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What is electrical engineering?
Electrical engineeringis a field of engineeringthat generally deals with the study and application of electricity, electronics, and electromagnetism.
Ohm's lawstates that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:
Applications of Ohms LawTheapplications of ohms laware that it helps us in determining voltage,current or resistance of a linear circuit when the other two quantities are known to us.Limitation of Ohms LawThelimitations ofOhms laware explained as follows:1) This law cannot be applied to unilateral networks.A unilateral network has unilateral elements like diode, transistors, etc., which do not have samevoltagecurrentrelation for both directions of current.2)Ohms lawis also not applicable for non linear elements.Non linear elements are those which do not givecurrentthrough it, is not exactly proportional to thevoltageapplied, that means the resistance value of those elements changes for different values ofvoltageand current. Examples of non linear elements are thyristor, electric arc, etc.
Statement of Coulombs LawFirst LawLike charge particles repel each other and unlike charge particles attract each other.
Second LawThe force of attraction or repulsion between two electrically charged particles is directly proportional to the magnitude of their charges and inversely proportional to the square of the distance between them.Formulas of Coulombs LawAccording to the Coulombs second law,
Where,1. F is the repulsion or attraction force between two charged bodies.2. Q1 and Q2 are the electrical charged of the bodies.3. d is distance between the two charged particles.4. k is a constant that depends on the medium in which charged bodies are presented. In S.I. system, as well as M.K.S.A. system k=1/4. Hence, the above equation becomes.
The value of 0= 8.854 X 10-12C2/Nm2.
Hence,Coulombs lawcan be written for medium as,
Then, in air or vacuum r= 1. Hence,Coulombs lawcan be written for air medium as,
The value of r would change depends on the medium. The expression for relative permittivity ris as follows;
Limitation of Coulombs Law1. Coulombs lawis valid, if the average number of solvent molecules between the two interesting charge particles should be large.2. Coulombs lawis valid, if the point charges are at rest.3. It is difficult to apply theCoulombs lawwhen the charges are in arbitrary shape. Hence, we cannot determine the value of distanced between the charges when they are in arbitrary shape.
Kirchhoff's LawsKirchhoff's current law and voltage law, defined by Gustav Kirchhoff, describe the relation of values of currents that flow through a junction point and voltages in a an electrical circuit loop, in an electrical circuit. Kirchhoff's current law (KCL) Kirchhoff's voltage law (KVL)Kirchhoff's Current Law (KCL)This is Kirchhoff's first law.The sum of all currents that enter an electrical circuit junction is 0. When the currents enter the junction have positive sign and the current that leave the junction have negative sign:
Another way to look at this law is that the sum of currents that enter a junction is equal to the sum of currents that leave the junction:KCL exampleI1andI2enter the junctionI3leave the junctionI1=2A,I2=3A,I3=-1A,I4= ?Solution:Ik=I1+I2+I3+I4= 0I4= -I1- I2- I3= -2A - 3A - (-1A) = -4ASinceI4is negative, it leaves the junction.Kirchhoff's Voltage Law (KVL)This is Kirchhoff's second law.The sum of all voltages or potential differences in an electrical circuit loop is 0.
KVL exampleVS= 12V,VR1= -4V,VR2= -3VVR3= ?Solution:Vk=VS+VR1+VR2+VR3= 0VR3=-VS-VR1-VR2= -12V+4V+3V = -5VThe voltage sign (+/-) is the direction of the potential difference.
