QUESTION BANK
III B.TECH I SEMESTER (EEE)
NAME OF THE SUBJECT: COMPLEX VARIABLES AND STATISTICAL METHODS
NAME OF THE FACULTY : Dr.A.S.R.Murthy or T.Kusuma
UNIT-1
1. Determine C-R equations in polar Co-ordinates.
2. Show that a function f(z)= 𝑥𝑦 is not analytic at the origin, although C-R equations are
satisfied at that point
3. If 𝑓 𝑧 = 𝑢 + 𝑖𝑣 is an analytic function of z and if 𝑢 − 𝑣 = 𝑒 𝑥 (𝑐𝑜𝑠𝑦 − 𝑠𝑖𝑛𝑦), find 𝑓 𝑧
in terms of z.
𝜕2
𝜕2
4. Prove that 𝜕𝑥 2 + 𝜕𝑦 2 𝑟𝑒𝑎𝑙𝑓(𝑧) 2 = 2 𝑓 1 (𝑧) 2 where f(z) is analytic
UNIT-2
7𝑧−2
1. Find the laurent’s series of 𝑧 𝑧+1 (𝑧−2) in the annuals 1< 𝑧 + 1 < 3.
2. Using Cauchy’s integral formula, Evaluate
3.
𝑠𝑖𝑛 2 𝑧
𝑐 (𝑧−𝜋 )3
6
𝑙𝑜𝑔𝑧
𝑐 (𝑧−1)3
1
𝑑𝑧 where C: 𝑧 − 1 = 2
𝑑𝑧, if C is the circle 𝑧 = 1
1
4. Expand f(z)= 𝑧 2 −3𝑧+2 in the region 0< 𝑧 − 1 < 1.
UNIT-3
𝑧3
1. Find the residue of 𝑓 𝑧 = 𝑧−1 4 𝑧−2 (𝑧−3) at 𝑧 = 1
2. Show by the method of residues
𝜋
𝑑𝜃
0 𝑎+𝑏𝑐𝑜𝑠𝜃
=
𝜋
𝑎 2 +𝑏 2
(a>b>0).
3. Find the poles and residues at each pole of the function
𝑧𝑠𝑖𝑛𝑧
(𝑧−𝜋)3
.
4. Find the poles and residues at each pole of 𝑡𝑎𝑛𝑕𝑧.
UNIT-4
1. Show that the image of the hyperbola x2-y2=1 under the Transformation w=1/z is the
lemniscates e2=cos2φ.
2. Under the Transformation w=1/z find the image of the circle 𝑧 − 2𝑖 =2.
3. Find the bilinear Transformation which maps the points 0,1, ∞ in the z-planes into -5,-1,3
respectively in the w-plane. What is the in variant point in this transformation?
2𝑧+3
4. Show that transformation 𝑤 = 𝑧−4 changes the circle 𝑥 2 + 𝑦 2 − 4𝑥 = 0 into the
straight line 4u+3=0
UNIT-5
1. State and prove Baye’s theorem. Companies A, B, C produce 30%, 45% and 25% of the
cars respectively. It is known that 2%, 3% and 2% of the cars produced from A, B, C are
defective. If a car purchased is found to be defective what is the probability that this car
is produced by company C?
2. In a normal distribution 31% of the items are 45 and 8% are over 64. Find the mean and
standard deviation of the distribution.
3. Fit a Poisson distribution to the following data
x 0
1
2
3 4 5 6 7
f 305 365 210 80 28 9 2 1
4. (a) Two dice are thrown five times, find the probability of getting 7 as sum (i) at least
once (ii) two time (iii) P(1<x<5).
(b)A can hit a target 3 times in 5 shots, B hits target 2 times in 5 shots, C hits target 3
times in 4 shots. Find the probability of the target being hit when all of them try.
UNIT-6
1. (a) Write a short note on interval estimation and Bayesian estimation.
(b) Explain the properties of a good estimator.
2. (a) A normal population has mean of 0.1 and standard deviation of 2.1. Find the
probability that mean of sample size 900 will be negative.
(b) A random sample of 500 apples was taken a large consignment and 60 were found to
be defective. Find the 98% confidence limit for the percentage no.of defective apples in
the consignment.
3. Mean life time of light bulbs produced by company is 1500hrs and S.D of 150hrs. Find
the probability that lighting will taken place for (a) at least 5000hrs (b) at most 4200hrs.
If three bulbs are connected such that when one bulb burns out, another bulb will go on.
Assume that life times are normally distributed.
4. Sample of size 2 are taken from the population 3 ,6 , 9, 15, 27 (i) with replacement
(ii) Without replacement Find
(a) The mean of the population
(b) The standard deviation of the population
(c) Mean of the sampling distribution of mean
(d) The standard deviation of the sampling distribution of means.
UNIT-7
1. (a) A coin is tossed 960 times and head turned up 183 times. Is the coin unbiased?
(b)A sample of 400 items is taken from a population whose standard deviation is 10. The
mean of the sample is 40. Test whether the sample has come from a population with
mean 38.Also calculate 95% confidence interval for the population.
2. A researcher wants to know the intelligence of students in a school. He selected 2 groups
of students .In the first group there 150 students having mean IQ of 75 with a S.D of 15
in the second group there are 250 students having mean IQ of 70 with S.D of 20.
