Kirchhoff's Law BEE LESSONS PDF

KIRCHHOFF’S LAW KIRCHHOFF’S LAW Kirchhoff’s two laws are used for analyzing a large variety of electric circuits as Ohm’s law by itself is not sufficient to analyze circuits. Gustav Robert Kirchhoff (1824-1887), a German physicist, stated two basic laws in 1847 concerning the relati...

KIRCHHOFF’S LAW KIRCHHOFF’S LAW Kirchhoff’s two laws are used for analyzing a large variety of electric circuits as Ohm’s law by itself is not sufficient to analyze circuits. Gustav Robert Kirchhoff (1824-1887), a German physicist, stated two basic laws in 1847 concerning the relationship between the currents and voltages in an electrical network. These laws are formally known as the Kirchhoff’s Current Law (KCL) and the Kirchhoff’s Voltage Law (KVL).  KIRCHHOFF’S CURRENT LAW (KCL) Based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change. The algebraic sum of currents entering a node or a closed boundary is zero. Mathematically, KCL implies that σ𝑁 𝑛=1 𝑖𝑛 = 0, where N is the number of branches connected to the node and 𝑖𝑛 is the nth current entering (or leaving) the node. By this law, currents entering a node may be regarded as positive, while currents leaving the node may be taken as negative or vice versa  By KCL at junction x, 𝑖1 − 𝑖2 − 𝑖3 + 𝑖4 = 0 Rearranging terms gives, 𝑖1 + 𝑖4 = 𝑖2 + 𝑖3 which implies that, “The sum of the currents entering a node is equal to the sum of the currents leaving the node.”  KIRCHHOFF’S VOLTAGE LAW (KVL) Based on the law of conservation of energy The algebraic sum of all voltages around a closed path (or loop) is zero Mathematically, KVL implies that σ𝑀 𝑚=1 𝑣𝑚 = 0, where M is the number of voltages in the loop (or the number of branches in the loop) and the 𝑣𝑚 is the mth voltage. SIGN CONVENTION  KVL can be applied by taking either a clockwise or a counterclockwise trip around the loop. Either way, the algebraic sum of voltages around the loop is zero By KVL , 𝑣1 − 𝑣2 − 𝑣3 + 𝑣4 − 𝑣5 = 0 Rearranging terms, 𝑣1 + 𝑣4 = 𝑣2 + 𝑣3 + 𝑣5 which may be interpreted as “sum of voltage sources = sum of voltage drops”  SAMPLE PROBLEM Find 𝐼1 , 𝐼2 , 𝐼𝐿  SAMPLE PROBLEM Find 𝐼1 , 𝐼2 , 𝐼𝐿 THANK YOU  DELTA – WYE TRANSFORMATION  DELTA – WYE TRANSFORMATION  Extra technique for transforming certain resistors, combinations that cannot be handled by the series and parallel equations  Also referred to as Pi-T transformation  Some resistors networks cannot be simplified using the usual by trying the parallel combinations. This situation can often be handled by trying the ∆-Y transformation or “Delta-Wye” transformation  The names Delta and Wye come from the shape of the schematics which resemble letter. The transformation allows you to replace three resistors in a ∆ configuration by three resistors in a Y configuration and the letter way around. Source: https://www.allaboutcircuits.com/textbook/direct-current/chpt-10/delta-y- and-y-conversions/  Resistors are sometimes interconnected to form rather complex networks  They may, in fact, be so complex that the common rules applicable to simple series and parallel circuits cannot be used for the calculations of equivalent resistances, branch currents and voltage drops  Under such conditions, it is generally necessary to convert all or parts of the complex circuits into electrically equivalent circuits that lend themselves to simple and straight forward solution  Two elemental arrangements of resistors within and parts of larger networks, that are frequently responsible for the difficulties indicated are ∆ - connected resistors, and Y – connected resistors.  