Control theory

Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.
Overview
Control theory is
a theory that deals with influencing the behavior of dynamical systems
an interdisciplinary subfield of science, which originated in engineering and mathematics, and evolved into use by the social sciences, like psychology, sociology and criminology.
An example
Consider an automobile's cruise control, which is a device designed to maintain a constant vehicle speed; the desired or reference speed, provided by the driver. The system in this case is the vehicle. The system output is the vehicle speed, and the control variable is the engine's throttle position which influences engine torque output.
A primitive way to implement cruise control is simply to lock the throttle position when the driver engages cruise control. However, on mountain terrain, the vehicle will slow down going uphill and accelerate going downhill. In fact, any parameter different than what was assumed at design time will translate into a proportional error in the output velocity, including exact mass of the vehicle, wind resistance, and tire pressure. This type of controller is called an open-loop controller because there is no direct connection between the output of the system (the vehicle's speed) and the actual conditions encountered; that is to say, the system does not and can not compensate for unexpected forces.
In a closed-loop control system, a sensor monitors the output (the vehicle's speed) and feeds the data to a computer which continuously adjusts the control input (the throttle) as necessary to keep the control error to a minimum (that is, to maintain the desired speed). Feedback on how the system is actually performing allows the controller (vehicle's on board computer) to dynamically compensate for disturbances to the system, such as changes in slope of the ground or wind speed. An ideal feedback control system cancels out all errors, effectively mitigating the effects of any forces that may or may not arise during operation and producing a response in the system that perfectly matches the user's wishes.

high voltage engineering

The term high voltage characterizes electrical circuits, in which the voltage used is the cause of particular safety concerns and insulation requirements. High voltage is used in electrical power distribution, in cathode ray tubes, to generate X-rays and particle beams, to demonstrate arcing, for ignition, in photomultiplier tubes, and high power amplifier vacuum tubes and other industrial and scientific applications.


The numerical definition of high voltage depends on the context of the discussion. Two factors considered in the classification of a "high voltage" are the possibility of causing a spark in air, and the danger of electric shock by contact or proximity. The definitions may refer either to the voltage between two conductors of a system, or between any conductor and ground.
In electric power transmission engineering, high voltage is usually considered any voltage over approximately 35,000 volts. This is a classification based on the design of apparatus and insulation.
The International Electrotechnical Commission and its national counterparts (IET, IEEE, VDE, etc.) define high voltage circuits as those with more than 1000 V for alternating current and at least 1500 V for direct current, and distinguish it from low voltage (50–1000 V AC or 120–1500 V DC) and extra low voltage (<50 V AC or <120 V DC) circuits. This is in the context of building wiring and the safety of electrical apparatus. In the United States 2005 National Electrical Code (NEC), high voltage is any voltage over 600 V (article 490.2). British Standard BS 7671:2008 defines high voltage as any voltage difference between conductors that is higher than 1000 V AC or 1500 V ripple-free DC, or any voltage difference between a conductor and Earth that is higher than 600 V AC or 900 V ripple-free DC. Electricians may only be licensed for particular voltage classes, in some jurisdictions.[1] For example an electrical license for a specialized sub-trade such as installation of HVAC systems, fire alarm systems, closed circuit television systems may only be authorized to install systems energized up to 30 volts between conductors, and may not be permitted to work on mains-voltage circuits. The general public may consider household mains circuits (100–250 V AC), which carry the highest voltages they normally encounter, to be high voltage. Voltages over approximately 50 volts can usually cause dangerous amounts of current to flow through a human being touching two points of a circuit, so safety standards generally are more restrictive where the chance of contact with such high voltage circuits exists. In digital electronics, a high voltage is the one that represents a logic 1; this may be only several hundred millivolts for some logic families. The definition of extra high voltage (EHV) depends on the context of the discussion. In electric power transmission engineering this refers to equipment designed for more than 345,000 volts between conductors. In electronics systems, a power supply that provides greater than 275,000 volts is known as an "EHV Power Supply". It is often used in experiments in physics. The accelerating voltage for a television cathode ray tube may be described as "extra high voltage" or "extra-high tension" (EHT), as compared to other voltage supplies within the equipment. This type of supply ranges from >5 kV to about 50 kV.