3. (a) In a sample of 1000 people in Karnataka 540 are rice eaters and the rest are wheat
eaters. Can we assume that both rice and wheat are equally popular in this state 1% level
of significance?
(b) A manufacturer claims that only 4% of his products are defective. A random sample
of 500 was taken among which 100 were defective. Test the hypothesis at 0.05 levels.
4. In two large populations, there are 30% and 25% respectively of fair haired people. Is this
difference likely to be hidden in samples of 1200 and 900 respectively from the 2
populations?
UNIT-8
1. A random sample of 10 boys had the following I.Qs: 70, 120, 110, 101, 88,83,95,98,107
and 100. (a) Do these data support the assumption of a population mean I.Q of 100?
(b) Find a reasonable range in which most of the mean I Q. values of samples of boys lie.
2. Two horses A and B were tested according to the time (in seconds) to run a particular
track with the following results
Horse A 28 30 32 33 33 29 34
Horse B 29 30 30 24 27 29
Test whether the two horses have the same running capacity
3. (a)The nicotine contents in milligrams in two samples of tobacco were found to be as
follows
Sample A 24 27 26 21 25 Sample B 27 30 28 31 22 36
Can it be said the two samples have come from the same normal population?
(b) 1000 students at college level were graded according to their I.Q and the economic
conditions of their home. Use chi-square test to find out whether there is any association
between condition at home and I.Q
Economic High low Total
Rich
460 140 600
Poor
240 160 400
Total
700 300 1000`
Three different machines are used for a production. On the basis of the outputs test
whether the machines are equally defective
Outputs
Machine1 Machine2 Machine3
10
9
20
5
7
16
11
5
10
10
6
4
IDEAL INSTITUTE OF TECHNOLOGY
Vidyutnagar Kakinada
Department of Electrical and Electronics Engineering
Subject: Electrical Measurements
Faculty: G.Ravi Kumar
Unit-1:
1.(a) Explain the principle of working of a repulsion type moving iron instrument
with a neat diagram?
(b)Discuss the various errors in moving iron instruments and suggest methods to
compensate these errors?
2.(a)Explain the constructional details of PMMC instrument with a neat sketch?
(b)Explain why PMMC instruments are the most widely used
instruments?Explain their advantages and disadvantages?
3.(a)Give the classification of electrical measuring instruments and give an
example of each?
(b)With a neat circuit diagram explain how temperature effect is corrected in the
shunts.
4.(a)The inductance of a moving iron instrument is given by L=(16+6Ѳ- Ѳ2)µH,
where Ѳ is the deflection in radians from zero position.The spring constant is
15×10-6 Nm/rad.Estimate the deflection for a current of 10 A.
(b)A coil of a moving coil voltmeter is 40mm long and 30mm wide and has 100
turns wound on it. The control spring exerts a torque of 0.25×10-3 Nm when the
deflection is 50 divisions on the full scale.If the flux density of the magnetic field
in the air gap is 1wb/m2 estimate the resistance that must be put in series with
the coil to give 1v/division.Resistance of voltmeter is 10000 ohms.
Unit-2:
1.(a)Draw and Explain the equivalent circuit and phasor diagram of a potential
transformer.
(b)A potential transformer with a nominal ratio of 2000/100 v, an RCF of 0.995
and a phase angle (Vs lags Vp) of 25min is used with a current transformer with a
current transformer with a nominal ratio of 100/5 A, an RCF of 1.005 and a phase
angle error(Is leads Ip) of 10 min to measure the power in a single phase inductive
load.The meters connected to these transformers give correct readings of 1.02V,
4 A and 375 watts.Determine the true values of voltage,current and power
supplied to the load.
2.(a) Obtain the differences between current transformer and potential
transformer?
(b) What are the major sources of errors in current transformers?Explain them
in detail?
(c) Draw the equivalent circuit of current transformer?
3.(a) With a neat sketch explain the working principle of a single phase
dynamometer type power factor meter ?
(b)The meter constant of a 230V, 10 A, watt hour meter is 1800 revolutions per
Kwh.The mater is tested at half load and rated voltage and unity power factor.The
meter is found to make 80 revolutions in 138 second.Determine the meter error at half
load?
4.Show that the power input in a 3-phase system is measured by the use of
(a) only one watt meter and
(b) Two watt meter
Indicate how the power is determined.comment on the accuracy of the measurements
when the load is unbalanced and the supply is a four wire system?
Unit 3:
1.Explain the testing of energy meter using R.S.S. meter?
2.Explain the working of a Trivector meter with a neat diagram?
3.Explain with the aid of a phasor diagram the error caused by the inductance of the
pressure coil of a dynamometer wattmeter.Indicate the dependence of the error on
load power factor and supply frequency?
4.What is creeping?How can it be prevented?
Unit-4:
1.Explain how an voltage can be measured by using a polar type potentiometer?
2.Draw the circuit diagram of a basic slide wire D.C. potentiometer.Explain its working?
3.Explain the working of a vibration galvanometer with a neat sketch?
4.Explain the standardization procedure of D.C. cromtons potentiometer?
Unit-5:
1.Name the different methods used for measurement of medium resistances.Explain
any one method to measure medium resistance with accuracy using a neat diagram?
