency is the number of cycles per second of voltage induced in the armature. The unit for frequency is hertz(Hz) 1 Hz is equal to 1 cycle per second.

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What is Peak to Peak ? "peak-to-peak" voltage , this is the voltage measured between the maximum positive and negative amplitudes on the sine wave. It is twice the amplitude. This value is the maximum voltage available, but is not all useable in practical applications.

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**What is a kWh or Kilowatt-hour?**

Electrical energy is the average amount of power used over a given time period and is commonly measured in "kilowatt-hours." Electric meters accurately measure the kilowatt-hour energy use by the customer. Let's calculate the energy use for a blow dryer. Say the blow dryer is rated at 1,500 watts by the manufacturer. This is how much electric power it uses when it operates. If the blow dryer is operated for a total of 2 hours each month, the blow dryer consumes 1,500 watts x 2 hours = 3000 watt-hours , or 3 kilowatt-hours.

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**How much electricity does it take to kill a person?**

At levels of current flow exceeding 1/10 of an amp or 100 milliamps, the heart stops. This is called fibrillation. A person may survive an electrocution if his or her heart can be started again. This is why CPR is such an important skill in the electrical industry.

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**Why are some electrical cords and wires fatter than others?**

The current carrying capacity of a particular wire is dictated by its "ampacity" - how many amps it can handle , and it is a function of : Cross section area or diameter of the wire, Larger diameter wires have larger cross section areas and can safely carry more electrical current Material type , the maximum ampacity for different types of wires is defined by electrical codes.

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