International safety symbol "Caution, risk of electric shock" (ISO 3864), colloquially known as high voltage symbol
Voltages of greater than 50 V applied across dry unbroken human skin are capable of producing heart fibrillation if they produce electric currents in body tissues which happen to pass through the chest area.[citation needed] The electrocution danger is mostly determined by the low conductivity of dry human skin. If skin is wet, or if there are wounds, or if the voltage is applied to electrodes which penetrate the skin, then even voltage sources below 40 V can be lethal if contacted.
Accidental contact with high voltage supplying sufficient energy will usually result in severe injury or death. This can occur as a person's body provides a path for current flow causing tissue damage and heart failure. Other injuries can include burns from the arc generated by the accidental contact. These can be especially dangerous if the victim's airways are affected. Injuries may also be suffered as a result of the physical forces exerted as people may fall from height or be thrown a considerable distance.
Low-energy exposure to high voltage may be harmless, such as the spark produced in a dry climate when touching a doorknob after walking across a carpeted floor.
Sparks in air



Long exposure photograph of a Tesla coil showing the repeated electric discharges
The dielectric breakdown strength of dry air, at Standard Temperature and Pressure (STP), between spherical electrodes is approximately 33 kV/cm.[2] This is only as a rough guide since the actual breakdown voltage is highly dependent upon the electrode shape and size. Strong electric fields (from high voltages applied to small or pointed conductors), often produce violet-colored corona discharges in air, as well as visible sparks. Voltages below about 500–700 volts cannot produce easily visible sparks or glows in air at atmospheric pressure, so by this rule these voltages are "low". However, under conditions of low atmospheric pressure (such as in high-altitude aircraft), or in an environment of noble gas such as argon, neon, etc., sparks will appear at much lower voltages. 500 to 700 volts is not a fixed minimum for producing spark breakdown, but it is a rule of thumb. For air at STP, the minimum sparkover voltage is around 380 volts.
While lower voltages will not generally jump a gap that is present before the voltage is applied, interrupting an existing current flow often produces a low voltage spark or arc. As the contacts are separated, a few small points of contact become the last to separate. The current becomes constricted to these small hot spots, causing them to become incandescent, so that they emit electrons (through thermionic emission). Even a small 9 V battery can spark noticeably by this mechanism in a darkened room. The ionized air and metal vapour (from the contacts) form plasma, which temporarily bridges the widening gap. If the power supply and load allow sufficient current to flow, a self-sustaining arc may form. Once formed, an arc may be extended to a significant length before breaking the circuit. Attempting to open an inductive circuit often forms an arc since the inductance provides a high voltage pulse whenever the current is interrupted. AC systems make sustained arcing somewhat less likely since the current returns to zero twice per cycle. The arc is extinguished every time the current goes through a zero crossing, and must reignite during the next half cycle in order to maintain the arc.
Unlike an ohmic conductor, the voltage at the ends of an arc decreases as the current increases. This makes unintentional arcs in electrical apparatus dangerous since once even a small arc is initiated, if sufficient current is available, the arc will grow. Such arcs can cause great damage to equipment and present a severe fire hazard. Intentionally produced arcs, such as used in lighting or welding, require some element in the circuit to stabilize the arc's current/voltage characteristics.
Electrostatic devices and phenomena

A high voltage is not necessarily dangerous if it cannot deliver substantial current. The common static electric sparks seen under low-humidity conditions always involve voltage buildups well above 700 V. For example, sparks to car doors in winter can involve voltages as high as 20,000 V[3]. Also, physics demonstration devices such as Van de Graaff generators and Wimshurst machines can produce voltages approaching one million volts, yet at worst they deliver a brief sting. These devices have a limited amount of stored energy, so the current produced is low and usually for a short time.[4] During the discharge, these machines apply high voltage to the body for only a millionth of a second or less. The discharge may involve extremely high power over very short periods, but in order to produce heart fibrillation, an electric power supply must produce a significant current in the heart muscle continuing for many milliseconds, and must deposit a total energy in the range of at least millijoules or higher. Alternatively, it must deliver enough energy to damage tissue through heating. Since the duration of the discharge is brief, it generates far less heat (spread over time) than a mobile phone.
Note that Tesla coils are a special case, and touching them is not recommended. Among other issues, they have a tendency to arc to their own bottom-end circuitry, which can introduce powerline frequency (50 Hz or 60 Hz, and capable in any case of depolarizing cells and stopping the heart) currents at lethally high voltages to the body.
Power lines



High tension power lines
Electrical transmission and distribution lines for electric power always use voltages significantly higher than 50 volts, so contact with or close approach to the line conductors presents a danger of electrocution. Contact with overhead wires is a frequent cause of injury or death. Metal ladders, farm equipment, boat masts, construction machinery, aerial antennas, and similar objects are frequently involved in fatal contact with overhead wires. Digging into a buried cable can also be dangerous to workers at an excavation site. Digging equipment (either hand tools or machine driven) that contacts a buried cable may energize piping or the ground in the area, resulting in electrocution of nearby workers. A fault in a high-voltage transmission line or substation may result in high currents flowing along the surface of the earth, producing an earth potential rise that also presents a danger of electric shock.
Unauthorized persons climbing on power pylons or electrical apparatus are also frequently the victims of electrocution.[5] At very high transmission voltages even a close approach can be hazardous since the high voltage may spark across a significant air gap.
For high voltage and extra-high voltage transmission lines, specially trained personnel use so-called "live line" techniques to allow hands-on contact with energized equipment. In this case the worker is electrically connected to the high voltage line but thoroughly insulated from the earth so that he is at the same electrical potential as the line. Since training for such operations is lengthy, and still presents a danger to personnel, only very important transmission lines are subject to maintenance while live. Outside these properly engineered situations, it should not be assumed that being insulated from earth guarantees that no current will flow to earth as grounding, or arcing to ground, can occur in unexpected ways, and high-frequency currents can cause burns even to an ungrounded person (touching a transmitting antenna is dangerous for this reason, and a high-frequency Tesla Coil can sustain a spark with only one endpoint).
Protective equipment on high-voltage transmission lines normally prevents formation of an unwanted arc, or ensures that it is quenched within tens of milliseconds. Electrical apparatus which interrupts high-voltage circuits is designed to safely direct the resulting arc so that it dissipates without damage. High voltage circuit breakers often use a blast of high pressure air, a special dielectric gas (such as SF6 under pressure), or immersion in mineral oil to quench the arc when the high voltage circuit is broken.
Arc flash hazard


