R10. , where the point a lies within the closed curve C (b) in positive and negative powers of z, if ! "

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2 Code No: R31021 COMPLEX VARIABLEDS AND STATISTICAL METHODS 1 (a) If the potential function is. Find the complex potential function. (b) Show that both the real and imaginary parts of an analytic function is harmonic. 2 (a) Evaluate, where the point a lies within the closed curve C (b) Expand in positive and negative powers of z, if 3 (a) (b) Find the poles and residues of Evaluate by contour integration R10! " Set No: 1 4 (a) Find the image of the semi-infinite strip #$%$& &' under the mapping ( )*+ (b) Find the bilinear transformation that maps the points 1-2i, 2+i, 2+3i respectively into 2+2i, 1+3i, 4. 5 (a) There are 12 cards numbered 1 to 12 in a box, if two cards are selected what is the probability that sum is odd (i) with replacement (ii) without replacement (b) Fit a binomial distribution for the following x f (a) Calculate the size of S.D. of means for the population 16, 14, 12, 8, 24, 20 by drawing samples of size 2 without replacement. Verify the results (b) A random sample of size 100 is taken from a population with, -./. given that the sample mean is /.1. Construct a 95% confidence interval for the population mean µ. 7 (a) The research investigator is interested in studying whether there is a significant difference in the salaries of MBA graduates in two metropolitan cities. A random sample of size 100 from Mumbai yields on average income of Rs.20,150. Another random sample of 60 from Chennai results in an average income of Rs.20,250. If the variances of both the populations are given as, 2*.3$%$$$ and, 2*.4%3$$ respectively. (b) In a city 250 men out of 750 were found to be smokers. Does this information support the conclusion that the majority of men in this city are smokers? 8 (a) In 16 one hour test runs, the gasoline consumption of an engine averaged 16.4 gallons with a S.D. of 2.1 gallons. Test the claim that the average gasoline consumption of this engine is 12.0 gallons per hour. (b) Explain in detail ANOVA for one-way classification. 1 of 1

3 R10 Set No: 2 Code No: R31021 COMPLEX VARIABLEDS AND STATISTICAL METHODS 1 (a) Find the analytic function whose real part is e x ( x cos y + y sin y)? (b) If f(z) is an analytic function of z, Prove that Re al f ( z) = 2 f ( z)? 2 2 x y 2 (a) z 3 Evaluate dz, c z 2 + 2z + 5 (iii) z i = 2? Where c is the circle (i) z = 1, (ii) z + 1 i = 1, (b) Obtain the Taylor s series expansion ( z) e z f = about z=2? z ( z +1) 3 (a) Find the poles and residues at each pole of tan hz? (b) Evaluate ax e dx x e (a) Find the image of the triangle with vertices i, 1+i and 1 in Z-plane under the transformation w=3z + 4-2i? (b) Find the bilinear transformation which maps the points z=0, -1, 5 in to the points -1, -2, -i? 5 (a) A test of multiple choice questions with four choices is held. A candidate appearing for the test either gussess or recalls or computes the answer for any question. The probability that he makes a guess is 1/6 and the probability that he calls the answer 1/3. The probability that he his answer is correct, given that he recalls it is 1/8. Find the probability that he computes the answer to the question, given that he answered it correctly. (b) A sales tax officer has reported that the average sales of the 500 business that he has to deal with during a year is Rs.36,000 with a standard deviation of 10,000. Assuming that the sales in these business are normally distributed, find (i) the number of business as the sales of which are Rs.40,000. (ii) the percentage of business the sales of which are likely to range between Rs.30,000 and Rs.40, of 2

