CSM 153 Circuit Theory Past Paper PDF

CSM 153 Circuit Theory Akwasi Acheampong Aning KNUST, GHANA January 24, 2023 1/41 Outline I 1 Syllabus, Assessment,Recommended Books, Basic Terms Course Outline, Assessment and Recommended Books 2 Unit One Charge and Mat...

CSM 153 Circuit Theory Akwasi Acheampong Aning KNUST, GHANA January 24, 2023 1/41 Outline I 1 Syllabus, Assessment,Recommended Books, Basic Terms Course Outline, Assessment and Recommended Books 2 Unit One Charge and Matter Force, Energy and Power Resistors, Capacitors and Inductors Inductors KNUST COVID-19 AWARENESS COVID-19 COVID-19: Caused by a virus known as Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2). Spreads very easily from person to person. Signs and symptoms Fever or chills cough, difficulty in breathing, cold headache, diarrhoea, loss of taste/smell and several non-specific symptoms Transmission Respiratory droplets airborne contaminated surfaces Prevention Adhere to the KNUST COVID-19 safety protocols Respiratory hygiene: Wear a nose mask, cough etiquettes Hand hygiene: Frequent hand washing, hand sanitizing Maintain ‘safe’ physical distancing Avoid crowds and confined/poorly ventilated spaces Virus is changing itself with even more serious ramifications, so it is important we all adhere to the safety protocols Circuit Theory Introduction Course Outline Unit 1: Basic Concepts and Elements Charge and Matter Force, Energy and Power Resistors, Capacitors and Inductors Unit 2: Direct Circuit Analysis Ohm’s law Series Circuit Parallel Circuit Methods of Analysis Unit 3: Networks Theorems Superposition Theorem Thevenin’s Theorem Norton’s Theorem Delta and Wye Networks Circuit Theory Introduction Course Outline Unit 4: Magnetism Field and Force Electromagnetics Ampere’s Law Biot-Savart Law Unit 5: AC Circuits Alternating Currents and Voltages R, L and C Elements Power in AC Circuits 5/41 Circuit Theory Introduction Assessment Exam = 70% Quiz, home works, attendance and Mid-semester Exam = 30% 6/41 Circuit Theory Introduction Recommended Books Giancoli, D. C. Physics: Principles with Applications 7th Edition. 2014. Randall D. Knight, Physics for Scientists and Engineers a Strategic Approach with Modern Physics 4/e, 2017 Raymond A. Serway and John W. Jewett Jr., Physics for Scientists and Engineers with Modern Physics, 10th Edition, 2019 Allan H. Robbins and Wilhelm C. Miller, Circuit Analysis: Theory and Practice, Fifth Edition, 2013 William H. Hayt, Jr., Jack E. Kemmerly and Steven M. Durbin Engineering Circuit Analysis, 8th Edition, 2012 John Bird, Electrical Circuit Theory and Technology Sixth edition, 2017 Any University Physics Book 7/41 Circuit Theory Introduction Course Objectives To introduce electric circuits and its analysis To impart knowledge on solving circuit equations using network theorems To develop a clear understanding of the important parameters of a magnetic circuit To introduce the phenomenon of resonance in coupled circuits. Learning Outcomes To be able to understand basic electrical properties Use node and mesh analyses methods for the analysis of linear circuits Analyze circuits by utilizing Superposition, Thevenin’s and Norton’s theorems. To be able to understand basic magnetic properties 8/41 Circuit Theory Introduction UNIT ONE Basic Concepts and Elements 9/41 Circuit Theory Basics method 10/41 Circuit Theory Introduction Charge and Matter The Structure of the Atom Sub-atomic particles make up atoms, which make up ordinary matter Thus, matter is made up of several sub-atomic particles (protons, electrons and neutrons) The protons and neutrons (nucleons) are closely packed to form the nucleus If the nucleus is considered a sphere, its diameter is of the order of 10−14 The total charge of electrons balance the total charge of protons The atom as a whole is electrically neutral (no charge) 11/41 Circuit Theory Introduction Charge and Matter The Structure of the Atom: The Neutron It has no electrical charge so it is electrically neutral It cannot be deflected by electric and magnetic fields because it has no charge They are more penetrating than the electron or the proton The Structure of the Atom: The Electron The electron has negative charge of 1.6x10−19C It can be deflected by electric and magnetic fields It is always deflected towards the positive plate in an electric field The Structure of the Atom: The Proton It has a positive charge equal in magnitude to the charge on the electron It can be deflected by electric and magnetic fields It is always deflected towards the negative plate in an electric field 12/41 Circuit Theory Introduction Charge and Matter The Structure of the Atom The protons and neutrons of an atom share a very small volume of space called the nucleus of the atom The electrons are attracted to the nucleus by a force called the electrostatic force or Coulomb force This force exists because the electrons and nuclei have electric charges of opposite