Semester 2–Engineering Chemistry II- Regulation 2008 Syllabus

Anna University

CY2161 ENGINEERING CHEMISTRY – II Syllabus

Regulation 2008

AIM

To impart a sound knowledge on the principles of chemistry involving the different application oriented topics required for all engineering branches.

OBJECTIVES

• The student should be conversant with the principles electrochemistry, electrochemical cells, emf and applications of emf measurements.

• Principles of corrosion control

• Chemistry of Fuels and combustion

• Industrial importance of Phase rule and alloys

• Analytical techniques and their importance.

UNIT I ELECTROCHEMISTRY 9

Electrochemical cells – reversible and irreversible cells – EMF – measurement of emf

– Single electrode potential – Nernst equation (problem) – reference electrodes – Standard Hydrogen electrode -Calomel electrode – Ion selective electrode – glass electrode and measurement of pH – electrochemical series – significance – + potentiometer titrations (redox – Fe² + vs dichromate and precipitation – Ag - vs CI titrations) and conduct metric titrations (acid-base – HCI vs, NaOH) titrations,

UNIT II CORROSION AND CORROSION CONTROL 9

Chemical corrosion – Pilling – Bedworth rule – electrochemical corrosion – different types – galvanic corrosion – differential aeration corrosion – factors influencing corrosion – corrosion control – sacrificial anode and impressed cathodic current methods – corrosion inhibitors – protective coatings – paints – constituents and functions – metallic coatings – electroplating (Au) and electroless (Ni) plating.

UNIT III FUELS AND COMBUSTION 9

Calorific value – classification – Coal – proximate and ultimate analysis metallurgical coke – manufacture by Otto-Hoffmann method – Petroleum processing and fractions

– cracking – catalytic cracking and methods-knocking – octane number and cetane number – synthetic petrol – Fischer Tropsch and Bergius processes – Gaseous fuels- water gas, producer gas, CNG and LPG, Flue gas analysis – Orsat apparatus – theoretical air for combustion.

UNIT IV PHASE RULE AND ALLOYS 9

Statement and explanation of terms involved – one component system – water system – condensed phase rule – construction of phase diagram by thermal analysis – simple eutectic systems (lead-silver system only) – alloys – importance, ferrous alloys – nichrome and stainless steel – heat treatment of steel, non-ferrous alloys – brass and bronze.

UNIT V ANALYTICAL TECHNIQUES 9

Beer-Lambert’s law (problem) – UV-visible spectroscopy and IR spectroscopy – principles – instrumentation (problem) (block diagram only) – estimation of iron by colorimetry – flame photometry – principle – instrumentation (block diagram only) – estimation of sodium by flame photometry – atomic absorption spectroscopy – principles – instrumentation (block diagram only) – estimation of nickel by atomic absorption spectroscopy.

TOTAL: 45 PERIODS

TEXT BOOKS:

1. P.C.Jain and Monica Jain, “Engineering Chemistry” Dhanpat Rai Pub, Co., New Delhi (2002).

2. S.S.Dara “A text book of Engineering Chemistry” S.Chand & Co.Ltd., New Delhi (2006).

REFERENCES:

1. B.Sivasankar “Engineering Chemistry” Tata McGraw-Hill Pub.Co.Ltd, New Delhi (2008).

2. B.K.Sharma “Engineering Chemistry” Krishna Prakasan Media (P) Ltd., Meerut (2001).

Semester 2–Engineering Physics II–Regulation 2008 Syllabus

Anna University

PH2161 ENGINEERING PHYSICS – II Syllabus

Regulation 2008

UNIT I CONDUCTING MATERIALS 9

Conductors – classical free electron theory of metals – Electrical and thermal conductivity – Wiedemann – Franz law – Lorentz number – Draw backs of classical theory – Quantum theory – Fermi distribution function – Effect of temperature on Fermi Function – Density of energy states – carrier concentration in metals.

UNIT II SEMICONDUCTING MATERIALS 9

Intrinsic semiconductor – carrier concentration derivation – Fermi level – Variation of Fermi level with temperature – electrical conductivity – band gap determination – extrinsic semiconductors – carrier concentration derivation in n-type and p-type semiconductor – variation of Fermi level with temperature and impurity concentration – compound semiconductors – Hall effect –Determination of Hall coefficient – Applications.

UNIT III MAGNETIC AND SUPERCONDUCTING MATERIALS 9

Origin of magnetic moment – Bohr magneton – Dia and para magnetism – Ferro magnetism – Domain theory – Hysteresis – soft and hard magnetic materials – anti – ferromagnetic materials – Ferrites – applications – magnetic recording and readout – storage of magnetic data – tapes, floppy and magnetic disc drives.

Superconductivity : properties - Types of super conductors – BCS theory of superconductivity(Qualitative) - High Tc superconductors – Applications of superconductors – SQUID, cryotron, magnetic levitation.

UNIT IV DIELECTRIC MATERIALS 9

Electrical susceptibility – dielectric constant – electronic, ionic, orientational and space charge polarization – frequency and temperature dependence of polarisation – internal field – Claussius – Mosotti relation (derivation) – dielectric loss – dielectric breakdown – uses of dielectric materials (capacitor and transformer) – ferroelectricity and applications.

UNIT V MODERN ENGINEERING MATERIALS 9

Metallic glasses: preparation, properties and applications.

Shape memory alloys (SMA): Characteristics, properties of NiTi alloy, application, advantages and disadvantages of SMA

Nanomaterials: synthesis –plasma arcing – chemical vapour deposition – sol-gels – electrodeposition – ball milling - properties of nanoparticles and applications.

Carbon nanotubes: fabrication – arc method – pulsed laser deposition – chemical vapour deposition - structure – properties and applications.