Significantly, the transformation of delta (∆) or of a star (Y) into an equivalent delta (∆) may often convert a circuit that is difficult to handle into one that is comparatively simple  These equations are used to transform a delta-connected set of resistances to a wye-connected (Y-connected) set of resistance Find 𝑅𝑒𝑞 EXAMPLE Find 𝑅𝑒𝑞 EXAMPLE THANK YOU OHM’S LAW  OHM’S LAW It states that the voltage across many types of conducting material is directly proportional to the current flowing through the material, or 𝑽 = 𝑰𝑹 where: V = voltage I = current R = resistance  Resistance is normally considered to be a positive quantity although negative resistance maybe stimulated with special circuitry. The simplest passive element, the resistor may be introduced by considering the work of an obscure German physicist, Georg Simon Ohm, who published a pamphlet in 1827 entitled “Die galvanische kette mathematish bearbetit” (The Galvanic Circuit Investigated Mathematically). On it were contained the results of one of the first efforts to measure currents and voltages and to describe and relate them mathematically. One result was the statement of the fundamental relationships called Ohm’s Law, even though it has been shown that this result was discovered 46 years earlier in England by Henry Cavendish. However, no one, including Ohm, knew of the work done by Cavendish because it was not uncovered and published until long after both were dead. Ohm’s pamphlet received much under served criticism and ridicule for several years after its first publication but it was later accepted and served to remove the obscurity associated with his name. ELECTRICAL POWER and ENERGY  ELECTRICAL POWER Is the rate of energy transfer Watt (W) – unit of electrical energy equal to one joule of energy consumed in one second 2 𝑉 𝑃 = 𝑉𝐼 = 𝐼2 𝑅 = 𝑅  ELECTRICAL ENERGY The capacity to do work 𝑊 = 𝑃𝑡 Where: W = Electrical energy (joule) P = Electrical power (watt) t = time (second)  SAMPLE PROBLEMS 1. A circuit has a resistance of 8 ohms. If a voltmeter connected across its terminals read 10V, how much current is flowing through the circuit? 2. The current flowing through a resistor is 0.8 A when a potential difference of 20 V is applied. Determine the value of the resistance. 3. Determine the voltage which must be applied to a 2 kΩ resistor in order that a current of 10 mA may flow. 4. A 200 V lamp has a hot resistance of 400 ohms. The power rating in watts of the lamp is ____. 5. An electric motor drives a mechanical load, taking 18.5 A from a 220 V source. Calculate the power input of the motor. 6. A 10 Hp motor runs at rated loads for 5 hours. How many kWh is consumed? 7. A heater draws 3A at 12V DC. How many joules does it consume in 15 minutes? 8. A certain generator has an output power of 1012 ergs per second. What is the output in KW?  CLASSIFICATION OF DC SOURCES IN TERMS OF THEIR ENERGY SOURCE 1. Chemical sources In which chemical energy is converted to electrical energy. Examples of such sources are primary and secondary cells (batteries) as well as fuel cells. 2. Solar and Photovoltaic cells In which heat energy is converted directly to electrical energy. Examples of such sources are copper oxide and selenium photovoltaic cells as well as p-n junction (silicon) solar cells and batteries. 3. Thermoelectric Generation in which heat energy is converted directly to electrical energy. Examples of such sources are thermocouples and semiconductor thermoelectric engines. 4. Piezoelectric Generation in which mechanical energy is converted directly to electrical energy as a result of the application of mechanical forces to crystals of quartz, Rochelle salt, barium titanate and so forth. Examples of such sources are ceramic phono cartridges and underwater sound transducers. 5. Electromagnetic generation in which electrical energy is converted to electrical energy in the presence of a magnetic field. Examples of such sources are various types of semiconductors using the Hall Effect. 6. Electrical Conversion in which alternating electrical energy is converted to direct (dc) electrical energy as a result of rectification or energy conversion. Examples of such sources are dc power supplies, dynamos called rotary converters, and motor- generator sets.  