2.Explain the loss of charge method for measuring high resistance with a neat
sketch.Mention the possible errors and suggest methods to minimize these?
3.why is kelvins bridge superior to the whet stone bridge for the purpose of low
resistance measurement?
4.Explain what do you mean by low,medium and high resistances?suggest various
suitable methods for measuring them giving justification.Explain any one method to
measure a low resistance with accuracy using a neat diagram?
Unit-6:
1.Draw the circuit diagram of H.V. schering bridge?
2.Draw the circuit diagram of Desauty’s bridge and phasor diagram under balance
condition.Derive the equation under balance condition?
3.Draw the circuit diagram and phasor diagram of owen’s bridge under balance
condition.Derive the equations under balanced condition?
4.Derive equation for balance and draw phasor diagram for schering bridge?
Unit-7:
1.Describe the method of measurement of iron loss using Lioyed-Fisher square?
2.Explain how B-H curve for the ring specimen by using potentiometer is obtained?
3.Explain the construction and working of the flux meter with a neat diagram?
4.Explain in detail Fahy’s permeameter?
Unit-8:
1.Explain the various performance parameters of digital voltmeters?
2.Define resolution and sensitivity of DVM?
3.Explain the operation of digital tachometer with neat circuit diagram?
4.Explain the principle of digital frequency meter?
IDEAL INSTITUTE OF TECHNOLOGY
UNIT-I
SUBJECT: ELECTRICAL MACHINES-III
FACULTYNAME: CH.DIVYASREE
1. Describe the main constructional features of cylindrical rotor and salient pole alternator.
2. Explain the differences between stationary armature and rotating armature. What are
the advantages of rotating armature over stationary armature?
3. (a) Derive EMF equation for an alternator from fundamentals
(b) Calculate the rms value of the induced emf per phase of a 4 pole, 3 phase, 50 Hz,
alternator with 3slots/pole/phase and 6conductors/slot in two layers. The coil span is
150 degree. The flux/pole has a fundamental component of 0.2 wb and a 16% third
harmonic component.
4. What is short pitch winding & distributed winding? Why the armature winding
distributed& short pitch type?
5. Calculate the EMF of a 4 pole, 3-Φ, star connected alternator running at 1500r.p.m
from the following data: Flux per pole = 0.1 wb, Total number of slots= 48, Conductors
per slot (in two layers) = 4, coil span = 150o
6. Explain the various winding factors? Explain the effects of each of them.
UNIT-II
1. A 3-Φ, star connected alternator is rated at 1600 kVA, 13500 V. The armatureffective
resistance & reactance is 1.5 Ω/ph. & 30 Ω/ph, respectively. Calculate percentage
regulation for a load of 1280 kW at power factors of
i. 0.8 lagging
ii. 0.8 leading
2. a) A 16 pole, 3-Φ star connected alternator has 144 slots. The coils are short pitched by
one slot. The flux per pole is Φ = 100 sinθ+ 30 sin 3θ+ 20 sin5θ. Find the harmonics as
percentage of phase voltage & line voltage.
(b) Define
i. synchronous reactance
ii. Synchronous impedance and
iii. Leakage reactance in an alternator
3. Explain the effect of armature reaction on the EMF induced. Is it possible to obtain load
voltage more than EMF induced? if yes, how?
(b) A 200 kVA, 480 V, 50 Hz, star connected synchronous generator with a rated field
current of 5A was tested and the following data were obtained:
OC test: 540 V between lines on open circuit.
SC test: 300 A.
When a DC voltage of 10 V was applied to two of its terminals, a current of 25 A
was measured, find the value of synchronous impedance, synchronous reactance voltage
regulation of 0.6 p.f leading
4. The phase EMF of a 3-Φ alternator consists of fundamental, 20 % 3rd harmonic& 10 %
fifth harmonic. The amplitude of fundamental is 1000 V. Calculate the RMS value of line
& phase voltage, when the alternator is connected in
i. Star
ii. Delta
5. a) Explain the characteristics and nature of harmonics present in generated emf of
alternator?
(b) The flux density distribution in the air gap of an alternator is
B =B1sinθ+B3sin3θ+B5sin 5θwb/m2, whereB3= 0.3B1&B5= 0.2B1. The total
Flux per pole is 0.08 wb. The coil span is 80% of pole pitch. Find the RMS
Value of EMF induced in single turn machine
UNIT-III
1. (a) What is voltage regulation? Discuss the synchronous impedance method
ofcalculating voltage regulation.
(b) A 500V, 50KVA, 1-phase alternator has an effective resistance of 0.2Ω.A field
Current of 10A produces an armature current of 200A on short circuit and an emf of
450V on open circuit. Calculate
i. Synchronous impedance and reactance
ii. Full-load regulation with 0.8p.f. lagg
2. Derive an expression for finding regulation of salient -pole alternator using two
Reaction theory .Draw its phasor diagram.