TEXT BOOKS:

TOTAL : 45 PERIODS

1. Charles Kittel ‘ Introduction to Solid State Physics’, John Wiley & sons, 7 edition, Singapore (2007)

2. Charles P. Poole and Frank J.Ownen, ’Introduction to Nanotechnology’, Wiley India(2007) (for Unit V)

REFERENCES:

1. Rajendran, V, and Marikani A, ‘Materials science’Tata McGraw Hill publications, (2004) New delhi.

2. Jayakumar, S. ‘Materials science’, R.K. Publishers, Coimbatore, (2008).

3. Palanisamy P.K, ‘Materials science’, Scitech publications(India) Pvt. LTd., Chennai, second Edition(2007)

4. M. Arumugam, ‘Materials Science’ Anuradha publications, Kumbakonam, (2006).

Semester 2–Mathematics–II Regulation 2008 Syllabus

Anna University

MA2161 MATHEMATICS – II Syllabus

Regulation 2008

UNIT I ORDINARY DIFFERENTIAL EQUATIONS 12

Higher order linear differential equations with constant coefficients – Method of variation of parameters – Cauchy’s and Legendre’s linear equations – Simultaneous first order linear equations with constant coefficients.

UNIT II VECTOR CALCULUS 12

Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal vector fields – Vector integration – Green’s theorem in a plane, Gauss divergence theorem and stokes’ theorem (excluding proofs) – Simple applications involving cubes and rectangular parallelpipeds.

UNIT III ANALYTIC FUNCTIONS 12

Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy

– Riemann equation and Sufficient conditions (excluding proofs) – Harmonic and orthogonal properties of analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation.

UNIT IV COMPLEX INTEGRATION 12

Complex integration – Statement and applications of Cauchy’s integral theorem and Cauchy’s integral formula – Taylor and Laurent expansions – Singular points – Residues – Residue theorem – Application of residue theorem to evaluate real integrals – Unit circle and semi-circular contour(excluding poles on boundaries).

UNIT V LAPLACE TRANSFORM 12

Laplace transform – Conditions for existence – Transform of elementary functions – Basic properties – Transform of derivatives and integrals – Transform of unit step function and impulse functions – Transform of periodic functions.

Definition of Inverse Laplace transform as contour integral – Convolution theorem (excluding proof) – Initial and Final value theorems – Solution of linear ODE of second order with constant coefficients using Laplace transformation techniques.

TEXT BOOK:

TOTAL : 60 PERIODS

1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3 Edition, Laxmi Publications (p) Ltd., (2008).

2. Grewal. B.S, “Higher Engineering Mathematics”, 40 Edition, Khanna Publications, Delhi, (2007).

REFERENCES:

1. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing Company, New Delhi, (2007).

2. Glyn James, “Advanced Engineering Mathematics”, 3 Edition, Pearson Education, (2007).

3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7 Edition, Wiley India, (2007).

4. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3 Edition, Narosa Publishing House Pvt. Ltd., (2007).

Semester 2 - TECHNICAL ENGLISH II–Syllabus–Regulation 2008

Anna University

HS2161 TECHNICAL ENGLISH II  - Syllabus

Regulation 2008

AIM:

To encourage students to actively involve in participative learning of English and to help them acquire Communication Skills.

OBJECTIVES:

1. To help students develop listening skills for academic and professional purposes.

2. To help students acquire the ability to speak effectively in English in real-life

situations.

3. To inculcate reading habit and to develop effective reading skills.

4. To help students improve their active and passive vocabulary.

5. To familiarize students with different rhetorical functions of scientific English.

6. To enable students write letters and reports effectively in formal and business situations.

UNIT I 12

Technical Vocabulary - meanings in context, sequencing words, Articles- Prepositions, intensive reading& predicting content, Reading and interpretation, extended definitions, Process description

Suggested activities:

1. Exercises on word formation using the prefix ‘self’ - Gap filling with preposition.

2. Exercises - Using sequence words.

3. Reading comprehension exercise with questions based on inference – Reading headings

4. and predicting the content – Reading advertisements and interpretation.

5. Writing extended definitions – Writing descriptions of processes – Writing paragraphs based on discussions – Writing paragraphs describing the future.

UNIT II 12

Phrases / Structures indicating use / purpose – Adverbs-Skimming – Non-verbal communication - Listening – correlating verbal and non-verbal communication - Speaking in group discussions – Formal Letter writing – Writing analytical paragraphs.

Suggested activities:

1. Reading comprehension exercises with questions on overall content – Discussions analyzing stylistic features (creative and factual description) - Reading comprehension exercises with texts including graphic communication

- Exercises in interpreting non-verbal communication.

2. Listening comprehension exercises to categorise data in tables.

3. Writing formal letters, quotations, clarification, complaint – Letter seeking permission for Industrial visits– Writing analytical paragraphs on different debatable issues.

UNIT III 12

Cause and effect expressions – Different grammatical forms of the same word - Speaking – stress and intonation, Group Discussions - Reading – Critical reading - Listening, - Writing – using connectives, report writing – types, structure, data collection, content, form, recommendations .

Suggested activities:

1. Exercises combining sentences using cause and effect expressions – Gap filling exercises using the appropriate tense forms – Making sentences using different grammatical forms of the same word. ( Eg: object –verb / object – noun )

2. Speaking exercises involving the use of stress and intonation – Group

discussions– analysis of problems and offering solutions.

3. Reading comprehension exercises with critical questions, Multiple choice question.

4. Sequencing of jumbled sentences using connectives – Writing different types of reports like industrial accident report and survey report – Writing recommendations.

UNIT IV 12

Numerical adjectives – Oral instructions – Descriptive writing – Argumentative paragraphs – Letter of application - content, format (CV / Bio-data) - Instructions, imperative forms - Checklists, Yes/No question form – E-mail communication.

Suggested Activities:

1. Rewriting exercises using numerical adjectives.

2. Reading comprehension exercises with analytical questions on content – Evaluation of content.

3. Listening comprehension – entering information in tabular form, intensive listening exercise and completing the steps of a process.

4. Speaking - Role play – group discussions – Activities giving oral instructions.

5. Writing descriptions, expanding hints – Writing argumentative paragraphs – Writing formal letters – Writing letter of application with CV/Bio-data – Writing general and safety instructions – Preparing checklists – Writing e-mail messages.

UNIT V 9

Speaking - Discussion of Problems and solutions - Creative and critical thinking – Writing an essay, Writing a proposal.

Suggested Activities:

1. Case Studies on problems and solutions

2. Brain storming and discussion

3. Writing Critical essays

4. Writing short proposals of 2 pages for starting a project, solving problems, etc.

5. Writing advertisements.

TOTAL : 60 PERIODS TEXT BOOK:

1. Chapters 5 – 8. Department of Humanities & Social Sciences, Anna

University, ‘English for Engineers and Technologists’ Combined Edition (Volumes 1 & 2), Chennai: Orient Longman Pvt. Ltd., 2006. Themes 5 – 8 (Technology, Communication, Environment, Industry)

REFERENCES:

1. P. K. Dutt, G. Rajeevan and C.L.N Prakash, ‘A Course in Communication Skills’, Cambridge University Press, India 2007.