TWO GENERAL TYPES OF ELECTRIC CIRCUIT 1. Direct Current – current that varies in magnitude but not in direction. Three Forms of Direct Current: Continuous Direct Current - one in which an energy transfer takes place unidirectionally, with changes in value from instant to instant that either zero or so small that they may be neglected. Unidirectional Direct Current – when the current does vary somewhat in magnitude but does not reverse in direction Pulsating Direct Current – one which the magnitude varies considerably and pulsates regularly there being no reversal in direction. 2. Alternating Current – one in which the direction alternates regularly and, unless otherwise definitely stated, changes periodically in magnitude as well as direction. Oscillating Current – although alternating in character, increases and decreases in magnitude and changes in direction periodically with respect to time according to some definite law, in general, successive waves of current do not have the same magnitude.  ELECTRIC CIRCUIT AN INTERCONNECTION OF ONE OR MORE ELECTRICAL DEVICES IN WHICH THERE SHOULD BE AT LEAST ONE CLOSED PATH IN WHICH CURRENT MAY FLOW. BASIC COMPONENTS OF AUXILIARY COMPONENTS OF ELECTRIC CIRCUIT ELECTRIC CIRCUIT 1. Voltage Source 1. Measuring instruments 2. Load 2. Disconnecting means 3. Connecting 3. Protective devices Conductors  SERIES CIRCUIT Characteristics of a Series Circuit: 1. Same current flows through all parts of the circuit 2. Different resistors have their individual voltage drops 3. Voltage drops are additive 4. Applied voltage equals the sum of different voltage drops 5. Resistances are additive 6. Powers are additive  PARALLEL CIRCUIT Characteristics of a Parallel Circuit: 1. Same voltage acts across all parts of the circuit 2. Different resistors have their individual current 3. Branch currents are additive 4. Conductances are additive 5. Powers are additive THANK YOU  ELECTRICAL SYMBOLS and INSTRUMENTS ELECTRICAL SYMBOLS Resistor Symbols are used for components in electrical circuit diagrams and some of the more common ones are shown in Figure 4.1.  ELECTRICAL INSTRUMENTS AMMETER is an instrument used to measure current and must be connected in series with the circuit. VOLTMETER is an instrument used to measure potential difference and must be connected in parallel with the part of the circuit whose potential difference is required. OHMMETER an instrument for measuring resistance. MULTIMETER universal instrument, may be used to measure voltage, current and resistance.  OSCILLOSCOPE may be used to observe waveforms and to measure voltages and currents. WATTMETER an instrument for the measurement of power in an electrical circuit. MEGGER may be used to measure both continuity and insulation resistance.  AMMETER VOLTMETER MULTIMETER OHMMETER OSCILLOSCOPE WATTMETER MEGGER Sources: https://dir.indiamart.com/impcat/analog-ammeter.html https://sci-supply.com/analog-dc-voltmeter-0-3-0-15v-dc/ https://www.elprocus.com/what-is-an-ohmmeter-circuit-diagram-types-and- applications/ https://ph.element14.com/fluke/fluke-117/multimeter-digital-hand-held- 6000/dp/1274602 https://www.tek.com/en/products/oscilloscopes/tbs1000 https://langlois-france.com/en/wattmeters/5295-wattmetre-mono-continu-triphase.html https://ph.rs-online.com/web/p/insulation-testers/7639264 https://www.lazada.com.ph/products/peakmeter-digital-tachometer-handheld-contact- motor-tachometer-lcd-speedometer-tach-rpm-meter-contact-type-digital-tachometer- wide-measuring-rang-5019999rpm-i415108947.html  CIRCUIT ELEMENTS  TYPES OF CIRCUIT ELEMENTS ACTIVE CIRCUIT PASSIVE CIRCUIT ELEMENTS ELEMENTS  Produces energy in the form of  Stores energy in the form of voltage voltage or current or current  They have