3. A 1 MVA, 11 kV, 3-Φ, star connected synchronous machine has following OCCtest data:
If
50 110 140 180
EOL(Kv)
7 12.5 13.75 15
(Where EOL is the line voltage at no load)
The short circuit test yielded full load current at a field current of 60 A. The
ZPF yielded a full load current at terminal voltage for a field current of 150
A. The armature resistance is negligible. Calculate the voltage regulation at
full load 0.866 pf lagging by Potier triangle method
4. With proper explanation & diagram, Justify the statement ‘MMF method for finding
voltage regulation is optimistic and EMF method for finding voltage regulation is
pessimistic
5. A 3-phase star connected, 1000KVA, 2000V, 50Hz,alternator gave the following. open
circuit and short circuit test readings.
Field current
10
20
25
30
40
50
Open circuit voltage
800 1500 1760 2000
2350
2600
Short circuit armature current A 200 250 300
Draw the characteristic curves and estimate the full load percentage regulation at
i. 0.8pf lagging and
ii. 0.8pf leading The armature effective resistance/phase may be taken as 0.2Ω
UNIT-IV
1. (a) Explain the ‘two bright one dark’ & ‘all dark’ method of synchronization of
alternators.
(b) The EMFs of two alternators are 3000at angle of 20 deg&2900 at angle of 0 deg
Volts. Their synchronous impedances are 2 + j20 Ω/ph & 2.5 + j30 Ω/ph. The load
impedance is 10 +j4 Ω/ph. Find the circulating current.
2. (a) Explain all the necessary conditions for successful parallel operation of alternators.
(b) A 2 MVA, 3-Φ, star connected, 4 pole, 750 RPM alternator is operating on6000 V
bus bars, resistance 6 Ω/ph. Find synchronizing power and torque for full
Load 0.8 power factor lagging
3. A 3 MVA,6-pole alternator runs at 1000 r.p.m in parallel with other machines on 3.3 KV
bus-bars. The synchronous reactance is 20%.Calculate the synchronizing power per one
mechanical degree of displacement and the corresponding synchronizing torque.
4. a) What is an infinite bus? State the characteristics of an infinite bus. What are the
operating characteristics of an alternator connected to an infinite bus?
b) Calculate the synchronizing torque for unit mechanical angle of phase displacement
for a 5000KVA, 3- phase alternator running at 1500 rpm when connected to 6600 volt.
50 Hz , bus-bars. The armature has a short circuit reactance of15%.
UNIT-V
1. (a) Prove that sharing of common load by the alternators in parallel depends upon input
to the prime movers.
(b) Two identical 2000KVA alternators operate in parallel. The governor of first
Machine is such the frequency drops uniformly for 50Hz on no-load to 48 H on full load. The
corresponding uniform speed drop of the second machine is 50 to 47.5Hz.
i. How will the two machines share a load of 3000kw?
ii. What is the maximum load at unity p.f. that can be delivered without over loading either
machine?
2. Describe the effect of sudden short circuit on the performance of synchronous
generator
3. Two single - phase alternators are connected in parallel, and the excitation of each
machine is such as to generate an open - circuit e.m.fs of 3500 V. the stator winding of
each machine has a synchronous reactance of 30Ω and negligible resistance if there is a
phase displacement of 40 electrical degrees between the e.m.fs calculate
i. The current circulating between the two machines,
ii. The terminal voltage and the power supplied from one machine to the Assume that
there is no external load. Sketch the phasor diagram.
4. Explain the construction & working principle of Synchronous motor.
(b) A 3- Φ, 400 V star connected SM has effective per phase armature resistance &
synchronous reactance of 0.2 Ω & 2 Ω respectively. It takes 20 A to deliver a certain load.
Calculate the excitation EMF induced in the motor if it works with
i. 0.8 pf lagging
ii. 0.8 pf leading
UNIT-VI
1. A 3-Φ, 6600 V, star connected synchronous motor has effective per phase synchronous
reactance / phase of 15 Ω & negligible armature resistance. For a certain load, the input
is 900 kW at normal voltage and the induced line EMF is 8900 V.Determine
(a) Line current
(b) Power factor
2. (a) Explain the construction of damper winding. Clearly show the location of damper
winding.
(b) With neat diagram & explanation, show how damper winding prevents oscillations.
3. (a) Explain the construction of ‘excitation circle’ for a synchronous motor.
(b) Calculate the synchronous coefficient (in kW & Nm per mechanical degree) at full load
for a 1 MVA, 0.8 pf lagging, 6.6 kV, 8 pole, star connected generator of negligible resistance &
synchronous reactance of 0.8pu
4. (a) Explain the various starting methods of synchronous motor.
(b) Explain the characteristics of synchronous induction motor
UNIT-VII
1. Explain the equivalent circuit of single phase Induction motor & give all necessary
equations.
2. (a) What are the causes of faulty starting of synchronous motor?
(b) The input to a 11KV, 3-phase star connected synchronous motor is 60A. The effective
resistance and synchronous reactance per phase are 1Ω and 30Ω. Find the power supplied to
the motor and the induced emf for power factor of0.8 leading
3. a) Explain the operation of ‘split phase single phase Induction motor with vector
diagram.
(b) Explain how the direction of a single phase Induction motor cab be reversed.
4. (a) Why single phase motors are not self starting?
(b) Explain the necessary arrangements made to make single phase Induction motor self
starting & with neat diagram explain the operations of same.
UNIT-VIII
1. Write short notes on following:
(a) Double revolving field theory.