sign The electron is negatively charged and the nucleus is positively charged The positive charge of the nucleus is entirely due to the charges of protons, since the neutrons do not have any net electric charge The charge of an object can be regarded as the algebraic sum of all the elementary atomic charges which make up the object The electric charge is an intrinsic property of the elementary particles, such as electron or proton, just as mass is an intrinsic property of matter Circuit Theory Introduction Charge and Matter The Structure of the Atom Thus, electric charge is a property (characteristic) associated with fundamental particles wherever they exist Mass can create a gravitational field g, which in turn can exert a force mg on a body of mass m Thus, mass m can create gravitational force Fg = mg Electric charge, like mass, is an important inherent property of matter which can be present in both large and small bodies Electric charge q can create electric field E in space, which can also exert a force qE on another body of charge q Thus, electric charge q can create electric or electrostatic force F E = qE These fields in turn transmit forces to other charged bodies and thereby affect their motion Therefore, the region in space around the charged body, where electric forces can be experienced defines electric field 14/41 Circuit Theory Introduction Charge and Matter The Structure of the Atom Another important feature of charge is that electric charge is always conserved In any interaction or reaction, the initial and final values of the total electric charge must be the same. Thus, total electric charge is neither created nor is it destroyed Matter or solid state materials may be classified into insulators, semiconductors and conductors Insulators From atomic point of view electrons in insulators are firmly (tightly) bound to the nucleus Thus unable to move under applied potential difference for electrical conduction Therefore, electrical conduction in insulators is by the mechanism of dielectric conduction 15/41 Circuit Theory Introduction Charge and Matter Semiconductors Electrons in semiconductors are relatively not firmly (tightly) bound to the nucleus Thus only few electrons are able to move under applied potential difference for electrical conduction However, electrons can be generated to take part in electronic semi-conduction Conductors In metallic conducting materials some of the electrons are very loosely bound to the nucleus Thus electrons can move about freely within the crystal structure Such electrons are called free electrons or conduction electrons Therefore, electric current through metals is by electronic conduction 16/41 Circuit Theory Force, Energy and Power method 17/41 Circuit Theory Introduction Force, Energy and Power Force The electrical force between two stationary charged particles is given by Coulomb’s Law The force is directly proportional to the product of the charges, q1 and q2 , on the two particles and inversely proportional to the square of the separation, r between the particles and directed along the line joining them The force is attractive if the charges are of opposite sign The force is repulsive if the charges are of like sign The force is a conservative force Mathematically the Coulomb’s law is: q1 q2 Fe = ke (1) r2 The SI unit of charge is the coulomb (C), ke is called the Coulomb 1 constant, that is: ke = = 8.9875x109 N.m2 /C 2 , and ε0 is the 4πε0 permittivity of free space with a value of: ε0 = 8.8542x10−12 C 2 /N.m2 Circuit Theory Introduction Force, Energy and Power Force The electrical force between the electron and proton is found from q1 q2 Coulomb’s law Fe = ke 2 = - 8.2x10−8 N r This can be compared with the gravitational force between the electron and the proton given by me m p Fg = G 2 = 3.6x10−47 N r Potential Electric potential V at a point in an electric field is defined as the potential energy per unit charge. i.e. U V= (2) q Similarly, electric potential can be defined as the work done per unit charge in moving the charge from infinity to the point W∞ V=− (3) q Circuit Theory Introduction Force, Energy and Power Potential Potential is a scalar quantity, and not a vector with SI unit Joule per Coulomb [JC −1 or Volt(V)] The potential can be positive, negative or zero depending on the signs and magnitude of q The potential energy per unit charge (potential) is independent of the charge q of the particle we use The potential is characteristic only of the electric field we are investigating The electric potential difference △V between any two points i and f in an electric field is equal to the difference in potential energy per unit charge between the two points △U W △ V = V f − Vi = =− (4) q q Therefore, potential difference between two points is the negative of the work done by the electrostatic force to move a unit charge from one point to the other in the field 20/41 Circuit Theory Introduction