2. Krishna Mohan and Meera Banerjee, ‘Developing Communication Skills’, Macmillan India Ltd., (Reprinted 1994 – 2007).

3. Edgar Thorpe, Showick Thorpe, ‘Objective English’, Second Edition, Pearson Education, 2007.

Extensive Reading:

1. Robin Sharma, ‘The Monk Who Sold His Ferrari’, Jaico Publishing House, 2007

Note:

The book listed under Extensive Reading is meant for inculcating the reading habit of the students. They need not be used for testing purposes.

Electric Circuit and Electron Device–Unit 1 - Version 2 Lectures

Anna University

Electric Circuit and Electron Device

UNIT-I – Version 2

CIRCUIT ANALYSIS TECHNIQUES

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INTRODUCTION

Circuit Definitions

• Node – any point where 2 or more circuit elements are connected together

– Wires usually have negligible resistance

– Each node has one voltage (w.r.t. ground)

• Branch – a circuit element between two nodes

• Loop – a collection of branches that form a closed path returning to the same node without going through any other nodes or branches twice

• Voltage-current characteristic of ideal resistor:

v(t) = R × i(t)

• A Node is a point of connection between two or more circuit elements

• Nodes can be “spread out” by perfect conductors

Ki rcho ff’s Current Law (KCL)

• The algebraic sum of all currents entering (or leaving) a node is zero

• Equivalently: The sum of the currents entering a node equals the sum of the currents leaving a node

• Mathematically:

• When applying KCL, the current directions (entering or leaving a node) are based on the assumed directions of the currents

• Also need to decide whether currents entering the node are positive or negative;

this dictates the sign of the currents leaving the node

• As long all assumptions are consistent, the final result will reflect the actual current directions in the circuit

Kirchoff’s Voltage Law (KVL)

· The algebraic sum of all voltage differences around any closed loop is zero

· Equivalently: The sum of the voltage rises around a closed loop is equal to the sum of the voltage drops around the loop

· Mathematically:

· Voltage polarities are based on assumed polarities

· If assumptions are consistent, the final results will reflect the actual polarities

· The algebraic sum of voltages around each loop is zero

· Beginning with one node, add voltages across each branch in the loop (if you encounter a

+ sign first) and subtract voltages (if you encounter a – sign first)

· Σ voltage drops - Σ voltage rises = 0

· Or Σ voltage drops = Σ voltage rises

NETWORK THEOREMS

• This chapter introduces important fundamental theorems of network analysis. They are the

• Superposition theorem

• Thevenin‟s theorem

• Norton‟s theorem

• Maximum power transfer theorem

Superposition Theorem

_ Used to find the solution to networks with two or more sources that are not in series or parallel.

_ The current through, or voltage across, an element in a network is equal to the algebraic sum of the currents or voltages produced independently by each source.

_ Since the effect of each source will be determined independently, the number of networks to be analyzed will equal the number of sources.

_ The total power delivered to a resistive element must be determined using the total current through or the total voltage across the element and cannot be determined by a simple sum of the power levels established by each source.

Théven in ’s Th eorem

_ Any two-terminal dc network can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

Thevenin’s Theorem can be used to:

_ Analyze networks with sources that are not in series or parallel.

_ Reduce the number of components required to establish the same characteristics at the output terminals.

_ Investigate the effect of changing a particular component on the behavior of a network without having to analyze the entire network after each change.

Procedure to determine the proper values of RTh and ETh

Preliminary

_ Remove that portion of the network across which the Thévenin equation circuit is to be found. In the figure below, this requires that the load resistor RL be temporarily removed from the network.

_ Mark the terminals of the remaining two-terminal network. (The importance of this step will become obvious as we progress through some complex networks.)

RTh:

_ Calculate RTh by first setting all sources to zero (voltage sources are replaced by short circuits, and current sources by open circuits) and then finding the resultant resistance between the two marked terminals. (If the internal resistance of the voltage and/or current sources is included in the original network, it must remain when the sources are set to zero.)

ETh:

_ Calculate ETh by first returning all sources to their original position and finding the open- circuit voltage between the marked terminals. (This step is invariably the one that will lead to the most confusion and errors. In all cases, keep in mind that it is the open-circuit potential between the two terminals marked in step 2.)

_ Draw the Thévenin equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit. This step is indicated by the placement of the resistor RL between the terminals of the Thévenin equivalent circuit.

Norton’s Th eore m

Norton‟s theorem states the following:

_ Any two-terminal linear bilateral dc network can be replaced by an equivalent circuit consisting of a current and a parallel resistor.

The steps leading to the proper values of IN and RN.

Preliminary steps:

_ Remove that portion of the network across which the Norton equivalent circuit is found.

_ Mark the terminals of the remaining two-terminal network.

Finding RN:

_ Calculate RN by first setting all sources to zero (voltage sources are replaced with short circuits, and current sources with open circuits) and then finding the resultant resistance between the two marked terminals. (If the internal resistance of the voltage and/or current sources is included in the original network, it must remain when the sources are set to zero.) Since RN = RTh the procedure and value obtained using the approach described for Thévenin‟s theorem will determine the proper value of RN.

Finding IN :

_ Calculate IN by first returning all the sources to their original position and then finding

the short-circuit current between the marked terminals. It is the same current that would be measured by an ammeter placed between the marked terminals.

Conclusion:

_ Draw the Norton equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit.

Maximum Power Transfer Theorem

_ For loads connected directly to a dc voltage supply, maximum power will be delivered to the load when the load resistance is equal to the internal resistance of the source; that is, when: RL = Rint

The maximum power transfer theorem states the following:

A load will receive maximum power from a network when its total resistive value is exactly equal to the Thévenin resistance of the network applied to the load. That is,

RL = RTh

Series resistors & voltage division

Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.