4 Code No: R31021 R10 Set No: 2 6 (a) What is the effect on standard error, if a sample is taken from an infinite population of sample size is increased from 400 to 900. (b) Write short notes on interval estimation and Bayesian estimation? 7 (a) The average marks scored by 32 boys are 72 with a S.D. of 8. While that for 36 girls is 70 with a S.D. of 6. Does this indicate that the boys perform better than girls at level of significance 0.05? (b) A sample of 100 workers in a large plant gave a mean assembly time of 294 seconds with a S.D. of 12 seconds in a time and motion study. Find a 95% confidence interval for the mean assembly time for all the workers in the plant. 8 (a) A process for making certain ball bearings is under control if the diameters of the bearings have a mean of cm. If a random sample of 10 of these bearings has a mean diameter of cm and S.D. of cm, is the process under control? (b) Experience shows that a fixed dose of a certain drug causes an average increase of pulse rate of 10 beats per minute with a S.D. of 4. A group of 9 patients given the same dose showed the following increase: 13, 15, 14, 10, 8, 12, 16, 9, 20. Test at 5% level of significance whether this group is different in response to the drug. 2 of 2

5 R10 Code No: R31021 COMPLEX VARIABLEDS AND STATISTICAL METHODS 1 (a) Write short notes on (i) Analytic Function (ii) Cauchy-Riemann Equations (iii) Harmonic Function (iv) Complex Potential Function (b) 1 Find an analytic function f(z) such that Re f ( z) 2 2 [ ] 3x 4y 3y Set No: 3 = and f (1+i) = 0? 2 (a) 7z 2 1 Find the Laurent series of ( z + ) z ( z 2) in the annulus 1 z + 1 3? (b) Using Cauchy s integral formula, evaluate cosh π z c dz, z z Where c is z = 2? 3 (a) Show that6 π cos 2θ 01 2a cosθ + a 2 π a 2 dθ = a 2 < 1 using residue Theorem? 1 a 2 (b) Evaluate dz 2 C ( z + 4) 2 where c: z i = 2? 4 (a) Prove that the transformation w = sin z maps the families of lines x=a and x=b in to two families of confocal central conics? (b) Show that under the transformation ( z i) ( z + i) w =,real axis in the z- plane is mapped in to the circle w = 1. Which portion of the z-plane corresponds to the interior of the circle? 1 of 2

6 Code No: R31021 R10 Set No: 3 5 (a) Two aeroplanes bomb target in succession. The probability of each correctly scoring a hit is 0.3 and 0.2 respectively. The second will bomb only if the first misses the target. Find the probability that (i) target is hit (ii) both fails to score hits. (b) If X is normally distributed with mean 2 and variance 0.1, then find 789#$.$/: 6 (a) A random sample of size 64 is taken from a normal population with µ=51.4 and = 68. What is the probability that the mean of the sample will (i) exceed 52.9 (ii) fall between 50.5 (iii) be less than 50.6 (b) Construct a 99% confidence interval for the true mean weight loss if 16 persons on diet control after one month had a mean weight loss of 3.42kgs with S.D. of 0.68kgs. 7 (a) A random sample of 500 pineapples was taken from a large consignment and 65 were found to be bad. Find the percentage of a bad pineapples in the consignment. (b) A machine produced 20 defective articles in a batch of 400. After overhauling it produced 10 defectives in a batch of 300. Has the machine improved. 8 (a) A manufacturer claims that any of his list of items cannot have variance more than 1 cm 2. A sample of 25 items has a variance of 1.2cm 2. Test whether the claim of the manufacturer is correct. (b) Two random samples drawn from normal populations are : I II Obtain the estimates of the variances of populations. Test whether two populations have the same variance. 2 of 2

7 R10 Code No: R31021 COMPLEX VARIABLEDS AND STATISTICAL METHODS 1 (a) 3 2 Show that u( x, y) = x 3xy is harmonic and find its harmonic conjugate? (b) Find an analytic function f(z) such that 1 2 Re f z = 3x 4y 3y and f ( 1 + i) = 0? 2 [ ( )] Set No: 4 2 (a) (b) Find the Taylor s series expansion f ( z) Expand ( z) 2 ( z z 2) 1 = with centre at i? ( 1 + z) 2 z + 3 f = in powers of z where z (i) z < 1, (ii) 1 < z < 2? 3 (a) Show that 0 2π 1+ 4cosθ d cos θ = 0? θ (b) Evaluate c 12 z ( )( ) dz 2z + 3 z where C is x + y = 4 by using Residue theorem? 4 (a) (b) 5 4z Show that the transformation W = transforms the circle z = 1 into a circle 4 z 2 of radius unity in w-plane and find the centre of the circle? 2 Show that the transformation w = z maps the circle 9// into the cardiod R=2 (1 + cos;) where ( 2< = in the w-plane? 5 (a) If the probability that a communication system will have high fidelity is 0.81 and the probability that it will have high fidelity and selectively is What is the probability that a system with high fidelity will also have high selectivity? (b) Determine the probability of getting at least 60 heads when 100 coins are tossed 1 of 2