Depending on the prospective short circuit current available at a switchgear line-up, a hazard is presented to maintenance and operating personnel due to the possibility of a high-intensity electric arc. Maximum temperature of an arc can exceed 10,000 kelvin, and the radiant heat, expanding hot air, and explosive vaporization of metal and insulation material can cause severe injury to unprotected workers. Such switchgear line-ups and high-energy arc sources are commonly present in electric power utility substations and generating stations, industrial plants and large commercial buildings. In the United States the National Fire Protection Association, has published a guideline standard NFPA 70E for evaluating and calculating arc flash hazard, and provides standards for the protective clothing required for electrical workers exposed to such hazards in the workplace.
[edit]Explosion hazard

Electrical equipment in hazardous areas
Even voltages insufficient to break down air can be associated with enough energy to ignite atmospheres containing flammable gases or vapours, or suspended dust. For example hydrogen gas, natural gas, or gasoline vapor mixed with air can be ignited by sparks produced by electrical apparatus. Examples of industrial facilities with hazardous areas are petrochemical refineries, chemical plants, grain elevators, and coal mines.
Measures taken to prevent such explosions include:
Intrinsic safety by the use of apparatus designed not to accumulate enough stored electrical energy to trigger an explosion
Increased safety, which applies to devices using measures such as oil-filled enclosures to prevent sparks
Explosion-proof (flame-proof) enclosures, which are designed so that an explosion within the enclosure cannot escape and ignite a surrounding explosive atmosphere (this designation does not imply that the apparatus will survive an internal or external explosion).
In recent years standards for explosion hazard protection have become more uniform between European and North American practice. The "zone" system of classification is now used in modified form in U.S. National Electrical Code and in the Canadian Electrical Code. Intrinsic safety apparatus is now approved for use in North American applications, though the explosion-proof (flame-proof) enclosures used in North America are still uncommon in Europe.


Electrical discharges, including partial discharge and corona, can produce small quantities of toxic gases, which in a confined space can be a serious health hazard. These gases include ozone and various oxides of nitrogen.
Lightning

The largest-scale sparks are those produced naturally by lightning. An average bolt of negative lightning carries a current of 30 to 50 kiloamperes, transfers a charge of 5 coulombs, and dissipates 500 megajoules of energy (enough to light a 100 watt light bulb for 2 months). However, an average bolt of positive lightning (from the top of a thunderstorm) may carry a current of 300 to 500 kiloamperes, transfer a charge of up to 300 coulombs, have a potential difference up to 1 gigavolt (a billion volts), and may dissipate enough energy to light a 100 watt light bulb for up to 95 years. A negative lightning stroke typically lasts for only tens of microseconds, but multiple strikes are common. A positive lightning stroke is typically a single event. However, the larger peak current may flow for hundreds of milliseconds, making it considerably hotter and more dangerous than negative lightning.
Hazards due to lightning obviously include a direct strike on persons or property. However, lightning can also create dangerous voltage gradients in the earth and can charge extended metal objects such as telephone cables, fences, and pipelines to dangerous voltages that can be carried many miles from the site of the strike. Although many of these objects are not normally conductive, very high voltage can cause the electrical breakdown of such insulators, causing them to act as conductors. These transferred potentials are dangerous to people, livestock, and electronic apparatus. Lightning strikes also start fires and explosions, which result in fatalities, injuries, and property damage. For example, each year in North America, thousands of forest fires are started by lightning strikes.
Measures to control lightning can mitigate the hazard; these include lightning rods, shielding wires, and bonding of electrical and structural parts of buildings to form a continuous enclosure.
High-voltage lightning discharges in the atmosphere of Jupiter are thought to be the source of the planet's powerful radio frequency emissions.