The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances N

Req = R1 + R2 + × × × + RN =

Parallel resistors & current division

Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

The equivalent resistance of a circuit with N resistors in parallel is:

Delta -> Star transformation

 

Star -> Delta transformation

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Electric Device and Electron Device–Circuit Analysis Techniques (Unit 1) Lectures

Anna University

Electric Circuit and Electron Device

UNIT-I

CIRCUIT ANALYSIS TECHNIQUES

Ohm’s Law

Temperature remaining constant, the potential difference (E) across the ends of a conductor is proportional to the current (I) flowing through it.

Mathematically, V=IR

Kirchhoff's Current Law (KCL)

"The algebraic sum of all currents entering and exiting a node must equal zero"

SI_in = SI_out

Similarly, at any instant the algebraic sum of all the currents at any circuit node is zero.
SI = 0

Kirchhoff's Voltage Law (KVL)

"The algebraic sum of all voltages in a loop must equal zero"

SE = SIZ

Similarly, t any instant the algebraic sum of all the voltages around any closed circuit is zero:
SE - SIZ = 0

Series and Parallel Resistor Combinations

There are two basic ways in which to connect more than two circuit components:

Series and Parallel.

• For analysis, series resistors/impedances can be replaced by an equivalent resistor/ impedance.

• Parallel resistors/impedances can be replaced by an equivalent resistor/ impedance.

Series Resistance

Two elements are in series if the current that flows through one must also flow through the other.

SERIES Req = R1 + R2 + R3

Req is equivalent to the resistor network on the left in the sense that they have the same i-v characteristics.

Parallel Resistance

Two elements are in parallel if they are connected between (share) the same two (distinct) end nodes.

PARALLEL

Inductors

Series and parallel inductances

Where, L = Inductance in henrys

Capacitors

Series and Parallel Capacitances

Where, C = Capacitance in farads

Mesh current method

The Mesh Current Method uses simultaneous equations, Kirchhoff's Voltage Law, and Ohm's Law to determine unknown currents in a network. It differs from the Branch Current method in that it does not use Kirchhoff's Current Law, and it is usually able to solve a circuit with less unknown variables and less simultaneous equations.

Steps to follow for the .Mesh Current method of analysis:

1. Draw mesh currents in loops of circuit, enough to account for all components.
2. Label resistor voltage drop polarities based on assumed directions of mesh currents.
3. Write KVL equations for each loop of the circuit, substituting the product IR for E in each resistor term of the equation. Where two mesh currents intersect through a component, express the current as the algebraic sum of those two mesh currents.
4. Solve for unknown mesh currents (simultaneous equations).
5. If any solution is negative, then the assumed current direction is wrong!
6. Algebraically add mesh currents to find current in components sharing multiple mesh currents.
7. Solve for voltage drops across all resistors (E=IR).

Node voltage method

The node voltage method of analysis solves for unknown voltages at circuit nodes in terms of a system of KCL equations. This analysis looks strange because it involves replacing voltage sources with equivalent current sources.

Node voltage rules:

1. Convert voltage sources in series with a resistor to an equivalent current source with the resistor in parallel.
2. Change resistor values to conductance.
3. Select a reference node(E0)
4. Assign unknown voltages (E1)(E2) ... (EN)to remaining nodes.
5. Write a KCL equation for each node 1,2, ... N. The positive coefficient of the first voltage in the first equation is the sum of conductances connected to the node. Repeat for coefficient of second voltage, second equation, and other equations. These coefficients fall on a diagonal.
6. All other coefficients for all equations are negative, representing conductances between nodes. The first equation, second coefficient is the conductance from node 1 to node 2, the third coefficient is the conductance from node 1 to node 3. Fill in negative coefficients for other equations.
7. The right hand side of the equations is the current source connected to the respective nodes.
8. Solve system of equations for unknown node voltages.

NETWORK THEOREMS:

Thevenin's Theorem:

• Any circuit with sources (dependent and/or independent) and resistors can be replaced by an equivalent circuit containing a single voltage source and a single resistor.

• Thevenin’s theorem implies that we can replace arbitrarily complicated networks with simple networks for purposes of analysis.

Norton's Theorem:

Any circuit with voltage sources, resistances (impedances) and open output terminals can be replaced by a single current source in parallel with single resistance (impedance), where the value of current source is equal to the current passing through the short circuit output terminals and the value of the resistance (impedance) is equal to the resistance seen into the output terminals.

Super Position Theorem:

In a linear, lumped element, bilateral electric circuit that is energized by two or more sources the current in any resistor is equal to the algebraic sum of the separate currents in the resistor when each sources acts separately. While one source is applied, the other sources are replaced by their respective internal resistances.

Super Position Theorem is not valid for power responses. It is applicable only for computing voltage and Current responses.

Maximum Power transfer Theorem:

The maximum Power transferred to a load resistor occurs when it has a value equal to the resistance of the network looking back at it from the load terminals (all sources being replaced by their respective internal resistances).

Duality:

Two electrical networks which are governed by the same type of equations are called duality.

For the networks to be duals it is necessary that the variables & elements of one network should also be the duals of variables & elements of other networks.

Method of drawing duality (or) dual network:

a) Place a dot in each independent loop of the given network. These dots placed inside the loops correspond to the independent node in the dual network.

b) A dot is placed outside the given network. This corresponds to the reference node of the dual network.

c) All the dots are connected by dotted lines crossing all the branches. The dotted lines should cross only one branch at a time.

d) The dual elements will form the branches connecting the corresponding nodes in the dual network.

Star-Delta Transformation:

The Star-Delta transformation techniques are useful in solving complex network.