function and provide  They do not have function to provide power gain power gain  Examples: DC generators, current,  Examples: resistors, capacitors, voltages, batteries inductors Source: https://www.escomponents.com/blog/2019/7/31/active-amp- passive-components-what-is-the-difference-between-the-two  ACTIVE CIRCUIT ELEMENTS INDEPENDENT SOURCE DEPENDENT SOURCE 1. Ideal Independent Voltage 1. Dependent/Controlled Source Source  in which the source quantity is  characterized by terminal voltage determined by a voltage or current and completely independent of the existing some other location in the current through it. electric system under examination. 2. Ideal Independent Current Source  the current through it is completely independent of the voltage across it. INDEPENDENT VOLTAGE SOURCE INDEPENDENT CURRENT SOURCE  DEPENDENT/ CONTROLLED CURRENT SOURCE DEPENDENT DEPENDENT VOLTAGE SOURCE CURRENT SOURCE  PASSIVE CIRCUIT ELEMENTS 1. RESISTOR Used to impede the flow of current. https://learn.sparkfun.com/tutorials/r TYPES OF RESISTORS esistors/all 1. Fixed value Resistor – fixed amount of resistance in the circuit. 2. Variable Resistor – the value of resistance is not fixed.  Resistor Color Coding https://electricalacademia.com/basic-electrical/resistor-color-code-resistor-color-bands- standard-resistor-values/ TOLERANCE ▪ Tolerance is the amount (in percent) by which the actual ohmic resistance can be different from the color coded value.  EXAMPLE BROWN BLACK ORANGE GOLD 1 0 103 ± 5% Rated Value : 10 k𝛺 Minimum Value : 10 k𝛺 - 5% (10k𝛺) = 9.5 k𝛺 Maximum Value : 10 k𝛺 + 5% (10k𝛺) = 10.5 k𝛺 Range : 9.5 k𝛺 – 10.5 k𝛺 Ohmic Value is 10 x 103 = 10,000 𝛺 ± 5% (𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝑅𝑎𝑡𝑒𝑑) % 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 1 − 𝑥 100 𝑅𝑎𝑡𝑒𝑑 SAMPLE PROBLEMS Find the Rated value, Minimum, Maximum, Ohmic values and Range of the given color bands. 1. Black, Yellow, White and Silver 2. Red, Red, Orange and No color 3. Red, Violet, Gray and Gold 4. Green, Blue, Brown and Silver 5. Green, Yellow, Red and No color 6. Blue, Blue, Black and Gold 7. Blue, Red, Gray and Gold 8. White, Violet, Green and Silver 9. Black, Red, Yellow and Silver 10. White, Orange, Violet and Gold  2. CAPACITORS Designed to store energy in its electric field. Often found in power supplies https://en.wikipedia.org/wiki/Cap acitor Capacitance – ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F) 𝑄 Where: C = capacitance (Farad) 𝐶= Q = charge (Coulombs) 𝑉 V = voltage (volt) 3. INDUCTORS Designed to store energy in its magnetic field. It consists of a coil conducting wire. https://components101.com/articles/typ es-of-inductors-and-their-applications Inductance – is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H) THANK YOU  Temperature - Resistance Effects  As Temperature increases, more electrons will escape their orbits, causing additional collision within the conductor. Any increase in the number of collision translates into a relative increase or decrease in resistance. For most conducting materials, the increase in the number of collisions translate into a relatively linear increase in resistance, as shown in Figure 3-6. The rate at which the resistance of a material changes with the variation on temperature is called Temperature Coefficient (α) of the material.  