8 Code No: R31021 R10 Set No: 4 6 (a) The average cost of studio condominium in the cedar lakes development is Rs.62,000 and the S.D. is Rs What is the probability that a condominium in this development will cost at least Rs.65,000. (b) A sample of 11 rats from a central population had an average blood viscosity of 3.92 with a S.D. of Estimate the 95% confidence limits for the mean blood viscosity of the population. 7 (a) Experience had shown that 20% of a manufactured product is of the top quality. In one day s production of 400 articles only 50 are of top quality. Test the hypothesis at 0.05 level. (b) Explain the procedure generally followed in testing of hypothesis. 8 (a) A random sample of size 25 from a normal population has the mean 47.5 and S.D Does this information tend to support or refuse the claim that the man of the population is (b) Two random samples drawn from normal populations are : I II Obtain the estimates of the variances of populations. Test whether two populations have the same variance. 2 of 2

9 Code No: R31025 R10 Set No: 1 Electrical Machines - III 1. (a) Explain the construction features and principle of operation of single phase induction motor. (b) Explain with neat diagrams the following types of single phase induction motors: (i) Capacitor start induction motor (ii) Capacitor start and capacitor run induction motor. 2. (a) With neat sketch, describe the constructional features and operation of salient pole alternator. (b) Explain about the integral slot winding and fractional slot winding. Discuss their merits and demerits. 3. (a)what is meant by synchronous reactance? Explain the term synchronous impedance of an alternator. (b) What is armature reaction? Explain the effect of armature reaction on the terminal voltage of an alternator at (i) unity power factor load (ii) zero lagging power factor load (iii) zero leading power factor load. Draw the relevant phasor diagrams. 4. (a) Explain the synchronous impedance method of determining the voltage regulation of an alternator. Comment on merits and limitations of this method. Why this method is considered as pessimistic method. (b) Explain procedure to determine d-axis and q-axis reactance of a synchronous machine in the laboratory. 5. (a) Discuss the conditions required for paralleling two synchronous generators. (b) A 1500 kva, 6600V 3-phase, 8 pole, 750 rpm, synchronous generator is operating on 6000 V bus bars. The synchronous reactance is 6 ohm/phase. Find the synchronizing power and torque per mechanical degree at full load and 0.8 power factor lag. 6. (a) What is a synchronous condenser? Explain its operation with the help of phasor diagram. What are its applications? (b) A 1000kVA, V, 3-phase star-connected synchronous motor has an armature resistance and reactance per phase of 3.5 ohms and 40 ohms respectively. Determine the induced e.m.f and angular retardation of the rotor when fully loaded at (i) unity power factor (ii) 0.8 power factor lagging (iii) 0.8 power factor leading. 1 of 2

10 Code No: R31025 R10 Set No: 1 7. (a) What is meant by hunting in a synchronous motor? Why is it undesirable? What is to be done for its minimization? (b) Give the connection diagram for starting of a synchronous motor using an auxiliary induction motor and outline the steps involved in the starting process. 8. Explain the construction and principle of operation of AC series motor. Also draw and explain its phasor diagram. Discuss its applications. ** 2 of 2