A star network of three resistances R_A, R_B and R_C connected together at common node N can be transformed into a delta network of three resistances R_AB, R_BC and R_CA by the above equations:

In general terms:
R_delta = (sum of R_star pair products) / (opposite R_star)

Delta-Star Transformation

A delta network of three impedances R_AB, R_BC and R_CA can be transformed into a star network of three impedances R_A, R_B and R_C connected together at common node N by the following equations:

In general terms:
R_star = (adjacent R_delta pair product) / (sum of R_delta)

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Electrical Machines–I All Units Question Bank–2012 Edition (Version 1)

DEPARTMENT OF ELECTRICAL AND ELECTRONICS

ENGINEERING

QUESTION BANK

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SUB.NAME: ELECTRICAL MACHINES -I

BRANCH : ELECTRICAL AND ELECTRONICS ENGINEERING

YEAR : II

 SEMESTER : IV

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UNIT I

INTRODUCTION

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PART – A

1. Mention the types of electrical machines.

2. State Ohm’s law for magnetic circuit.

3. Define leakage flux

4. Define magnetic reluctance

5. State stacking factor.

6. Mention some magnetic materials

7. What is magnetostriction?

8. Define statically induced emf.

9. Define dynamically induced emf.

10. State Fleming’s right hand rule.

11. State Fleming’s Left hand rule.

12. What are the losses called as core loss?

13. Define coercivity.

14. What are factors on which hysteresis loss?

15. What is core loss? What is its significance in electric machines?

16. What is eddy current loss?

17. How hysteresis and eddy current losses are minimized?

PART – B

1. (a) Explain about the magnetization curve of Ferro –magnetic material. (8) (b) Derive the relation between mutual inductance and self inductances of two magnetically coupled coils. (8)

2. (a) Explain AC operation of magnetic circuits. (8) (b) Explain in detail about hysteresis and eddy current losses. (8)

3. (a)Write in detail about magnetically induced emf & force and derive the relevant expression. (8) (b) An electromagnetic relay has an exciting coil of 800 turns. The coil has a cross section of 5 cm x 5cm. Find

1. coil inductance if the air gap length is 0.5 cm.

2. field energy stored for a coil current of 1.25 A.

3. Permeance at air gap. (8)

4. Explain in detail about three basic rotating electric machine types. (16)

5. (a) Compare magnetic and electric circuit. (8) (b) An iron rod 1.8 cm diameter is bent to form a ring of mean diameter 25cm and wound with 250 turn of wire. A gap of 1mm exists in between the end faces. Calculate the current required to produce a flux of 0.6mWb. Take relative permeability of iron as 1200. (8)

6. (a) Explain the two different types of magnetic circuits with neat diagram. (8) (b) When two coils are connected in series, their effective inductance is found to be 10H .When the connections of one coil are reversed , the effective inductance is 6H.If the coefficient of coupling is 0.6, calculate the self inductance of each coil and the mutual inductance. (8)

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UNIT II

TRANSFORMERS

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PART-A

1. Mention the difference between core and shell type transformers?

2. What is the purpose of laminating the core in a transformer?

3. Does transformer draw any current when secondary is open? Why?

4. Define voltage regulation of a transformer?

5. Define all day efficiency of a transformer?

6. Why transformers are rated in KVA?

7. What are the typical uses of auto transformer?

8. What are the applications of step-up & step-down transformer?

9. How transformers are classified according to their construction?

10. Explain on the material used for core construction?

11. How does change in frequency affect the operation of a given transformer?

12. What is the angle by which no load current will lag the ideal applied voltage?

13. List the arrangement of stepped core arrangement in a transformer?

14. What is the function of transformer oil in a transformer?

15. Can the voltage regulation go negative if so under what condition?

16. Distinguish power transformers & distribution transformers?

17. What is the purpose of providing Taps in transformer and where these are provided?

18. What are the typical uses of auto transformer?

19. How does change in frequency affect the operation of a given transformer?

20. Why are breathers used in transformers?

21. What is the function of transformer oil in a transformer?

PART-B

1. (a) Explain the principle and operation of auto transformer. (8) (b)Draw and explain the no load phasor diagram of a single phase transformer. (8)

2. (a) Derive the emf equation of single phase transformer. (8) (b) A 120kVA, 6000/400V, Y/Y, 3-phase, 50Hz transformer has a iron loss of 1800W.

The maximum efficiency occurs at ¾ full loads. Find the efficiency of the transformer at

(i) Full load and 0.8 pf

(ii) The maximum efficiency at unity pf. (8)

3. A100 kVA, 6.6kV/415V, single phase transformer has an effective impedance of (3+8j) _ referred to HV side. Estimate the full load voltage regulation at 0.8 pf lagging and 0.8 leading pf. (16)

4. (a) Explain the working of auto transformer and prove that when transformation ratio approaches unity, the amount copper used approaches smaller value. (8)

(b)The emf per turn of a single phase, 6.6kV/440V, 50 Hz transformer is approximately 12V. Calculate the number of turns in the HV and LV windings and the net cross sectional area of the core for a maximum flux density of 1.5T. (8)

5. (a) Obtain the equivalent circuit of a 200/400V,50Hz,single phase transformer from the following test data: OC test: 200V,0.7A,70W on LV side SC test: 15V, 10A, 85W on HV side. (10) (b)With the help of circuit diagrams, explain any two types of three phase transformer connections. (6)

7. Draw the circuit diagrams for conducting OC and SC tests on a single phase transformer. Also explain how the efficiency and voltage regulation can be estimated by these tests. (16)

8. What is the sumpner’s test? Draw the circuit diagram to conduct this test and explain its

principle. (16)

9. (a) Derive the condition for maximum efficiency in a transformer. (8)

(b) A11000/230 V, 150 KVA, 1-phase, 50 Hz transformer has core loss of 1.4kW and F.L cu loss of 1.6 Kw .Determine (i) The kVA load for maximum efficiency and the value of maximum efficiency at unity p.f. (ii) The efficiency at half F.L 0.8 pf leading. (8)

10. Explain in detail about parallel operation of single phase transformers. (16)

11. Data of a 500KVA, 3300/400 V, 50 Hz, single phase transformer is given below.

S.C test: 1250 W, 100 V –secondary short circuited with full load current in it O.C test: 1000 W –with normal primary voltage.

Calculate the full load regulation and efficiency at a power factor of 0.8(lag). (16)

12. (a) Derive the equivalent circuit of a single phase two winding transformer. (8) (b) The maximum efficiency of a single phase 250kVA, 2000/250 V transformer occurs at 80% of

full load and is equal to 97.5% at 0.8 pf .determine the efficiency and regulation on full load at 0.8pf lagging if the impedance of the transformer is 9 percent. (8)

13. Explain in detail about tap changing of transformers. (16)

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UNIT III

ELECTROMECHANICAL ENERGY CONVERSION

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PART-A

1. What is an electromechanical system?

.2. Describe multiply excited magnetic field system.