(b) Capacitor Start single phase induction
2. (a) Explain capacitor split phase motor.
(b) A 220V, 4 pole, 50Hz, capacitor split phase motor has the following impedance at
standstill. Auxiliary winding ra= 3Ω xa= 6ΩMain winding rm= 2Ω xm= 5Ω.The resistance of the
rotor winding when referred to the main stator winding is 0.5Ω. Assuming the number of turns
of the main winding and Auxiliary winding are equal, estimate the starting torque, maximum
starting torque and the capacitance to be inserted to get maximum starting torque
3. a) Explain about two-value capacitor run motor.
(b) Explain the static characteristics of stepper motor
(c) Explain the role of compound winding in the operation of AC series motor.
4. a) Compare AC series motor & Universal motor.
(b) Compare variable reluctance stepper motor & permanent magnet stepper motor
5. (a) Give the applications of various types of permanent magnet motors.
(b) Explain the working principle of permanent magnet motor
’.
IDEAL INSTITUTE OF TECHNOLOGY
LINEAR &DIGITAL IC APPLICATIONS
UNIT –I
1.Draw the circuit diagram of DIBO.Perform the DC analysis.
2. Explain the various types of level translator circuits.
3.Derive the necessary equation for CMRR in DIBO.
4 .Explain the classification of IC ‘s in detail .
UNIT –II
1.Differentiate the characteristics of ideal opamp & practical opamp.
2. Explain the block diagram of opamp..
3.How can we measure Input offset voltage,output offset voltage, slew rate,PSSR,CMRR of a Op Amp
4 .Explain Various frequency compensation techniques
UNIT –III
1.Draw and explain the practical differentiator and ideal differentiator circuits.
2. How can you generate Square wave,Traingular wave with Op Amp
3.Describe the terms Inverting comparator,Non Inverting comparator
4 .Discuss clearly how an opamp is used as log and anti log amplifiers
UNIT –IV
1.Derrive the necessary expression for the pulse width of a one shot in 555 timer.
2. Derive the necessary expression for Hysterisis voltage with the help of a 555 timer
3.Define the term lock range,capture range with proper explanations
4 .Explain the applications of PLL as a AM,FM,FSK demodulators
UNIT –V
1.derive the necessary equation to determine the bandwidth of a Second Order HPF
2.(a). Explain weighted resistor DAC.
(b).Explain inverted R-2R DAC
3(a).What are the different types of ADC’s ?Explain briefly.
(b).Explain Successive Approximation ADC
4 .What is a all pass filter.Explain
UNIT –VI
1.Draw the functional table for any one of decoder circuit.
2.(a). Draw the functional table for 8:1 mux.
(b).Draw the functional table for 8:3 priority encoder
3.Draw the circuit diagram for binary adder subteractor .Explain.
4 .Draw the circuit diagram of combinational multiplier .Explain with an Example.
UNIT –VII
1.Convert RS flip flop in to D flip flop..
2. Explain various counter applications.
3.Explain Ring counter and Johnson counter.
4 .Explain in detail the modes of operation of shift register.
UNIT –VIII
1.Explain the terms PLAS &PLDs
2. Explain the advantages and disadvantages of SRAM.
3.Discuss various types of ROMs.
4 .Differentiate PROM,PLA,PAL..
IDEAL INSTITUTE OF TECHNOLOGY
Vidyutnagar Kakinada
Department of Electrical and Electronics Engineering
Subject: Power Electronics
Faculty: M.M.Swapna
UNIT-I
1. Draw and explain static characteristics of SCR.
2. Explain the dynamic turn-on and turn-off times of SCR with neat waveforms.
3. Explain the dynamic turn-on and turn-off times of SCR with neat waveforms.
4. a) Discuss briefly IGBT characteristics.
b) Explain transfer and output characteristics of MOSFETs.
UNIT-II
1. State the main features of Firing circuits and briefly explain RC firing circuit with waveforms.
2. The dv/dt and di/dt rating of an SCR are 200V/µsec. and 20A/µSec. The supply voltage is
400V maximum. Neglecting load impedance, calculate the value of series inductance to limit
di/dt and the value of snubber circuit components necessary to prevent dv/dt triggering.
3. (a) Explain the necessity of series and parallel connection of SCRs.
b) What is String efficiency in series and parallel connection of SCR’s? Explain.
c) What are the problems arising in series and parallel connections.
4 (a) Explain in detail the Two-Transistor analogy of SCR with proper sketches.
(b) It is required to operate 250A SCR in parallel with 350A SCR with their respective on-state
voltage drop of 1.6V and 1.2V. Calculate the value of R to be inserted in series with each SCR
so that they share the load of 600A proportion to their current rating.
UNIT-III
1 (a) With the help of circuit diagram and necessary waveforms, explain the operation of single
phase half controlled bridge converter feeding R load and derive the expression for load voltage
and load current for firing angle(α)= 30deg.
(b) A single phase half controlled bridge converter is supplied a 230V, 50Hz.
Determine the average load voltage for firing angle of 60deg. If load current of 30A is
continuous and constant, what is the value of load resistance?
2. (a) With the help of circuit diagram and necessary waveforms, explain the operation of single
phase half controlled bridge converter with R-L load and derive the load voltage and load current
for firing angle(α)= 30deg
(b) Discuss briefly the importance of freewheeling diode in converter circuits.