active filter

An example of high-pass active filter of the Sallen Key topology. The operational amplifier, U1, is used as a buffer amplifier.
An active filter is a type of analog electronic filter, distinguished by the use of one or more active components i.e. voltage amplifiers or buffer amplifiers. Typically this will be a vacuum tube, or solid-state (transistor or operational amplifier).
Active filters have three main advantages over passive filters:
Inductors can be avoided. Passive filters without inductors cannot obtain a high Q (low damping), but with them are often large and expensive (at low frequencies), may have significant internal resistance, and may pick up surrounding electromagnetic signals.
The shape of the response, the Q (Quality factor), and the tuned frequency can often be set easily by varying resistors, in some filters one parameter can be adjusted without affecting the others. Variable inductances for low frequency filters are not practical.
The amplifier powering the filter can be used to buffer the filter from the electronic components it drives or is fed from, variations in which could otherwise significantly affect the shape of the frequency response.
Active filter circuit configurations (electronic filter topology) include:
Sallen and Key, and VCVS filters (low dependency on accuracy of the components)
State variable and biquadratic filters
Twin T filter (fully passive)
DABP Dual Amplifier Bandpass
Wien notch
Multiple Feedback Filter
Fliege (lowest component count for 2 opamp but with good controllability over frequency and type)
Akerberg Mossberg (one of the topologies that offer complete and independent control over gain, frequency, and type)
All the varieties of passive filters can also be found in active filters. Some of them are:
High-pass filters – attenuation of frequencies below their cut-off points.
Low-pass filters – attenuation of frequencies above their cut-off points.
Band-pass filters – attenuation of frequencies both above and below those they allow to pass.
Notch filters – attenuation of certain frequencies while allowing all others to pass.
Combinations are possible, such as notch and high-pass (for example, in a rumble filter where most of the offending rumble comes from a particular frequency), e.g.Elliptic filters.

Voltage spike

In electrical engineering, spikes are fast, short duration electrical transients in voltage (voltage spikes), current (current spike), or transferred energy (energy spikes) in an electrical circuit.
Fast, short duration electrical transients (overvoltages) in the electric potential of a circuit are typically caused by
lightning strikes
power outages
tripped circuit breakers
short circuits
power transitions in other large equipment on the same power line
malfunctions caused by the power company
electromagnetic pulses (EMP) with electromagnetic energy distributed typically up to the 100 kHz and 1 MHz frequency range.
Inductive spikes
In the design of critical infrastructure and military hardware, one concern is of pulses produced by nuclear explosions , whose nuclear electromagnetic pulse (EMP) distribute large energies in frequencies from 1 kHz into the Gigahertz range through the atmosphere.
The effect of a voltage spike is to produce a corresponding increase in current (current spike). However some voltage spikes may be created by current sources. Voltage would increase as necessary so that a constant current will flow. Current from a discharging inductor is one example.
For sensitive electronics, excessive current can flow if this voltage spike exceeds a material's breakdown voltage, or if it causes avalanche breakdown. In semiconductor junctions, excessive electrical current may destroy or severely weaken that device. An avalanche diode, transient voltage suppression diode, transil, varistor, overvoltage crowbar, or a range of other overvoltage protective devices can divert (shunt) this transient current thereby minimizing voltage.
While generally referred to as a voltage spike, the phenomenon in question is actually an energy spike, in that it is measured not in volts but in joules; a transient response defined by a mathematical product of voltage, current, and time.
Voltage spike may be created by a rapid buildup or decay of a magnetic field, which may induce energy into the associated circuit. However voltage spikes can also have more mundane causes such as a fault in a transformer or higher-voltage (primary circuit) power wires falling onto lower-voltage (secondary circuit) power wires as a result of accident or storm damage.
Voltage spikes may be longitudinal (common) mode or metallic (normal or differential) mode. Some equipment damage from surges and spikes can be prevented by use of surge protection equipment. Each type of spike requires selective use of protective equipment. For example a longitudinal mode voltage spike may not even be detected by a protector installed for normal mode transients.

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GATE Syllabus for Electrical Engineering

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory: Fourier transform, Laplace transform, Z-transform.

ELECTRICAL ENGINEERING

Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere’s and Biot-Savart’s laws; inductance; dielectrics; capacitance.

Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms.

Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; autotransformer; energy conversion principles; DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors.

Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of overcurrent, differential and distance protection; solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transmission and FACTS concepts.

Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state space model; state transition matrix, controllability and observability.

Electrical and Electronic Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; instrument transformers; digital voltmeters and multimeters; phase, time and frequency measurement; Q-meters; oscilloscopes; potentiometric recorders; error analysis.

Analog and Digital Electronics: Characteristics of diodes, BJT, FET; amplifiers - biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers - characteristics and applications; simple active filters; VCOs and timers; combinational and sequential logic circuits; multiplexer; Schmitt trigger; multi-vibrators; sample and hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing.

Power Electronics and Drives: Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters - fully controlled and half controlled; principles of choppers and inverters; basis concepts of adjustable speed dc and ac drives.

GATE EE – 2002 Electrical Engineering Question Paper

SECTION – A
1. This question consists of TWENTY-FIVE sub-questions (1.1 œ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed.