3. Define co energy.

4. How energy is stored?

5. Define field energy.

6. Write the expression for the principle of energy conversion.

7. What is the significance of co energy?

8. How the energy stored in magnetic field?

9. Give any four examples if single excited magnetic system.

10. Write the applications of singly excited and doubly excited magnetic system .

11. State the necessary conditions for the production of steady torque the interaction of stator and rotor fields in an electric machine.

PART-B

1. Derive the expression for field energy produced in a doubly excited magnetic field system? (16)

2. The magnetic flux density on the surface of an iron face is 1.6 T which is a typical saturation level

value for ferromagnetic material. Find the force density on the iron face. (16)

3. What are the special applications where the electric field is used as a coupling medium for electromechanical energy conversion? Also explain why electric field coupling is preferred in such applications? (16)

4. Find an expression for the force per unit area between the plates of a parallel plate condenser in terms of the electric field intensity. Use both the energy and co energy methods. Find the value of the force per unit area when E = 3 x 106 V/m, the breakdown strength of air. (16)

5. Explain with neat diagram and sufficient expressions, the multiply excited magnetic field systems. (16)

6. Explain i - characteristics of a magnetic system. Also derive the expression for co energy density. Assume i - relationship of the magnetic circuit is linear. (16)

7. Explain the concept of singly – excited machines and derive the expression for the electromagnetic torque. (16)

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UNIT IV

BASIC CONCEPTS IN ROTATING MACHINES

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PART-A

1. Define the term pole pitch

2. Define pitch factor

3. Define the term breadth factor

4. Write down the advantages of short pitched coil.

5. What is distributed winding?

6. Explain the following terms with respect to rotating electrical machines.

7. Write the expressions for the synchronous speed.

8. Write the mmf equation of dc machine.

9. What is meant by electromagnetic torque?

10. State the torque equation for round rotor machine.

11. Define rotating magnetic field.

PART-B

1. Derive the expression for the r.m.s value of emf induced in a.c. machines. (16)

2. Prove that mmf wave of a single phase ac winding is pulsating or standing. (16)

3. Prove that the resultant mmf wave of three phase ac winding is rotating in space with

speed but its magnitude is constant. (16)

4. Derive the torque equation for round rotor machine. (16)

5. Explain the various concepts of magnetic fields in rotating machines. (16)

6. Explain with neat diagram the concept of mmf space wave of a single coil. (16)

7. Write in detail about mmf space wave of three phase distributed winding. (16)

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UNIT V

DC MACHINES

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PART – A

1. What is prime mover?

2. Give the materials used in machine manufacturing

3. How will you change the direction of rotation of a d.c motor?

4. What is back emf in d.c motors?

5. Under what condition the mechanical power developed in a dc motor will be maximum?.

6. What is the function of a no-voltage release coil provided in a dc motor starter?

7. Name the two types of automatic starters used for dc motors.

8. Enumerate the factors on which the speed of a dc motor depends.

9. List the different methods of speed control employed for dc series motor

10. Name the different methods of electrical breaking of dc motors.

11. Under what circumstances does a dc shunt generator fail to build up?

12. To what polarity the interpoles excited in dc motors?

13. What is back emf in d.c motors?

14. Name any four applications of DC series motor.

15. Why DC motors are not operated to develop maximum power in practice?

16. Name the starters used for series motors.

17. Name Different types of starters.

18. Name the Protective devices in a starter.

20. What are the modification in ward Leonard linger system?

21. What type of DC motors are suitable for various torque operations?

22. Define speed regulation.

23. What are the performance curves?

24. To what polarity are the interpoles excited in dc generators?

25. Why are carbon brushes preferred for dc machines?

26. What are the various types of commutation?

27. Name the two methods of improving commutation.

28. What is reactance emf in dc machine?

29. Define the term commutation in dc machines.

30. How and why the compensating winding in dc machine excited?

PART-B

1. (a) Describe with sketches the construction of a DC machine. (8) (b) Derive the EMF equation of DC generator. (8)

2. Draw and explain the no-load and load characteristics of DC shunt, series and compound generators. (16)

3. Explain the effect of armature reaction in a DC shunt generator. How is its demagnetizing and cross-magnetizing ampere turns calculated? (16)

4. Explain the process of commutation in a DC machine. (16)

5. With a aid of a circuit diagram, describe the procedure for paralleling two DC shunt generators and for transferring the load from one machine to the other. (16)

6. A 4-pole, 50 kW, 250 V, wave wound shunt generator has 400 armature conductors. Brushes are given a lead of 4 commutator segments. Calculate the demagnetization ampere-turns per pole if shunt field resistance is 50 ohm. Also calculate extra shunt field turns per pole to neutralize the demagnetization. (16)

7. A 4-pole, lap connected DC machine has 540 armature conductors. If the flux per pole is .03 Wb and runs at 1500 RPM, determine the emf generated. If this machine is driven as a shunt generator with same field flux and speed, calculate the line current if the terminal voltage is 400V.Given the RSH=450ohm and RA=2phm. (16)

8. Two separately excited DC generators are connected in parallel and supply a load of 200A. The machines have armature circuit resistances of 0.05 ohm and 0.1 ohm and induced emfs of 425V and 440V respectively. Determine the terminal voltage, current and power output of each machine. The effect of armature reaction is to be neglected. (16)

9. (a) Explain the principle of operation of a DC motor. (8) (b) A shunt machine, connected to 200V mains has an armature resistance of 0.15 _ and field resistance is 100 _. Find the ratio of its speed as a generator to its speed as a motor, line current in each case being 75 A. (8)

10. (a) Draw and explain the mechanical characteristics of DC series and shunt motor. (8)

(b) A 230V, DC shunt motor, takes an armature current at 3.33A at rated voltage and at a no load speed of 1000RPM. The resistances of the armature circuit and field circuit are 0.3 _ and 160 _ respectively. The line current at full load and rated voltage is 40A. Calculate, at full load, the speed and the developed torque in case the armature reaction weakens the no load flux by 4%. (8)

11. (a) Describe the working of 3 point starter for DC shunt motor with neat diagram. (8)

(b)Explain Ward-Leonard method of speed control in DC motors. (8)

12. (a) Derive an expression for the torque developed in a DC machine. (8)

(b) A 220V, Dc shunt motor with an armature resistance of 0.4 ohm and a field resistance of 110ohm drives a load, the torque of which remains constant. The motor draws from the supply, a line current of 32A when the speed is 450 RPM. If the speed is to be raised to 700RPM, what change must be effected in the value of the shunt field circuit resistance? Assume that the magnetization characteristic of the motor is a straight line. (8)