The heat which is produced due to the flow ofcurrentwithin an electric wire, is expressed in Joules. Now the mathematical representation or explanation ofJoules lawis given in the following manner.
i) The amount of heat produced incurrentconducting wire, is proportional to the square of the amount ofcurrentthat is flowing through the circuit, when theelectrical resistanceof the wire and the time ofcurrentflow is constant.
i.e. H i2(When R & t are constant)ii) The amount of heat produced is proportional to theelectrical resistanceof the wire when thecurrentin the circuit and the time ofcurrentflow is constant.i.e. H R (when i & t are constant)iii) Heat generated due to the flow ofcurrentis proportional to the time ofcurrentflow, when theresistanceand amount ofcurrentflow is constant.i.e. H t (when i & R are constant)When these three conditions are merged, the resulting formula is like this
Here H is the heat generated in Joules, i is thecurrentflowing through the circuit in ampere and t is in seconds. When any three of these are known the other one can be equated out.Here, J is a constant, known as Joules mechanical equivalent of heat. Mechanical equivalent of heat may be defined as the number of work units which, when completely converted into heat, furnishes one unit of heat.Obviously the value of J will depend on the choice of units for work and heat.It has been found thatJ = 4.2 joules/cal (1 joule = 107ergs) = 1400 ft. lbs./CHU = 778 ft. lbs/B Th UIt should be noted that the above values are not very accurate but are good enough for general work.Now according to Joules law I2Rt = work done in joules electrically when I ampere ofcurrentare maintained through aresistorof R ohms for t second.
By eliminating I and R in turn in the above expression with the help ofOhms law, we get alternative forms as
Gausss theoremThis theorem states that the total electric flux through any closed surface surrounding a charge, is equal to the net positive charge enclosed by that surface.Suppose the charges Q1, Q2_ _ _ _Qi, _ _ _ Qnare enclosed by a surface, then the theorem may be expressed mathematically by surface integral as
where D is the flux density in coulombs/m2and dS is the outwardly directed vector..Fleming Left Hand Rule
Fleming Right Hand Rule
Faradays LawsFaradays First LawAny change in themagnetic fieldof a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, thecurrentwill also circulate through the circuit and thiscurrentis called induced current.Method to changemagnetic field:1. By moving a magnet towards or away from the coil2. By moving the coil into or out of themagnetic field.3. By changing the area of a coil placed in themagnetic field4. By rotating the coil relative to the magnet.Faradays Second LawIt states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.
Lenzs LawLenzs law states that when an emf is generated by a change inmagnetic fluxaccording toFaradays Law, the polarity of the induced emf is such, that it produces ancurrentthatsmagnetic fieldopposes the change which produces it.The mathematical expression formagnetic fluxdensity was derived by Jean Baptiste Biot and Felix Savart. Talking the deflection of a compass needle as a measure of the intensity of a current, varying in magnitude and shape, the two scientists concluded that anycurrentelement projects into space amagnetic field, themagnetic flux densityof which dB, is directly proportional to the length of the element dl, thecurrentI, the sine of the angle and between direction of thecurrentand the vector joining a given point of the field and thecurrentelement and is inversely proportional to the square of the distance of the given point from thecurrentelement, r. this isBiot Savart lawstatement.
Where, K is a constant, depends upon the magnetic properties of the medium and system of the units employed. In SI system of unit,
Therefore finalBiot Savart lawderivation is,
Any linear circuit containing several voltages and resistances can be replaced by just a Single Voltage in series with a Single ResistorNortons TheoremAny linear circuit containing several voltages and resistances can be replaced by just a Single Voltage in parallel with a Single ResistorSuperposition theorem
Thesuperposition theoremforelectrical circuitsstates that for a linear system the response (voltageorcurrent) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internalimpedances
Delta to Star Network.
Star to Delta Transformation
Maximum Power Transfer TheoremSuppose we have avoltage sourceorbatterythats internalresistanceis Riand a load resistance RLis connected across thisbattery.Maximum power transfer theoremdetermines the value ofresistanceRLfor which, the maximum power will be transferred from source to it. Actually the maximum power, drawn from the source, depends upon the value of the loadresistance. There may be some confusion let us clear it.
Power delivered to the loadresistance,
To find the maximum power, differentiate the above expression with respect to resistance RLand equate it to zero. Thus,
Thus in this case, the maximum power will be transferred to the load when loadresistance is just equal to internal resistance of thebattery.