1.1 A current impulse, 5 d (t), is forced through a capacitor C. The voltage, V (t), across the capacitor is given by

1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is

1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by
(a) B œ N + 1 (b) B + N
(c) N œ B + 1 (d) N œ 2B -1

1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode?
(a) A circle of unit radius (b) An ellipse
(c) A parabola
(d) A straight line inclined at 45° with respect to the x-axis

1.5 Given a vector field the divergence theorem states that

1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply?
(a) reduces (b) increases
(c) remains the same
(d) increase or reduces depending upon the rotor resistance

1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve
(a) Curve A
(b) Curve B
(c) Curve C
(d) Curve D

1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal?
(a) Voltage induced across the low voltage winding
(b) Core flux
(c) Load current
(d) Current drawn from the source

1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in 400V

Fig.1.9. The reading of the voltmeter, V, ~ V 50 Hz will be
(a) 0 V (b) 400 V
(c) 600 V (d) 800 V 4

1.10 The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal
available at Q is
(a) 10 kHz

(b) 2.5 kHz
(c) 20 kHz
(d) 5 kHz

1.11 The forward resistance of the diode shown in Fig.1.11 is 5 and the remaining parameters are same as those of an ideal diode. The dc component of the source current is

1.12 The cut-in voltage of both Zener diode D and diode D shown in Fig.1.12 is 0.7 V, while break down voltage of D is 3.3 V and reverse breakdown voltage of D is 50 V. the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage (V ) are

(a) 3.3 V in the positive half cycle and 1.4 V in the negative half cycle
(b) 4 V in the positive half cycle and 5 V in the negative half cycle
(c) 3.3 V in both positive and negative half cycles
(d) 4 V in both positive and negative half cycles

1.13 The line-to-line input voltage to the 3 R
phase, 50 Hz, ac circuit shown in Fig.1.13 is 100 V rms. Assuming that the phase sequence is RYB, the
wattmeters would read.
(a) W = 886 W and W = 886 W
(b) W = 500 W and W = 500 W
(c) W = 0 W and W = 1000 W

(d) W = 250 W and W = 750 W

1.14 The logic circuit used to generate the active low chip select (CS) by an 8085 microprocessor to address a peripheral is shown in Fig.1.14. The peripheral will respond to addresses in the range.
(a) E000-EFFF
(b) 000E-FFFE
(c) 1000-FFFF
(d) 0001-FFF1

1.15 Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is 0.25 cm and the distance between their centers is 1m. If this distance is doubled, then the inductance per unit length
(a) doubles (b) halves
(c) increases but does not double (d) decreases but does not halve

1.16 Consider a power system with three identical generators. The transmission losses are negligible. One generator (G1) has a speed governor which maintains its speed constant at the rated value, while the other generators (G2 and G3) have governors with a droop of 5%. If the load of the system is increased, then in steady state.
(a) generation of G2 and G3 is increased equally while generation of G1 is
unchanged.
(b) generation of G1 alone is increased while generation of G2 and G3 is
unchanged.
(c) generation of G1, G2 and G3 is increased equally.
(d) generation of G1, G2 and G3 is increased in the ratio 0.5:0.25:0.25.

1.17 A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at
(a) the upper surface of the conductor
(b) the lower surface of the conductor
(c) the ground surface
(d) midway between the conductor and ground

1.18 Consider the problem of relay co-ordination for the distance relays R1 and R2 on adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone 2 of relays R1 and R2.

1.19. Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is

1.20. Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is

1.22. The state transition matrix for the system with initial state X(0) is X AX =
(a) sI A – - (b) e X (c) Laplace inverse
(d) Laplace inverse of [ sI A X(0)]

1.23. A six pulse thyristor rectifier bridge is connected to a balanced 50 Hz three phase ac source. Assuming that the dc output current of the rectifier is constant, the lowest frequency harmonic component in the ac source line current is
(a) 100 Hz (b) 150 Hz (c) 250 Hz (d) 300 Hz

1.24. What is the rms value of the voltage waveform shown in Fig.1.24?

(a) 200 V (b) 100 V (c) 200 V (d) 100 V

1.25 A step down chopper is operated in the continuous conduction mode in steady state with a constant duty ratio D. If V is the magnitude of the dc output voltage 0 and if V is the magnitude of the dc input voltage, the ratio
V is given by
(a) D (b) 1 – D (c) 1 (d) 1

2. This question consists of TWENTY-FIVE sub-questions (2.1 œ 2.25) of TWO marks each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed.