Any material for which resistance increases as temperature increases is to have a positive temperature coefficient (+α) For semiconductor materials, as the temperature increases the number of charge electron increases, resulting in more current. Therefore, an increase in temperature results in a decrease in resistance. Semiconductors have negative temperature coefficient (-α)  Referring to fig 3-6, applying similar triangle we obtain; 𝑅2 𝑅1 = 𝑇+𝑡2 𝑇+𝑡1 This expression may be rewritten to solve for the resistance, R2 at any temp t2 as follows; 𝑇+𝑡2 𝑅2 = (𝑅1 ) 𝑇+𝑡1 Temperature coefficient  1 1 1 = 2 = 𝑇+𝑡1 𝑇+𝑡2  Derived formula of R2 in terms of α 𝑅2 = 𝑅1 [1 +  1 (𝑡2 − 𝑡1 ) where: 𝑅1 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅 2 = 𝑓𝑖𝑛𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 T = inferred absolute temperature (temperature when resistance of a given material is zero) 𝑇1 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇2 = 𝑓𝑖𝑛𝑎𝑙 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 1 = temperature coefficient of t 1  2 = temperature coefficient of t 2  SAMPLE PROBLEMS 1. The tungsten filament in an incandescent lamp has a resistance of 9.8Ω at a room temp of 200 C and a resistance of 132Ω at normal operating temp. Using the temp coefficient formula for resistance calculate the temperature of the heated filament. 2. A coil of copper wire has a resistance of 62 Ω at room temperature of 240 C. What will be its resistance at a.)800 C and b.) -200 C. 3. The temperature coefficient of resistance of a conductor is 0.0039 per degree C at 20-degree C. Find the resistance of the conductor in ohms at 70 degree C if its resistance at 20 degree C is 4 ohms. 4. When 120 V is applied across a certain light bulb, a 0.5-A current flows, causing the temperature of the tungsten filament to increase to 2600 °C. What is the resistance of the light bulb at the normal room temperature 20 °C?  CONDUCTORS UNDERGOING DRAWING PROCESS In the process, the waste of the material is assumed negligible (efficiency is 100%), thus keeping the volume to be constant all throughout the process. With the volume of the material constant, resistance varies directly as the square of the length. 𝑅2 𝐿2 2 = ( ) 𝑅1 𝐿1  With the volume of the material constant, resistance varies inversely as to the fourth power of the diameter. 𝑅2 𝑑1 4 = ( ) 𝑅1 𝑑2  SAMPLE PROBLEMS 1. A kilometer of wire having a diameter of 11.7 mm and a resistance of 0.031 ohm is drawn down so that its diameter is 5.0 mm. what does its resistance become? 2. A one – meter rod of 2 – cm diameter is drawn until its resistance is 100 times the initial resistance. Its length afterward is? 3. A copper wire of unknown length has a resistance of 0.80 ohm. By successive passes through drawing lies, the length of the wire is increased to 2 and ½ times its original value. Assuming that resistivity remains unchanged during the drawing process, determine the new value of its resistance.  CONDUCTANCE A measure of the material’s ability to conduct electric current. Reciprocal of resistance Measure in mho (Ʊ), siemens (S) 1 𝐴 𝜎𝐴 𝐺= = = 𝑅 𝜌𝑙 𝑙 Siemens (formerly mho) unit of conductance Named after the German engineer, Ernst Werner von Siemens Conductivity (𝜎) reciprocal of resistivity 1 𝜎= 𝜌 Where: G = conductance (siemens) R = resistance (ohms) σ = conductivity (siemens per meter) 𝜌 = resistivity (ohms- meter) L = length (meter)  SAMPLE PROBLEMS 1.The resistance of 120 meters of wire is 12 ohms. What is its conductance? 2. Find the conductance of a round piece of iron with a cross-sectional radius of 0.001 meters and length of 0.1 meters. (conductivity of iron is 1.03 𝑥 107 siemens/m) THANK YOU ELECTROMOTIVE FORCE (EMF)  ELECTROMOTIVE FORCE  Also known as electric pressure  Commonly called voltage  Unit is volt (V)  When an emf is applied to the ends of a conductor it is proper to refer to existence of a potential difference between such ends.  Several methods are employed to develop an emf:  Combining certain kinds of metals and chemical into a device (device)  Building a machine which generates voltage when conductors are rotated near magnets Electrical Resistance and Resistivity  BRIEF HISTORY One of the fundamental relationships of circuit theory is that between voltage, current and resistance. This relationship and the properties of resistance were investigated by the German physicist Georg Simon Ohm. Ohm found that current depended on both voltage and resistance. From his investigation he was able to define the resistance of a wire and show that the current was inversely proportional to this resistance.  