13. Explain the different methods used for the speed control of D.C. shunt motor. (16)

14. With the help of neat circuit diagram, explain swinburne’s test and derive the relations for efficiency (both for generator and motor) also state the merits and demerits of this method. (16)

15. (a)Explain in detail about circuit model of D.C. machine. (8)

(b) A 440 V D.C shunt motor takes 4A at no load . its armature and field resistances are 0.4 ohms

and 220 ohms respectively .estimate the kW output and efficiency when the motor takes 60A on full load. (8)

16. (a) Derive an expression for the torque developed in the armature of a D.C. motor. (8) (b) Determine developed torque and shaft torque of 220V, 4 pole series motor with 800 conductors wave-connected supplying a load of 8.2 kW by taking 45A from the mains. The flux per pole is 25m/Wb and its armature circuit resistance is 0.6 ohm. (8)

17. With the help of neat circuit diagram, explain Hopkinson’s test and derive the relations for efficiency (both for generator and motor) also state the merits and demerits of this method. (16)

18. (a) Explain in detail about different methods of excitation. (8) (b)Derive the expression for efficiency of D.C. machines. (8)

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Electrical Machines–I - Question Bank–2011 Edition

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Anna University

ELECTRICAL MACHINES –I

QUESTUION BANK – 2011 Edition

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UNIT I

INTRODUCTION

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PART –A

1. What are the three basic rotating Electric machines?
2. Name the three materials used in machine manufacture.
3. What is magneto motive force?
4. Define Leakage flux and leakage inductance.
5. Explain Flux Fringing at air – gap .
6. Write short note on stacking factor and give its value .
7. Give the classification of material based on relative permeability μ_{r .}
8. Define relative permeability μ_{r .}
9. What is B-H curve and sketch it ?

10. Define Faraday’s law of induction.

11. What is Lenz’s law?

12. Define statically induced emf and dynamically induced emf .

13. Write the Lorentz force equation.

14. Give few magnetic properties.

15. What is magnetic permeability ?

PART - B

1. Compare the various magnetic materials ?
2. Derive the expression of the flux , relucatance of the magnetic material with air gap .
3. Derive the inductance ,energy and power of a magnetic circuit with two windings.
4. Differentiate between Electric nad magnetic circuits.
5. Explain with a neat diagram the B-H curve .

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UNIT II

TRANSFORMERS

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1. What is a Transformer?
2. Enumerate the various kinds of transformers.
3. Why is the transformer windings are divided into several coils ?
4. Draw the phasor diagram of an ideal transformer.
5. Give the two general types of transformer.
6. What is an air – core transformer?
7. Draw the equivalent circuit of single phase transformer.
8. Name the two tests that are used to determine parameters of equivalent circuit, voltage regulation and efficiency.
9. State the different losses in transformer.
10. Define hysteresis and eddy current losses.
11. What is Steinmetz’s constant and give its range.
12. Define efficiency and All day efficiency.
13. Enumerate the various testing of transformers.
14. What is Auto – transformer?
15. Distinguish between transformer and Auto – transformer.
16. What is tap- changer ?
17. Classify the various types of tap- changer.
18. What are the different three phase connections?
19. What is the EMF equation of a transformer?
20. Define voltage regulation.
21. What is transformation ratio?
22. At what frequency core loss and iron loss are equal?
23. What is polarity test in transformers?
24. What is equivalent resistance of transformer ? How it is calculated in primary terms ?
25. Define all- day efficiency .
26. What is equivalent reactance of transformer ? How it is calculated in primary terms ?
27. What are the two components of core loss ?
28. Draw the phasor diagram of inductive and capacitive load.
29. At what condition core loss and iron loss equal ?
30. Define voltage transformation ratio.

PART- B

1. Explain the operation of transformer in no load and loaded

condition with phasor diagram.

1. Draw the equivalent circuit of a transformer and derive the

components with respect to primary side .

1. Derive the EMF equation of a transformer .
2. Explain with a neat diagram the O.C and S.C test of transformer.
3. What is auto- transformer ? State the application of auto- transformer .
4. Explain the parallel operation of transformer.
5. What is tap – changer and explain its various types.
6. Explain the various testing of transformers.
7. What are the various losses of the transformers and give its efficiency .

10.What is voltage regulation.

11. Draw the various three phase connections.

12. What is sumpner’s test ? Draw the circuit diagram to

conduct the test .

13. Explain Scott connection and explain in detail .

14. Explain Hysteresis and eddy current loss.

15. What is polarity test of transformer ?

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Unit III - ELECTROMECHANICAL ENERGY CONVERSION

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Part A

1. Write the applications of singly excited and multiple excited magnetic systems.

2. Define field energy and co energy.

3. Why all the practical energy conversion devices do makes use of magnetic field as coupling medium rather than electric field?

4. Draw the i-λ characteristic of a non linear magnetic circuit when the armature is moved from x₁ to x₂.

5. Draw an energy flow diagram of an electromechanical energy conversion device when it acts as a motor.

6. Draw an energy flow diagram of an electromechanical energy conversion device when it acts as a generator.

7. Define excitation.

What is electromechanical energy conversion?

8. List three types of electromechanical energy conversion devices.

9. What is energy balance equation? Write it for the generating as well as motoring device.

10. Draw a single excited magnetic system.

11. Draw a double excited magnetic system.

12. State the assumptions made for analyzing singly excited system.

13. What is co energy? What is its use?

14. Write the expression for mechanical force for singly excited system.

15. State examples of singly excited system.

16. State examples of multiply excited system.

17. Write the expression for energy in terms of λ₁, λ₂, θ for doubly excited system.

18. State the advantages of electromechanical energy conversion principles.

Part B

1. Derive the expression for field energy and co energy in a doubly excited system assuming constant current system.

2. Derive the expression for field energy and co energy in a doubly excited system assuming constant voltage system.

3. Two coupled coils have self and mutual inductance of

L₁₁ = 2+ (1/2x), L₂₂ = 1+ (1/2x), L₂₁ = 1/2x

over a certain range of linear displacement x. The first coil is excited by a constant current of 20A and the second by a constant current of -10A.