2.1 A two port network, shown in Fig.2.1 is described by the following equations.
The admittance parameters Y , Y Y for the network shown are

(a) 0.5 mho, 1 mho, 2 mho and 1 mho respectively
(b) 1
3 mho, – 1 6 mho, – 1 6 mho and 1 3 mho respectively
(c) 0.5 mho, 0.5 mho, 1.5 mho and 2 mho respectively
(d) 2 – mho, 3 – mho, 3
7 7 mho and 2 5 5 mho respectively

2.2. In the circuit shown in Fig.2.2, what value of C will cause a unity power factor at the ac source?
(a) 68.1 F
230V (b) 165 F C Z
=30 40°
L ~
50Hz (c) 0.681 F
(d) 6.81 F

2.3. A first order, low pass filter is given with R = 50 and C = 5 F. What is the
frequency at which the gain of the voltage transfer function of the filter is 0.25?
(a) 4.92 kHz (b) 0.49 kHz (c) 2.46 kHz (d) 24.6 kHz

2.4. A series R-L-C circuit has R = 50 , L = 100 H and C = 1 F. the lower half
power frequency of the circuit is
(a) 30.55 kHz (b) 3.055 kHz (c) 51.92 kHz (d) 1.92 kHz

2.5. A 200 V, 2000 rpm, 10A, separately excited dc motor has an armature resistance of 2 . Rated dc voltage is applied to both the armature and field winding of the motor. If the armature drawn 5A from the source, the torque developed by the motor is
(a) 4.30 Nm (b) 4.77 Nm (c) 0.45 Nm (d) 0.50 Nm

2.6. The rotor of a three phase, 5 kW, 400V, 50 Hz, slip ring induction motor is wound for 6 poles while its stator is wound for 4 poles. The approximate average no load steady state speed when this motor is connected to 400V, 50 Hz supply is
(a) 1500 rpm (b) 500 rpm (c) 0 rpm (d) 1000 rpm

2.7. The flux per pole in a synchronous motor with the field circuit ON and the stator disconnected from the supply is found to be 25 mWb. When the stator is connected to the rated supply with the field excitation unchanged, the flux per pole in the machine is found to be 20 mWb while the motor is running on no load. Assuming no load losses to be zero, the no load current down by the motor from the supply
(a) lags the supply voltage (b) leads the supply voltage
(c) is in phase with the supply voltage (d) is zero

2.8. An 11 V pulse of 10 s duration is applied to the circuit shown in Fig.2.8.
Assuming that the capacitor is completely discharged prior to applying the pulse, the peak value of the capacitor voltage is
(a) 11 V (b) 5.5 V
(c) 6.32 V (d) 0.96 V

2.9. The output voltage (V ) of the Schmitt trigger shown in Fig.2.9 swings between +15V and – 15V. Assume that the operational amplifier is ideal. The output will change from +15V to œ15V when
the instantaneous value of the input sine wave is
(a) 5 V in the positive slope only
(b) 5 V in the negative slope only
(c) 5 V in the positive and negative slopes
(d) 3 V in the positive and negative slopes

2.10. For the circuit shown in Fig.2.10, the Boolean expression for the output Y in terms of inputs P, Q, R and S is

2.11. In the circuit shown in Fig.2.11, it is found that the input ac voltage (v) and current i are in phase. The coupling coefficient is K = , where M is the
mutual inductance between the two coils. The value of K and the dot polarity of K the coil P-Q are
(a) K = 0.25 and dot at P
(b) K = 0.5 and dot at P
(c) K = 0.25 and dot at Q
(d) K = 0.5 and dot at Q

2.12. Consider the circuit shown in Fig.2.12. If the frequency of the source is 50 Hz, then a value of t which results in a transient free response is
(a) 0 ms
(b) 1.78 ms
(c) 2.71 ms
(d) 2.91 ms

2.13. A three phase thyristor bridge rectifier is used in a HVDC link. The firing angle a (as measured from the point of natural commutation) is constrained to lie between 5° and 30°. If the dc side current and ac side voltage magnitudes are constant, which of the following statements is true (neglect harmonics in the ac side currents and commutation overlap in your analysis)
(a) Reactive power absorbed by the rectifier is maximum when a = 5°
(b) Reactive power absorbed by the rectifier is maximum when a = 30°
(c) Reactive power absorbed by the rectifier is maximum when a = 15°
(d) Reactive power absorbed by the rectifier is maximum when a = 10°

2.14. A power system consists of 2 areas (Area 1 and Area 2) connected by a single tie line (Fig.2.14). It is required to carry out a load flow study on this system. While entering the network data, the tie-line data (connectivity and parameters) is inadvertently left out. If the load flow program is run with this incomplete data
(a) The load-flow will converge only if the slack bus is specified in Area 1
(b) The load-flow will converge only if the slack bus is specified in Area 2
(c) The load-flow will converge if the slack bus is specified in either Area 1 or
Area 2
(d) The load-flow will not converge if only one slack bus is specified.