Resistance of Conductors Resistance of a material depends upon several factors: Type of material Length of the conductor Cross-sectional area Temperature The resistance of a conductor is dependent upon the type of material. The resistance of a metallic conductor is directly proportional to the length of the conductor.  The resistance of a metallic conductor is inversely proportional to the cross-sectional area of the conductor Factors governing the resistance of a conductor at a given temperature may be expressed mathematically: 𝜌𝑙 R= 𝛺 𝐴 Where: ρ = resistivity or specific resistance l = length A = cross-sectional area  Resistivity (ρ) has a unit of Ω-m if the length is in meter and area is in meter square, and a unit of CM-ohms/ ft if the length is in feet and the area is in CM. Since most conductor are circular its cross-sectional area 2 𝑑2 𝐴= 𝜋𝑟 = 𝜋 4 Where: r = radius d = diameter Units of cross-sectional area of a conductor: - square meter - square feet - Circular Mil (CM) - Square-Mil (sq.mil)  CROSS- SECTIONAL AREA Circular Mil (CM) Square Mil Standard unit of Unit of cross-sectional measurement of a area whose sides are round wire cross- equal to 1 mil sectional area. Diameter is one mil. 𝑨 = 𝒔𝟐 𝑨 = 𝒅𝟐 𝑨 = 𝝅𝒓𝟐 s FOR CONVERSION CIRCULAR MIL (CM) SQUARE MIL a wire that has a diameter of s = 1mil 1 mil, has an area of 1 CM 𝝅𝒅𝟐 𝑨 = 𝒔𝟐 𝑨= 𝑨 = (𝟏 𝒎𝒊𝒍)𝟐 𝟒 𝝅 4 𝑨 = (1mil)2 ; 1 sq. mil = CM 𝟒 𝜋 𝜋 ;1 CM = sq. mil 4 CONVERSION: 𝜋 1000 mil = 1 inch 1 CM = x 10−6 sq. inch 4 4 1 sq. inch = 106 sq. mils = 𝜋 x 106 CM 1000 CM = 1 MCM  VOLUME TO RESISTANCE Since volume of the body is 𝑉 = 𝜋𝑟 2 ℎ = 𝐴𝑙 from r 𝜌𝑙 R= ; 𝐴 𝑉 if L = 𝐴, then H=l 𝑉 𝜌( ) 𝑽 𝐴 R= 𝐴 R=𝝆 (𝑨𝟐 ) 𝑉 if A = 𝑙 , then 𝜌𝑙 𝒍𝟐 R= 𝑉 R= 𝝆 (𝑽) (𝑙) Elements/ Resistivity Alloy (Ω-CM/ft) Copper, 10.37 annealed Aluminum 17 Tungsten 33 Zinc 36 Nickel 47 Manganin 265 Nichrome 600 Resistivity of Common Elements at 20℃  SAMPLE PROBLEMS 1. Most homes use solid copper wire having a diameter of 1.63 mm to provide electrical distribution to outlets and light sockets. Determine the resistance of a 75 meters solid copper wire having the above diameter. 2. Calculate the resistance of the following conductor at 20ºC (a) material: copper with length 1000 ft and area of 3,200 CM (b) material: aluminum with length 4 miles and diameter of 162 mils. 3. The heating unit for an electric iron has a resistor of 12 ohms. If the cross-sectional area of the material is rectangular, 0.0045 in x 0.125 in., and its total length is 13 ft, determine the resistivity of the material used.  ACTIVITY 1. The substation bus bar is made-up of 2 inches round copper 20 ft long. What is the resistance of each bar if resistivity is 1.724 × 10−6 ohm-cm. 2. Determine the resistance of a bus bar made of copper if the length is 10 meters long and the cross-section is 4 × 4 𝑐𝑚2. Use 1.7241 micro ohm-cm as the resistivity. 3. What is the size in square millimeter if the cable of 250 MCM size? THANK YOU ELECTRIC CHARGE AND ELECTRIC CURRENT LEARNING OBJECTIVES 1.Understand the electron theory of electricity. 2.Determine the electric charge, current temperature-resistance effect. 3.Define Ohm’s Law and apply mathematical formulas in solving basic electrical problems. 4.Define the two general types of electric circuit 5.Understand electrical circuits and apply the power, current, resistance and voltage equations.  ELECTRIC CHARGE and ELECTRIC CURRENT Coulombs - unit of electric charge For each negatively charged electron it is 𝟏. 𝟔𝟎𝟐 𝐱 𝟏𝟎−𝟏𝟗 𝑪 1 Coulomb of electric charge is 𝟔. 𝟐𝟒 𝐱 𝟏𝟎𝟏𝟖 𝒆 When one coulomb of electric charge passes a given point every second the electric current is said to be one ampere. One coulomb per second is one ampere. 