Find a) Mechanical work done if x changes from 0.5 to 1m.

b) Energy supplied by each electrical source in part (a).

c) Change in field energy in part (a).

Hence verify that the energy supplied by the sources is equal to the increase in the field energy plus the mechanical work done.

4. Derive the expression for torque in a singly excited system.

5. Write a note on energy balance equation.

6. For a singly excited system derive the expression for magnetic field energy stored.

7. For a singly excited system derive the expression for electrical energy input.

8. Explain the concept of co energy with i-λ curve.

9. Consider an attracted armature relay is excited by an electric source. Explain about the mechanical force developed and the mechanical energy output with necessary equations, for linear and non linear cases.

10. Write in brief about multiple-excited magnetic field system.

11. Explain the i-λ characteristic of a magnetic system. Also derive expression for co energy density assumed the i-λ relationship of the magnetic circuit is linear.

12. Give a brief note on flow of energy in electromechanical devices.

13. The magnetic flux density on the surface of an iron face is 1.8T which is typical saturation level value for ferromagnetic material. Find the force density on the iron face.

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Unit IV - BASIC CONCEPTS IN ROTATING MACHINES

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Part A

1. Explain the following terms with respect to rotating electrical machines

a) Pole pitch.

b) Chording angle.

2. Write the relation between electrical and mechanical degree.

3. Define the term synchronous speed, breadth factor.

4. What are the advantages when the stator coils are short pitched?

5. State the essential parts of any rotating machine.

6. State the expression for the generated voltage in a dc machine.

7. What is full pitch and short pitch winding?

8. What is concentrated and distributed winding?

9. State the expression for coil span factor. What is its effect?

10. State the expression for distribution factor. What is its effect?

11. State the assumptions made while obtaining mmf space wave of a single coil.

12. Draw the mmf space wave of a single coil.

13. Draw the mmf space wave of one phase of distributed winding.

14. What is rotating magnetic field.

15. State the assumptions made in deriving the torque equation for round rotor machine.

16. State the torque equation for round rotor machine.

Part B

1. Derive the expression for generated voltage in DC machine.

2. Derive the expression for generated voltage in AC machine.

3. Explain the various types of three phase AC windings.

4. Draw and explain the mmf space wave of a single coil.

5. Draw and explain the mmf space wave of one phase of distributed winding.

6. Derive the expression for peak value of the fundamental mmf space wave of single phase distributed winding.

7. Explain the concept of rotating magnetic field.

8. Explain about rotating mmf waves in AC machines.

9. A 4 pole machine as 60 slots and 8 conductors per slot. The total flux per pole is 20 m Wb. For a relative speed of 1500 rpm between field flux and armature winding calculate the generated armature voltage if the machine is a) a DC machine with lap-connected winding.

b) A 3 phase star-connected machine with winding factor equal to 0.96. All the turns in each phase are in series.

10. Derive the torque equation of a round rotor machine. Also clearly state what are the assumptions made?

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Unit V - DC MACHINES

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Part A

1. State Fleming right hand rule.

2. List the main parts of DC machine.

3. State the functions of yoke in a DC machine.

4. State the functions of poles in a DC machine.

5. Compare lap and wave winding.

6. State the number of parallel paths in a lap and wave connected armature winding.

7. State the various types of DC generators.

8. What are the causes of failure to excite self excited generator?

9. What is a magnetization characteristic?

10. Sketch the load characteristics of dc shunt generator, dc series generator and dc compound generator.

11. State the applications of various types of dc generators.

12. Define commutation.

13. Name the methods of improving commutation.

14. State the expression for reactance voltage.

15. Define armature reaction.

16. Name the various methods of decreasing the effects of armature reaction.

17. What are the effects of armature reaction?

18. Define critical field resistance in dc shunt generator.

19. What is back emf in dc motor? State its expression.

20. State the voltage and power equations of a dc motor.

21. State the various types of dc motors.

22. Draw the mechanical characteristics of all types of dc motor.

23. What is the necessity of starter for a dc motor?

24. State the function of overload release in dc motor starters.

25. Why dc series motor is never started on no load?

26. How to change the direction of rotation of dc motor?

27. List the various methods of controlling speed of dc shunt motor.

28. List the various methods of controlling speed of dc series motor.

29. State the various losses in dc machine.

30. Draw the power flow diagram for a dc generator and dc motor.

31. Write the condition for maximum efficiency.

32. Name the various methods of testing dc machine.

33. State the advantages and disadvantages of Swinburne’s test.

34. State the advantages and disadvantages of Hopkinson’s test.

35. State the advantages and disadvantages of Brake test.

36. What is the necessity for the parallel operation of dc machine?

Part B

1. Explain with a neat sketch, the construction of a dc machine.

2. Derive from first principles an expression for emf in dc generator.

3. In a particular dc machine, if P = 8, Z = 400, N = 300 rpm and Φ = 100 m Wb, calculate generated emf if winding is connected in lap and wave fashion.

4. Draw the circuit diagrams of dc separately and self excited generator indicating all the currents and voltages.

5. Explain the working of a single turn alternator. How it can be used as a dc generator?

6. With neat diagrams explain the phenomenon of armature reaction in a dc machine. Discuss its effects.

7. Develop an expression for the demagnetizing and cross magnetizing armature ampere-turns in a dc generator.

8. Explain how the effect of armature reaction can be neutralized by using inter poles and compensating winding.

9. Explain clearly the process of commutation in a dc machine. What causes sparking at the commutator surface?

10. Explain the various methods of commutation.

11. Draw the performance characteristics of different types of dc generators and explain them.

12. A 4 pole lap wound dc shunt generator has a useful flux per pole of 0.6 Wb. The armature winding consists of 200 turns, each turn having a resistance of 0.003Ω. Calculate the terminal voltage when running at 1000 rpm if armature current is 45A.

13. Sketch and explain the mechanical and electrical characteristics of all types of dc motors.

14. Explain the operation of three point starter with a neat sketch.

15. Explain the methods of speed control of dc series motor.

16. Explain the methods of speed control of dc shunt motor.

17. Explain Ward-Leonard system of speed control of a dc machine.

18. Explain Swinburne’s test for finding efficiency of a dc machine.

19. Describe Hopkinson’s test in detail with its advantages and disadvantages.

20. Explain how two dc shunt genitors can be connected in parallel.

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