2.15. A transmission line has a total series reactance of 0.2 pu. Reactive power compensation is applied at the midpoint of the line and it is controlled such that the midpoint voltage of the transmission line is always maintained at 0.98 pu. If voltage at both ends of the line are maintained at 1.0 pu, then the steady state power transfer limit of the transmission line is
(a) 9.8 pu (b) 4.9 pu (c) 19.6 pu (d) 5 pu

2.16. A generator is connected to a transformer which feeds another transformer through a short feeder (see Fig.2.16). The zero sequence impedance values are expressed in pu on a common base and are indicated in Fig.2.16. the Thevenin equivalent zero sequence impedance at point B is

(a) 0.8 + j0.6 (b) 0.75 + j0.22 (c) 0.75 + j0.25 (d) 1.5 + j0.25

» ÿ » ÿ ” which of the following statements is true?
2.17. For the system 2 3 1 , X X u = + … Ÿ … Ÿ
(a) The system is controllable but unstable
(b) The system is uncontrollable but unstable
(c) The system is controllable but stable
(d) The system is uncontrollable but stable

The root 2.18. A unity feedback system has an open loop transfer function,
2.19. The transfer function of the system described

” 2.20. For the system 2 0 1 ; 4 0 , X X u y X = + = with u as unit impulse and with » ÿ … Ÿ … Ÿ zero initial state, the output, y, becomes
(a) 2 e (b) 4 e (c) 2 e (d) 4 e 2t 2t 4t 4t

2.21. The eigen values of the system represented by are X X =

(a) 0, 0, 0, 0 (b) 1, 1, 1, 1 (c) 0, 0, 0, -1 (d) 1, 0, 0, 0

2.22. In the chopper circuit shown in Fig.2.22 the input dc voltage has a constant . the output voltage V is assumed ripple-free. The V switch S is operated with a switching time period T and a duty ratio D. what is the value of D at the boundary of continuous and discontinuous conduction of the inductor current i ?

2.23. Fig. 2.23 (a) shows an inverter circuit with a dc source voltage V . The
semiconductor switches of the inverter are operated in such a manner that the pole voltages v and v are as shown in Fig.2.23 (b). What is the rms value of the pole-to-pole voltage v ?

2.24. In the circuit shown in Fig.2.24, the switch is closed at time t = 0. The steady state value of the voltage v is
(a) 0 V
(b) 10 V -
(c) 5 V
(d) 2.5 V

2.25. In the single phase diode bridge rectifier shown in figure 2.25, the load resistor is R = 50 . The source voltage is =200 sin( t), where =2 50 radians per second. The power dissipated in the load resistor R is
(a) 3200
(b) 400
(c) 400 W
(d) 800 W

SECTION – B
This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more than fifteen questions are attempted, score off answers that are not to be evaluated. Otherwise only the first fifteen unscored answers will be considered.
3. The magnetic vector potential in a region is defined by sin . . An – y A e x a = infinitely long conductor, having ac ross section area, a = 5mm and carrying a dc current, I = 5A in they y direction, passes through this region as shown in Fig.P3. Determine the expression for (a) and (b) force density exerted on the B conductor.

4. A constant current source is supplying 10A to a circuit shown in Fig.P4. the switch S, which is initially closed for a sufficiently long time, is suddenly opened. Obtain the differential equation governing the behaviour of R the inductor current and hence obtain the complete time response of the inductor current. What is the 5H energy stored in L, a long time after the switch is opened?

5. An electrical network is fed by two ac sources, as shown Fig.P5. Given that Z =
Obtain the Thevenin equivalent circuit (Thevenin voltage and impedance) across terminals x and y, and y determine the current I through the load Z

6. In the resistor network shown in Fig.P6, all resistor values are 1 . A current of 1A passes from terminal a to terminal b, as shown in the figure. Calculate the voltage between terminals and . [Hint: You may exploit the symmetry of the a b circuit].

7. A 230V, 250 rpm. 100A separately excited dc motor has an armature resistance of 0.5 . the motor is connected to 230V dc supply and rated dc voltage is applied to the field winding. It is driving a load whose torque speed characteristic is given by T = 500 – 10 , where is the rotational speed expressed in rad/sec and T is
the load torque in Nm. Find the steady state speed at which the motor will drive the load and the armature current drawn by it from the source. Neglect the rotational losses of the machine.

8. A single phase 6300 kVA, 50 Hz, 3300V/400V distribution transformer is connected between two 50 Hz supply systems, A and B as shown in Fig.P8. the transformer has 12 and 99 turns in the low and high voltage windings
respectively. The magnetizing reactance of the transformer referred to the high voltage side is 500 . The leakage reactance of the high and low voltage
windings are 1.0 and 0.012 respectively. Neglect the winding resistance and
core losses of the transformer. The Thevenin voltage of system A is 3300V while that of system B is 400V. the short circuit reactance of systems A and B are 0.5 and 0.010 respectively. If no power is transferred between A and B, so that the two system voltages are in phase, find the magnetizing ampere turns of the transformer.