3. Compare the performance, advantages and applications of semi converter over full converter.
4. (a) Explain the operation of 1-Ф have wave controlled rectifier with R-L load.
(b) A 230V, 50Hz, one pulse SCR controlled converter is triggered at a firing angle of 40deg
and the load current extinguishes at an angle of 210o . Find the circuit turn-off time, average
output voltage and the average load current for R=5Ω and L=2 mH
UNIT-IV
1. (a) Describe how a freewheeling diode improves power factor in a converter system?
(b) With the help of circuit diagram and waveforms explain the operation of single phase
midpoint converter when it is feeding RL load. Derive the expression for load voltage
2. Describe the working of single phase full converter in the inverter mode with RLE load.
Illustrate your answer with waveforms for source voltage, E, Load voltage and current. Assume
continuous conduction.
3. A single phase full converter feeding RLE load has the following data. Source
voltage=230V, 50Hz; R=2.5Ω, E=100V, Firing Angle=300. Assume continuous
conduction
and compute average value of load current and load voltage.
4. Derive the expressions for the following performance factors of single-phase fully
Controlled bridge converter.
(a)Input power factor (b) Voltage ripple factor
(c) Active power input (d) Reactive power input
UNIT-V
1. (a) Explain the principle of operation of three phase semi-converter with R-load with
associated waveforms.
(b) Compare 3-phase mid-point converters and bridge type converters and bring out important
features.
2. (a) Explain the four quadrant operation of dual converter with suitable diagrams.
(b) Derive the expression for output voltage of single-phase full converter by considering source
inductance.
3. Explain the operation of a three phase fully controlled bridge converter feeding RL-load with
the help of waveforms. Derive the expression for load voltages. Draw the wave forms for α= 30o.
4. (a) Explain the operation of three phase half wave controlled converter with resistive load.
Draw associated waveforms.
(b) What are the effects of source inductance on the operation of 3-phase controlled rectifier?
UNIT-VI
1 (a) Explain the operation of single-phase to single-phase step-up cyclo- converter
(b) A single-phase bridge-type cyclo-converter has input voltage of 230V, 50Hz and load of
R=10Ω. Output frequency is one-third of input frequency. For a firing angle delay of 300 ,
Calculate rms value of output voltage and rms current of each converter.
2. Explain why the single-phase ac voltage regulator using two SCRs must have its trigger
sources isolated from each other.
3. A three-phase, three-wire bidirectional controller supplies a star connected resistive load of
R=5Ω and line-to-line input voltage is 210V(RMS) 50 Hz. The firing angle α=600 Calculate
(i) the RMS output phase voltage,E0 (ii) the input power factor, pf and(iii) the expression for
instantaneous output voltage .
4. Explain the modes of operation of TRIAC with suitable diagrams.
UNIT-VII
1a) What is current limit control? How does it differ from TRC? Which of these control
strategies are preferred over the other and why?
b) For type-A chopper of dc source voltage of 230V and load resistance of 10Ω, take a voltage
drop of 2V across chopper when it is on. For a duty cycle of 0.4, calculate average and rms
values of output voltage.
2. A step-up chopper has input voltage of 220V and output voltage of 660V. If the conducting
time of thyristor-chopper is 100µs, compute the pulse width of output voltage. In case the outputvoltage pulse width is halved for constant frequency operation, find the average value of new
output voltage?
3. Derive the expressions for I0 max and I0 min for type A chopper.
4. A simple d. c. chopper is operating at a frequency of 2 kHz from a 96V d. c. source to apply a
load resistance of 8Ω. The load time constant is 6ms. If the average load voltage is 57.6V, find
the Ton period of the chopper, the average load current, and magnitude of the ripple current.
UNIT- VIII
1. Why voltage control is needed in inverter circuits? Explain in detail.
2. State the various methods of voltage control in inverter circuits and explain each of them
briefly.
3 What is a Pulse Width Modulation? List the various PWM techniques. How do these differ
from each other?
4. Design a self commutated inverter circuit to operate at a frequency of 3 kHz with and
optimum distortion. The load specifications are as follows: R= 5Ω, L=5mH, Edc=100V. Also
compute output power.
POWER SYSTEMS-II
(Electrical and Electronics Engineering)
Unit-1
1.
2.
3.
4.
(a) A 3- phase 50Hz transmission line has conductor of section 90 sq.mm. And effecting
diameter of 1 cm and are placed at the vertices of an equilateral triangle of side 1m. The line is 40
km long and delivers a load of 10MW at 33kv and pf=0.9. Compute the efficiency and regulation of
the line. Neglect capacitance and assume temperature of 20degree centigrade.
(b) Derive an expression for the capacitance per km of single phase line taking into account
the effect of ground.
(a) Show how the capacitance of a 3-phase transmission line with unsymmetrical spacing
between conductors can be calculated. Assume no transposition.
(b) A 1-phase overhead line consists of a pair of parallel wires 10mm in diameter spaced
uniformly 2 meters apart in air. Find the capacitance per km length. If the line is 30 km long and its
one end is connected to 50kv, 50Hz system what is the charging current with the other end open
circuited?