Force, Energy and Power Potential For a potential energy to exist, we must have a system of two or more charges Potential energy belongs to the system and changes only if a charge is moved relative to the rest of the system The electric field is a measure of the rate of change of the electric potential with respect to position The work done △W in moving the unit charge through a small distance △x toward the charge is given by △ W = F(− △ x) (5) Thus dW = −Fdx = Edx" # Z r r qdx q 1 q W=V=− 2 =− − = (6) ∞ 4πε0 x 4πε0 x ∞ 4πε 0r the potential, V is equal to the work done per unit test charge, A positively charged particle produces a positive electric potential and a negatively charged particle produces a negative electric potential Circuit Theory Introduction Force, Energy and Power Potential When dealing with energies of electrons, molecules or atoms, the joule appears to be a very large unit of energy For this reason alternative unit of energy called the Electronvolt (eV) is used Electronvolt is defined as the energy gained by an electron accelerated through a potential difference of one volt (1V) The electronvolt is the energy that can be acquired by a particle, which carries a charge of the magnitude of the charge on the electron (q = e) and moved through a potential difference of 1V Current The charge is related to the current Q = It (7) Electrical conduction in a wire (metal) is due to the movement of free electrons Emf set up an electric field in the metal and the electron are then accelerated by the field and they gain velocity and energy Circuit Theory Introduction Force, Energy and Power Current The moving electrons collide with atoms of the metal vibrating about their fixed mean position and give up some of their energy to the atoms The amplitude of vibrations of the atoms increases and the temperature of the metal rises On the average the electrons drift in the opposite direction to the electric field with a mean speed. Therefore the drift constitute electric current Power Power is the rate of doing work or, equivalently, as the rate of transfer of energy. The symbol for power is P The charge is related to the current W V2 P= = V I = I2R = (8) t R 23/41 Circuit Theory Resistors, Capacitors and Inductors method 24/41 Circuit Theory Introduction Circuit Elements: Resistors Resistors are specifically designed to possess resistance and are used in almost all electronic and electrical circuit Resistors are the simplest components in any circuit but their effect is very important in determining the operation of a circuit Resistance is represented by the symbol R and is measured in units of ohms (after Georg Simon Ohm). The symbol for ohms is the capital Greek letter omega (Ω) The resistance of a material is dependent upon several factors Type of material Length of the conductor l Cross-sectional area A and Temperature T The resistance R and the resistivity ρ are related by the equation ρl R= (9) A 25/41 Circuit Theory Introduction Circuit Elements: Resistors There are two main types of resistors: Fixed Resistors are resistors with constant resistance values and Variable resistors are three terminal resistors are used to adjust the volume of our radios, set the level of lighting in our homes, and adjust the heat of our stoves and furnaces Large resistors have their resistor values and tolerances printed on their cases Smaller resistors are too small to have their values printed on the component They are usually covered by an epoxy or similar insulating coating over which several coloured bands are printed radially The coloured bands provide a quickly recognizable code for determining the value of resistance, the tolerance (in percentage), and occasionally the expected reliability of the resistor 26/41 Circuit Theory Introduction Circuit Elements: Resistors The coloured bands are always read from left to right, left being defined as the side of the resistor with the band nearest to it The first two bands represent the first and second digits of the resistance value The third band is called the multiplier band and represents the number of zeros following the first two digits; it is usually given as a power of ten The fourth band indicates the tolerance of the resistor, and the fifth band (if present) is an indication of the expected reliability of the component The reliability is a statistical indication of the expected number of components that will no longer have the indicated resistance value after 1000 hours of use Circuit Theory Introduction Fixed Resistors: Colour Codes Variable Resistors method 28/41 Circuit Theory Introduction Circuit Elements: Capacitors A capacitor is an electrical device that is used to store electrical energy Next to the resistor, the capacitor is the most commonly encountered component in electrical circuits Capacitors are used extensively in electrical and electronic circuits To smooth rectified ac outputs In telecommunication equipment – such as radio receivers - for tuning to the required frequency In time delay circuits In electrical filters In oscillator circuits and In magnetic resonance imaging (MRI) in medical body scanners Capacitance is the electrical property of capacitors: it is a measure of how much charge a capacitor can hold A capacitor consists of two conductors separated by an insulator. One of its basic forms is the parallel-plate capacitor It consists of two metal plates separated by a non-conducting material (i.e., an insulator) called a dielectric The dielectric may be air, oil, mica, plastic, ceramic, or other suitable insulating material 29/41 Circuit Theory Introduction Capacitors The amount of charge Q that a capacitor can store depends on the applied voltage V For a conductor of any geometrical shape the capacitance, C is defined as the ratio of charge on the conductor to the potential it is raised. Thus Q C= (10) V The unit of capacitance C is the farad, F Circuit Theory Capacitors and Inductors Capacitors A capacitor is an electronic device for storing electrical energy as potential energy in an electric field When a capacitor is charged the plates acquire equal but opposite charges of + q and – q. However, we refer to the An arrangement of two isolated absolute charge q of a conductors of any shape form a capacitor capacitor Conventionally, an arrangement consisting of two parallel conducting plates of area, A separated by a distance, d form a parallel-plate capacitor Circuit Theory Capacitors and Inductors Capacitors When a capacitor is charge, a potential difference, V is set up between the plates The charge Q and the potential difference V for a capacitor are proportional to each other i.e. Q ∝ V Q = CV (11) where C is a proportional constant, called capacitance of the capacitor ∴ Q C= V For a conductor of any geometrical shape the capacitance, C is defined as the ratio of charge on the conductor to the potential it is raised i.e. C = (Charge on conductor)/(Potential it is raised) For a parallel-plate capacitor, capacitance C is defined as the ratio of charge on each (either) plate to the potential difference between the plates Capacitance is a measure of the charge a capacitor can store. Thus, the higher the capacitance, the greater or more charge it can store SI Unit of capacitance: coulomb per volt CV −1 = 1 Farad (1F) Practical unit are: microfarad (1mF = 10−6 F) and (1pF = 10−12 F) Circuit Theory Introduction Capacitors For a parallel-plate capacitor, capacitance C is defined as the ratio of charge on each (either) plate to the potential difference between the plates The capacitance of a parallel plate capacitor is: ε0 A C= (12) d C increases as we increase the area A or decrease separation d of the plates For a Parallel Plate Capacitor, the capacitance depends only on the following factors: Area (Geometry) of the plates A Separation (distance) between the plates d The nature of material (dielectric material) between the plates For an isolated sphere, the capacitance is: Q C= = 4πε0 R (13) V C is independent of the charge on the spherical conductor but depends only on the radius R Circuit Theory Capacitors and Inductors Capacitors this implies Q E= (16) Aε0 The potential difference between plates is given by Consider parallel-plates of a capacitor each of area A and charge Z d magnitude Q on plates V=− Edr = Ed (17) 0 Assuming the plates are so large and close together, we can neglect edge V effects of the electric field E= (18) d The electric field E between the Q V Q ε0 A plates is given by Thus = ⇒ = Aε0 d V d σ E= (14) ε0 ε0 A C= (19) and d Q σ= (15) A C increases as we increase the area A or and σ is the surface charge density decrease separation d of the plates Circuit Theory Capacitors and Inductors Capacitors Capacitors in Series For three capacitors in series the equivalent capacitance Ceq is given by 1 1 1 1 = + + (20) Ceq C1 C2 C3 For three capacitors in Capacitors in Parallel parallel the equivalent capacitance Ceq is given by Ceq = C1 + C2 + C3 (21) Potential energy U stored in a capacitor is given by any of the following Q2 CV 2 QV U= = = (22) 2C 2 2 Circuit Theory Capacitors and Inductors Dielectrics A dielectric is an insulating material such as mica, paper, mineral oil or plastic, which can be used to fill Dielectric constant (relative the space between the plates of a capacitor permittivity) εr of a material When a dielectric slab is inserted between the plates of is the ratio of the a capacitor, the charge Q stored increases by a factor capacitance with dielectric to k, called dielectric constant of the insulating material capacitance without In effect, the potential difference V between the plates dielectric between the plates rather decreases by a factor k Potential energy U stored in In general, in a region or space completely filled by a a capacitor is given by any of dielectric material of dielectric constant k, all the following electrostatic