9. A 440 V, 50 Hz, 6 pole and 960 rpm star connected induction machine has the following per phase parameters referred to the stator:
R = 0.6 R = 0.3 X = 1

The magnetizing reactance is very high and is neglected. The machine is
connected to the 440V, 50 Hz supply and a certain mechanical load is coupled to it. It is found that the magnitude of the stator current is equal to the rated current of the machine but the machine is running at a speed higher than its rated speed. Find the speed at which the machine is running. Also find the torque developed by the machine.

10. A 415 V, 2 pole, 3 phase, 50 Hz, star connected, non-salient pole synchronous motor has synchronous reactance of 2 per phase and negligible stator resistance. At a particular field excitation, it draws 20 A at unity power factor from a 415 V, 3 phase, 50 Hz supply. The mechanical load on the motor is now increased till the stator current is equal to 50A. The field excitation remains unchanged. Determine:
(a) the per phase open circuit voltage E
(b) the developed power for the new operating condition and corresponding
power factor.

11. For the circuit shown in Fig.P11, I = 1mA, = 99 and V = 0.7 V. Determine ß
(a) the current through R and R .
(b) the output voltage V
(c) the value of R

12. Determine the transfer function for the RC network shown in Fig.P12(a).
This network is used as a feedback circuit in an oscillator circuit shown in
Fig.P12(b) to generate sinusoidal oscillations. Assuming that the operational
amplifier is ideal, determine R for generating these oscillations. Also, determine the oscillation frequency if R = 10 k and C = 100 pF.

13. The ripple counter shown in Fig.P13 is made up negative edge triggered J-E flips flops. The signal levels at J and K inputs of all the flip-flops are maintained at logic 1. Assume that all outputs are cleared just prior to applying the clock signal.
(a) Create a table of Q ,Q ,Q and A in the format given below for 10 successive input cycles of the clock CLK1.
(b) Determine the module number of the counter.
(c) Modify the circuit of Fig.P13 to create a modulo-6 counter using the same components used in the figure.

14. A long lossless transmission line has a unity power factor (UPF) load at the receiving end and an ac voltage source at the sending end (Fig.P14). the
parameters of the transmission line are as follows:
Characteristic impedance Z =400 , propagation constant =1.2 10 rad/km, and length l = 100 km. The equation relating sending and receiving end
questions is V V l jZc lI cos sin ß ß = +
Complete the maximum power that can be transferred to the UPF load at the
receiving end if 230 . V kV

15. Two transposed 3 phase lines run parallel to each other as shown in Fig.P15. the equation describing the voltage drop in both lines is given below.

Compute the self and mutual zero sequence impedances of this system i.e.
compute Z , Z , Z in the following equations

V = Z I + Z I Í

V = Z I + Z I Í

Where V , V , I , I are the zero sequence voltage drops and currents for Í Í

the two lines respectively.

16. A synchronous generator is to be connected to an infinite bus through a
transmission line of reactance X = 0.2 pu, as shown in Fig.P16. the generator
data is as follows:
0.1 , 1.0 , x pu E pu H=5MJ/MVA, mechanical power P = 0.0 pu, = 2 50 ‘ ‘ = = p ×rad/sec. All quantities are expressed on a common base.
The generator is initially running on open circuit with the frequency of the open circuit voltage slightly higher than that of the infinite bus. If at the instant of switch closure d 0 and , compute the maximum value of so = = =
that the generator pulls into synchronism.

17. A single input single output system with y as output and u as input, is described
d y dy du 2
by + + = – 2 10 5 3 y u .
dt dt dt For the above system find an input u(t), with zero initial condition, that produces the same output as with no input and with the initial conditions.

18. Obtain a state variable representation of the system governed by the differential
d y dy y u t e 2 ( )
equation + – = 2 , with the choice of state variables as – 1
dt dt 2 ˜ ’ dy
x y x y e = = – , . Also find x (t), given that u(t) is a unit step function

19. The open loop transfer function of a unity feedback system is given by
Sketch the root locus as a varies from 0 to 8 . Find the angle and real axis
intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any.

20. In Fig.P20, the ideal switch S is switched on and off with a switching frequency f = 10 kHz. The switching time period is T = t + t = 100 s. The circuit is O N OF F operated in steady state at the boundary of continuous and discontinuous conduction, so that the inductor current i is as shown in Fig.P20. Find
(a) The on-time t of the switch.
ON
(b) The value of the peak current I .

21. In the circuit shown in Fig.P21, the source I is a dc current source. The switch S is operated with a time period T and a duty ratio D. You may assume that the capacitance C has a finite value which is large enough so that the voltage. V has negligible ripple. Calculate the following under steady state conditions, in terms of D, I and R.
(a) The voltage V , with the polarity shown in Figure P21.
(b) The average output voltage V , with the polarity shown.

22. The semiconductor switch S in the circuit of Fig.P22 is operated at a frequency of 20 kHz and a duty ratio D = 0.5. The circuit operates in the steady state. Calculate the power-transferred form the dc voltage source V to the dc voltage source V.