(a) Derive expression of the capacitance per phase of a 3-phase line with (i) equilateral and
(ii) unsymmetrical spacing. Assume transposition in (ii)
(b) A wire 4 mm in diameter is suspended at a constant height 10 meters above the sea level
which constitute the return conductor. Calculate the inductance of the system per km
(a) Derive expressions for the flux linkages of one conductor in a group of n conductorscarrying
currents whose sum is zero. Hence derive an expression for inductance ofcomposite conductors of
a 1-phase line consisting of m strands in one conductor and nstrands in the other conductor.
(b) Explain the concept of self GMD and mutual GMD for evaluating inductance of
transmission lines.
Unit-2
1 Derive the A,B,C,D parameters of medium lines from
(a) Nominal T method
(b) Nominal π method.
2.
A transmission line has a series impedance of 20+j40 ohms and a shunt admittance of
ohms. Find A,B,C,D constraints based on
(a) Nominal T method (b) Nominal π method
4x10-4
3. (a) A 3-phase 50Hz over head transmission line has the following distributed constraints
R=28 ohms, Inductive reactance= 63 ohms, capacitive reactance= 4x10-4 mho. If the load at the
receiving end is 75 MVA at 0.8 pf. Lagging with 132 kv between lines, calculate (i) Voltage (ii)
Current (iii) Power facto at the sending end (iv) Regulation (v) Efficiency of transmission for this
load. Use Nominal π method and also draw phasor diagram.
(b) Explain the classification of lines based on their length of transmission.
4. (a) Evaluate the generalized circuit constraints for short and medium (both T and π)
transmission lines
(b) A 3-phase 50Hz over head transmission line has the following distributed constraints R=28
ohms, Inductive reactance= 63 ohms, capacitive reactance= 4x10-4 mho. If the load at the receiving
end is 75 MVA at 0.8 pf. Lagging with 132 kv between lines, calculate (i) Voltage (ii) Current (iii)
Power facto at the sending end (iv) Regulation (v) Efficiency of transmission for this load. Use
Nominal T method and also draw phasor diagram.
Unit-3
1. (a) What do understand by long transmission lines? How capacitance effects are taken into
account in such lines?
(b) For a 215 kv, 400km, 60 Hz, 3-phase long transmission line, Z=(0.1+j0.5) Ω/km, and
y=j3.2x10-6 mho/km. The line supplies a 150 µW load at unity pf. Determine (i) The voltage
regulation (ii) The sending end power (iii) The efficiency of transmission.
2. Starting from first principle show that surges behaves as travelling waves. Find expressions for
surge impedance and wave velocity.
3.
Deduce expression for the magnitudes of incident and reflected voltages at any point on
a transmission line in terms of voltage and current at receiving end characteristic impedance and
propagation constant of the line. Show how these expressions are useful in determining voltage
and current distribution along the line.
4. (a)With reference to long transmission line, give physical interpretation of the terms of impedance
and propagation constant? What is meant by surge impedance?
(b) Determine ABCD constant for 3-phase 50 Hz transmission line 200 km long having the
following distributed parameters. L= 1.20x10-3 H/km, C= 8x10-9 F/km, R = 0.15 Ω/km,G=0
Unit-4
1. Explain the variation of current and voltage on an overhead line when one end of the line is Short
circuited. Assume at the other end a source of constant voltage V is switched in the case.
2. Explain the variation of current and voltage on an overhead line when one end of the line isOpen
circuited. Assume at the other end a source of constant voltage V is switched in the case.
3. Starting from first principles show that surges behave as travelling waves. Find expressions for
surge impedance and wave velocity.
4. How can the analysis of a wave travelling on a line terminated by an inductance be
carried out? Derive the expression for the voltage across the terminating inductance connected at
the end of a line on which a step wave of magnitude ‘V’ is travelling.
Unit-5
1. (a) What are the factors which effect corona?
(b) A 132 kv line with 1.956 cm dia. Conductor is built so that corona takes place if the line voltage
exceeds 210kv (rms). If the value of potential gradient at which ionisation occurs can be taken as
30 kv per cm, find the spacing between the conductors.
(c) a Explain the Ferranti effect on EHV transmission lines with neat phasor diagram
b) Estimate the corona loss for a 3-phase, 130 kV, 50 Hz, 250 km long transmission
line consisting of three conductors, each of 12 mm diameter and spaced 2.8 meter
apart in an equilateral triangle formation. The temperature of air is 350C and the
atmospheric pressure is 750 mm of mercury. Taking the irregularity factor as 0.85.
2. (a) Write short notes on (i) Skin Effect (ii) Proximity Effect (iii) Advantages of bundle
conductors for overhead transmission lines.
(b) A certain 3-phase equilateral transmission line has a total corona loss of 53 KW at 106
KV and a loss of 98 KW at 110.9 KV. What is the disruptive critical voltage? What is the
corona loss at 113 KV?
3. (a) What is corona? Explain the theory of corona formation in detail?
(b) A conductor with 3.0 cm dia is passed centrally through a porcelain bushing ?r=4 having
internal and external diameters of 3.5 cm and 9 cm respectively. The voltage between the
conductor and an earthed clamp surrounding the porcelain is 25 kv rm. Determine whether
corona will be present is the air space around the conductor.