11 Code No: R31025 R10 Electrical Machines - III 1. (a) Using double field revolving theory explain the toque - slip characteristics of single phase induction motor and prove that it cannot produce any starting torque. (b) Discuss the performance of (i) shaded pole motor (ii) single phase capacitor start induction motor. 2. (a) Derive the e.m.f equation of an alternator and explain how the induced e.m.f in the armature winding is affected by (i) pitch factor and (iii) distribution factor. (b) Find the number of armature conductors in series per phase required for the armature of a 3 phase 50 Hz, 10-pole alternator with 90 slots. The winding is to be star connected to give a line voltage of 11000V. The flux per pole is 0.16 weber. Assume the coil pitch as 8 slots. 3. (a) Explain the load characteristics of an alternator. (b) What is synchronous impedance? How can it be measured in laboratory? (c) Explain the methods to suppress harmonics in an alternator. Set No: 2 4. (a) Define voltage regulation of an alternator. With necessary diagram, explain zero power factor method to determine the voltage regulation of an alternator. (b) Discuss the two reaction theory of salient pole synchronous machine. 5. (a) Explain dark lamp method of synchronizing an alternator with the bus bar. (b) Explain the operation of a synchronous generator delivering constant load with variable excitation. 6. (a) Explain the principle of operation of a 3-phase synchronous motor. (b) A 2000 V, 3-phase star-connected synchronous motor has an effective resistance and synchronous reactance per phase of 0.2 ohms and 2.2 ohms respectively. The input is 800 kw at normal voltage and induced line e.m.f is 2500 V. Calculate line current and power factor. 7. (a) Show that starting torque of a synchronous motor is zero. (b) What is hunting? What are the factors that cause hunting? What are the effects hunting? Explain the methods used to eliminate the hunting in synchronous motor. 8. Explain why a universal motor operate both on AC and DC supply. What are the differences in construction between universal motor and DC series motor? Discuss its applications. * 1 of 1

12 Code No: R31025 R10 Set No: 3 Electrical Machines - III 1. (a) Prove that a single phase induction motor winding when excited by a single phase supply produces two equal and opposite revolving fields. (b) With a neat diagram and characteristics, explain the operation of capacitor start and capacitor run induction motor. 2. (a) Compare salient pole and non-salient pole synchronous machines. (b) A 3 phase, 25 Hz, star connected alternator has 12 poles. The armature has 180 slots containing a two layer winding with 4 conductors per slot. All the conductors are connected in series. The flux per pole is lines sinusoidally distributed and the machine is driven at its rated speed. The coil throw is 12 slots. Determine the e.m.f induced per phase and the voltage between the terminals. 3. (a) Explain the phenomena of armature reaction when an alternator is delivering a load current at (i) purely lagging power factor (ii) unity power factor (iii) purely leading power factor. (b) Determine the values of pitch factor and distribution factor for a three phase winding with 4 slots/pole/phase and a coil span of 10 teeth. Calculate the percentage increase in the r.m.s value of phase voltage due to a 25% 3 rd harmonic. 4. (a) A 3-phase, star connected alternator is rated at 1600 kva, V. The armature effective resistance and synchronous reactance are 1.5 ohms and 30 ohms respectively per phase. Calculate the percentage regulation for a load of 1280 kw at power factors of (i) 0.8 leading (ii) unity (iii) 0.8 lagging. (b) Explain the MMF method of determining the voltage regulation of an alternator. 5. (a) Show that the maximum power that an alternator can supply when connected to constant voltage constant frequency bus bars increases with the excitation. (b) Compare the sub-transient, transient and steady state reactance of an alternator. 6. (a) Derive an expression for the power developed in a 3-phase synchronous motor. (b) The synchronous reactance per phase of a 3-phase, star connected 6600 V synchronous motor is 20 ohms. For a certain load the input is 900 kw at normal voltage and induced line e.m.f is 8500 V. Determine line current and power factor. 1 of 2

13 Code No: R31025 R10 Set No: 3 7. (a) Explain the operation of a synchronous induction motor with a neat diagram. (b) Explain excitation circle of a synchronous motor. (c) Explain why a Synchronous motor is not self-starting. Briefly explain the following starting methods in detail (i) Auxiliary motor starting (ii) Induction motor starting. 8. Describe the construction and principle of operation of reluctance motor with neat diagrams. Draw its speed-torque characteristics and explain. Give applications of reluctance motor. * 2 of 2