𝑸 𝑰= 𝒕 where I = current (Ampere) Q = charge (coulomb) t = time (second) during which electron move If the current is constant, charge is transferred at a constant rate 𝐐 = 𝑰𝒕 For non-uniform current, the transferred charge will vary with the current changes, 𝒒 = 𝒊𝒕 PREFIX SI symbol Exponent Form 18 Exa E 10 15 Peta P 10 12 Tera T 10 9 Giga G 10 6 Mega M 10 3 Kilo k 10 -1 deci d 10 -2 centi c 10 -3 milli m 10 -6 micro µ 10 -9 nano n 10 -12 pico p 10 -15 femto f 10 -18 atto a 10  SAMPLE PROBLEMS 1. What current must flow if 0.24 coulombs is to be transferred in 15 ms? 2. If current of 15 A flows for four minutes, find the quantity of electricity transferred.  ACTIVITY 1. A cloud of 2.5 × 1019 electrons move past a given point every 2 seconds. How much is the intensity of the electron flow? 2. The current in an electric lamp is 5 amperes. What quantity of electricity flows towards the filament in 6 minutes? 3. A constant current of 4 A charges a capacitor. How long will it take to accumulate a total charge of 8 coulombs on the plates? Resources ▪ Charles K Alexander, Matthew Sadiku, Fundamentals of Electric Circuits, 6th ed., McGraw-Hill Education, 2016 THANK YOU  ELECTRON THEORY OF ELECTRICITY LEARNING OBJECTIVES 1.Understand the electron theory of electricity. 2.Determine the electric charge, current temperature-resistance effect. 3.Define Ohm’s Law and apply mathematical formulas in solving basic electrical problems. 4.Define the two general types of electric circuit 5.Understand electrical circuits and apply the power, current, resistance and voltage equations. What is ELECTRICITY? A form of energy that is created from the movement of electrons of atoms. When the electrons move from one atom to the next, energy is created.  Electron Theory of Electricity All matter is composed of atoms which are made up of fundamental subatomic particle called protons, neutrons, and electrons. Each atom represents a sort of microscopic solar system in which the nucleus contains protons and around which the electrons revolve in definite orbits. As the atoms become increasingly complex, the positive charge of the nucleus is strengthened by acquiring additional protons.  Electrons rises proportionately to provide a structure that is electrically neutral. Neutrons are also added to nucleus but have no effect upon the atomic charge. Protons and neutrons are bunched together in a central core. Electrons are presumed to revolve in orbits or shells around the nucleus.  Electron Shell and Orbits Electron orbit the nucleus of an atom at certain distance from the nucleus Electrons near the nucleus have less energy than those in more distant orbits. Energy levels orbit from the nucleus corresponds to a certain energy level orbits are grouped into shells (energy band) each shell has a fixed maximum number of electrons the shells are designated K, L, M, N and so on with K being the closest to the nucleus  Valence Electrons and Conductivity in Solids the outermost shells known as the valence shell and electrons in this shell are called VALENCE ELECTRONS Solid materials may be classified as conductors, insulators, and semiconductors Classification depends upon the number of valence electrons Conductor : material that easily conducts electric current. Valence electron < 4 ex. Copper, silver, gold and aluminum  Insulators : material that does not conduct electrical current under normal conditions. valence electron > 4 ex. Phosphorus Semiconductor : material that is between conductors and insulators in its ability to conduct electrical current valence electron = 4 ex. Germanium, silicon and carbon Copper atom Semiconductor material Resources ▪ https://www.youtube.com/watch?v=EJeAuQ7pkpc&t=4s (Introduction to Electricity) ▪ John Bird, Electrical Circuit Theory and Technology, Routledge, 2017 THANK YOU