4. (a) Deduce from first principle expressions for the disruptive critical voltage between two smooth
circular wires and potential gradient any point along a line joining theircentres.
(b) Find the ratio of critical voltage when the distance between the conductors is halved,
other data remaining the same.
(c) What is meant by the disruptive critical voltage and visual critical voltage? State the
effects of conductor size, spacing and condition of the surface of conductors on these
voltages
(d) Find the critical disruptive voltage and the critical voltages for local and general
corona on a 3- phase overhead transmission line, consisting of 3-stranded copper
conductors spaced 2.2 m apart at the corners of an equilateral triangle. Air temperature
and pressure are 21o C and 73.6 cm of Hg respectively. Take conductor diameter 10
mm, irregularity factor 0.85, local and general surface factors 0.7 and 0.8 respectively.
Unit-6
1. (a) Derive expressions for sag and tension in a power conductor strung between two
supports at unequal heights taking into account the wind and ice loadings also.
(b) Describe the vibration of power conductors and explain the methods used to damp out
these vibrations.
(c) Explain what is meant by a string efficiency of a suspension insulator consists of a
number of units. What causes the efficiency to be less than 100 percent? Describe any
one method of improving the same.
2. (a) Derive the sag magnitude when
(i) When supports are at equal levels
(ii) When supports are at unequal levels
(b) A 132 kv transmission line has the following data:
Wt. Of conductor = 680 kg/km ; Length of span =260 m
Ultimate strength = 3100 kg
; Safety factor = 2
Calculate the height above ground at which the conductor should be supported. Ground
clearance required is 10 meters.
(c) Each line of a three phase system is suspended by a string of 3 identical insulators of
self capacitance C farad. The shunt capacitance of the connecting metal work of each
insulator is 0.3C to earth and 0.2C to line. Calculate the string efficiency of the
system if the guard ring increases the capacitance to the line of the metal work of the
lowest insulator to 0.35C.
3. (a) Derive and explain the sag magnitude under wind and ice loading conditions.
(b) The towers of height 30m and 90 m respectively support a transmission line conductor at
water crossing. The horizontal distance between the towers is 500 m. Is the tension in the
conductor is 1600 kg. Find the minimum clearance of the conductor and water and clearance
mid-way between the supports. Weight of conductor is 1.5 kg/m. Bases of the towers can be
considered to be at water level.
(c)What are the advantages of suspension type insulators over pin type insulators
(d) Find the potential difference across each unit of over head suspension insulators
connecting of four similar units. The potential between the line conductor and the earth
is 56 kV and the ratio of capacity of each insulator to the capacity relative to earth, of
each intermediate section of connecting work is 6:1. It is assumed that no leakage takes
place. Also find the string efficiency.
4. (a) Is sag a necessity or an evil? Discuss and what are the mechanical principles should be followed
while designing the transmission line?
(b) A transmission line conductor at a river crossing is supported from two towers at heights
of 45 meters and 75 meters above water level. The span length is 300 meters. Weight of the
conductor 0.85kg/m. Determine the clearance between the conductor and water at a point
midway between towers if the tension is the conductor is 2050 kg.
Unit-7
1. (a) Write a short note on different types of insulators used for overhead lines and their
applications. Show with the help of a neat sketch, the electrostatic field of a pin insulator
and explain how far the shape of modern insulator conforms to these requirements.
(b) What are the basic tests to be carried out on insulators?
2. Explain the various methods for equalizing the potential across the various units in an
insulator string and discuss the methods for improving the string efficiency in a string of insulators.
3. (a) A string of 6 insulator units has mutual capacitance 10 times the capacitance to ground.
Determine the voltage across each unit as a fraction of the operating voltage. Also determine
the string efficiency.
(b) Write short notes on pin type insulator? What are its limitations?
4. (a) Write short notes on different types of insulators used for overhead lines.
(b) Each conductor of a 33kv, 3-phase system is suspended by a string of three similar
insulators; the capacitance of each disc is nine times the capacitance to ground. Calculate the
voltage across each insulator. Determine the string efficiency also.
Unit-8
1. (a) What are the types of power factor improvement equipments? Explain in details.
(b) A single phase motor connected to 400V, 50 Hz supply takes 31.7 A at a power factor of
0.7 lagging. Calculate the capacitance required in parallel with the motor to raise the power
factor to 0.9 lagging
2. (a) Explain any two methods of voltage control in a power system.
(b) A 3-phase, 50 Hz, 400V motor develops 100 HP, the power factor being 0.75 lagging
and efficiency 93 %. A bank of capacitors is connected in delta across the supply terminals
and power factor raised to 0.95 lagging. Each of the capacitance units is built of 4 similar
100V capacitors. Determine the capacitance of each capacitor
3. (a) Explain in detail how to control voltage by using
(a ) shunt capacitors
(b) Synchronous capacitors
(c ) Tap changing transformers
(d) Booster transformer.
4. A 3-phase overhead line has per phase resistance and reactance of 6 ohms and 20 ohms
respectively. The sending end voltage is 66 KV while the receiving end voltage is
maintained at 66 KV by synchronous phase modifier. Determine the KVAr of the modifier
when the load at the receiving end is 75 MW at pf. 0.8 lagging also determine the maximum
load that can be transmitted.