14 Code No: R31025 R10 Set No: 4 Electrical Machines - III 1. (a) Explain the cross-field theory as applied to a single phase induction motor. (b) Describe the constructional features and operating characteristics of a shaded-pole motor. 2. (a) Discuss the constructional details of the synchronous machine. Explain where the round rotor alternator is preferred. (b) A 3-phase, 8 pole, 50 Hz star connected alternator has 96 slots with 4 conductors, coil span is 10 slots and the flux per pole is 0.06 Wb. Determine, distribution factor and the line e.m.f generated. 3. (a) Draw the phasor diagram of the alternator of a loaded alternator for the following conditions: (i) lagging power factor (ii) leading power factor (iii) unity power factor. (b)explain the concept of replacing the armature reaction by a reactance. 4. (a) Explain the A.S.A method of determining the voltage regulation of an alternator. (b) Derive an expression for finding voltage regulation of salient pole alternator using two-reaction theory. Draw its phasor diagram. 5. (a) Show that changing of field excitation results in a change of power factor without affecting the kw division between two alternators. (b) Derive an expression for synchronizing power of an alternator. 6. (a) Describe briefly the effect of varying excitation upon armature current and power factor of a synchronous motor when the input to the motor is maintained constant. Draw the relevant characteristics. (b) A 3-phase star-connected synchronous motor takes 20 kw at 400 V from the mains. The synchronous reactance is 4 ohms and effective resistance is negligible. If the exciting current is so adjusted that the back e.m.f is 550 V, calculate the line current and power factor of the motor. 7. (a) What is meant by constant power circle for synchronous motor? Explain. (b) What are the methods for starting the synchronous motors? Explain them. 8. Describe the construction and principle of operation of permanent magnet DC motor. What are the advantages and disadvantages of permanent magnet DC motor over conventional shunt DC motor? Give some important applications of permanent magnet DC motor. ** 1 of 1

15 R10 Set No: 1 Code No: R31022 ELECTRICAL MEASUREMENTS 1 a). Why the deflection and controlling torques are necessary in indicating instrument? Obtain the expression for deflection for a spring controlled moving iron instrument? b). Define Guarantee error? Explain various types of errors with appropriate examples? 7m 8m 2 a). Explain the construction and working of a 3-phase rotating filed power factor meter? 8 m b). A current transformer has two primary turns and 198 secondary turns and secondary impedance of The impedance connected to the secondary is and secondary current is 5 A. The ampere turns required to supply excitation and iron losses are respectively 8 and 4 V induced in the secondary. Determine (i) the primary current (ii) the phase angle error of the transformer. 7 m 3 a). Explain the construction and working of dynamometer type wattmeter? Derive its torque 10 m equation, when it used on a.c? b). Describe method of extending range of wattmeter using instrument transformers? 5 m 4 a). Explain with neat diagram the working of Verni type potentiometer? 8 m b). Calculate the inductance of a coil from the following measurements on a.c. potentiometer. The voltage drop across a 0.1 standard resistor connected in series with the coil. Voltage across test coil through a 100/1 voltage ratio box =, the frequency is 50 Hz. 7 m 1 of 2

16 Code No: R31022 R10 Set No: 1 5 a). Describe with a diagram of connections the loss of charge method of determining the insulation resistance of a length of cable. Prove the formula used for this determination? b). A Kelvin s double bridge having the ratio arm P = Q = p = q = The emf of battery is 50 V and resistance of 2 including battery circuit. The galvanometer has resistance of 500 and the resistance of the link connecting the unknown resistance to standard resistance may be neglected, the bridge is balanced when the standard resistance S = Determine (a) the value of unknown resistance (b) Determine the deflection of the galvanometer when unknown resistance R is changed by 0.2 % from its value at balance. The galvanometer has sensitivity of 200 mm/µa. 8 m 7 m 6 a). In what way Anderson's bridge is advantageous than Maxwell s bridge? 8 m b). The four arms of the bridge at balance has the following parameters : Arm ab: an imperfect capacitor C 1 with an equivalent series resistance r 1 Arm bc: a non inductive resistor R 3 = 200, Arm cd: a non inductive resistor R 4 = 2850, Arm da: an imperfect capacitor C 2 = 0.5 µf with an equivalent series resistance r 2 = 0.4 and an series resistance R 2 = 4.8, A supply at 450 Hz is connected between a and c and the detector is connected between b and d. Calculate the values of C 1 and r 1 and also dissipating factor for the capacitor? 7 m 7 a). Describe Hibbert s magnetic standard and B.H. Curve? 8 m b) Describe the Lloyd Fisher square method for measurement of iron losses? 7 m 8 a). Describe any one technique used in DVMs and state their advantages and disadvantages? 8 m b) Explain the operation of digital frequency meter with suitable diagram? 7 m