equations containing ε0 are to be replaced C by kε0 εr = (24) C0 Thus, a point charge inside a dielectric produces an electric field E given by where C is capacitance with plates filled with dielectric Q material and C0 is E= (23) 4πkε0 r2 capacitance of the same This shows that for a fixed distribution of charges the capacitance with plates in effect of dielectric is to weaken the electric field that free space (vacuum) or air. would have been present between the plates Circuit Theory Capacitors and Inductors Dielectrics ε0 A The energy of a capacitor can be thought of as For parallel plate capacitor C0 = stored in the electric field between the plates. In any d εA →− and C = electric field E in free space the energy density u d (energy per unit volume) is C ε εr = = (25) u= 1 ε0 E 2 (26) C0 ε0 2 ∴ ε = εr ε0 = kε0 1 1 u= kε0 E 2 = εE 2 (27) Hence, the dielectric constant or 2 2 relative permittivity is the ratio of the When a dielectric is present, equation (27) holds permittivity of a material to permittivity Uses of Capacitors of free space and has no dimensions Capacitors are widely used in electronic Dielectric strength: The strength of a circuits in devices. They are used to store dielectric is the potential gradient charge and released later when needed (electric field) at which its insulation Capacitors are used to block power surges of breaks down and a spark passes charge and energy to protect devices through the material Every dielectric material has a Used in filter circuits in rectifiers to obtain d.c. characteristic dielectric strength, outputs which is the maximum value of Can be made in the form of very tiny electric field that it can withstand capacitors to serve as memory for binary code without breakdown in the RAM of computers 37/41 Circuit Theory Introduction Circuit Elements: Inductors Inductance is due entirely to the magnetic field created by the current, and its effect is to slow the build-up and collapse of the current and in general oppose its change A component called an inductor is used when the property of inductance is required in a circuit The basic form of an inductor is simply a coil of wire Factors which affect the inductance of an inductor include: the number of turns of wire - the more the turns the higher the inductance the cross-sectional area of the coil of wire - the greater the cross-sectional area the higher the inductance the presence of a magnetic core - when the coil is wound on an iron core the same current sets up a more concentrated magnetic field and the inductance is increased the way the turns are arranged: a short, thick coil of wire has a higher inductance than a long, thin one Circuit Theory Capacitors and Inductors Inductors Effect of Dielectric in a Capacitor Factors which affect the Inductance is the name given to the inductance of an inductor property of a circuit where there is an the number of turns of wire – the emf induced into the circuit by the more the turns the higher the change of flux linkages produced by a inductance current change The cross-sectional area of the coil of When the emf is induced in the same wire – the greater the cross-sectional circuit as that in which the current is area the higher the inductance changing, the property is called self The presence of a magnetic core – inductance, L when the coil is wound on an iron core the same current sets up a more When the emf is induced in a circuit by a concentrated magnetic field and the change of flux due to current changing in inductance is increased an adjacent circuit, the property is called The way the turns are arranged – a mutual inductance, M. The unit of short, thick coil of wire has a higher inductance is the henry, H inductance than a long, thin one Inductor is used when the property of We will look at inductance and inductance is required in a circuit. The induction in detail under basic form of an inductor is simply a coil electromagnetism of wire Circuit Theory Capacitors and Inductors Multiple Choice Question 1 A conductor is distinguished from an insulator 1 If the potential difference across a with the same number of atoms by the number resistor is doubled: of: 1 only the current is doubled ANS 1 nearly free atoms 2 only the current is halved 2 electrons 3 only the resistance is doubled 3 nearly free electrons ANS 4 only the resistance is halved 4 protons 5 both the current and resistance 5 molecules are doubled 2 Two small charged objects attract each other 2 A certain wire has resistance R. with a force F when separated by a distance d. Another wire, of the same material, If the charge on each object is reduced to has half the length and half the one-fourth of its original value and the diameter of the first wire. The distance between them is reduced to d/2 the resistance of the second wire is: force becomes: 1 R/4 1 F/16 2 R/2 2 F/8 3 R 3 F/4 ANS 4 2R ANS 4 F/2 5 4R 5 F Circuit Theory Introduction Circuit Elements