17 Code No: R31022 R10 Set No: 2 ELECTRICAL MEASUREMENTS 1 a). Explain deflecting system, controlling system and damping system with reference to an b). electrical indicating instrument? A current of is passed through the moving coil and moving iron ammeter. Find the current reading value in both the meters? 2 a). Explain the principle of working of dynamometer 1-phase power factor meter? How would b). the accuracy of such instrument be affected by the frequency and wave form variation? A potential transformer has a ratio of 2000/100 V. The primary winding resistance and reactances are 300 and 600 respectively. The secondary winding resistance and reactances are 0.75 and 1.5 respectively. Determine the voltage ratio correction factor, ratio error and phase angle error when the burden on the secondary of the transformer is (i) 75 VA at 0.6 p.f lagging (ii) 50 VA at unity p.f lagging 10 m 5 m 8 m 7 m 3 a). Explain the construction and principle of operation of a dynamometer type watt meter? How 10 m it can be made to measure power in DC and AC? b). Briefly describe about various compensations provided in single phase energy meter? 5 m 4 a). Explain how potentiometer is employed in measuring resistance, power and calibration of wattmeter? b). During the measurement of a low resistance using a potentiometer the following readings were obtained. Voltage drop across the low resistance under test V voltage drop across the 0:1 standard resistance V. Calculate the value of un known resistance, Current and power lost in it 1 of 2 8m 7m

18 Code No: R31022 R10 Set No: 2 5 a). Explain with the help of connection diagram how would you determine the value of low resistance by Kelvin s double bridge? Derive the formula used? b). The following results were obtained by loss of charge method of testing cable: discharged immediately after charging the deflection is 200 divisions. Discharged after 30 s after charging i) deflection of 125 divisions ii) when parallel with a resistance of 10 M, deflection of 100 divisions. Calculate the insulation resistance of the cable. 10 m 5 m 6 a). Derive the equations for balance in the case of Schering bridge. Draw the phasor-diagram for balance condition? b). The four arms of the bridge at balance has the following parameters : 8 m 7 m Arm ab: an imperfect capacitor C 1 with an equivalent series resistance r 1 Arm bc: a non inductive resistor R 3 = 200, Arm cd: a non inductive resistor R 4 = 2850, Arm da: an imperfect capacitor C 2 = 0.5 µf with an equivalent series resistance r 2 = 0.4 and an series resistance R 2 = 4.8, A supply at 450 Hz is connected between a and c and the detector is connected between b and d. Calculate the values of C 1 and r 1 and also dissipating factor for the capacitor? 7 Describe the Lloyd Fisher square for measurement of iron losses in a specimen of lamination. Describe how corrections for resistance of Wattmeter pressure coil and resistance of secondary windings are applied? 15 m 8 a). Explain constructional details and working dual slope integrating type DVM? 8 m b) Explain constructional details and working digital tachometer? 7 m

19 Code No: R31022 R10 Set No: 3 ELECTRICAL MEASUREMENTS 1 a). Classify the electrical measuring instruments based on how the deflecting torque is b). produced? The coil of a moving coil galvanometer is wound on a non-magnetic former whose height and width are both 2 cm. It moves in a constant field of 0.12 wb/m 2. The moment of inertia of its moving parts kg-m 2, and the control spring constant is Nm/rad. Calculate (i) the number of turns that must be wound on the coil to produce a deflection of with a current of 10 ma (ii) the resistance of the coil to produce critical damping? (iii) 2 a). Draw and explain the working of 3-phase electrodynamometer type power factor meter? 8 m b). A potential transformer has a ratio of 2000/100 V. The primary winding resistance and reactances are 110 and 75 respectively. The secondary winding resistance and reactances are 0.5 and respectively. When it is operated on no load it takes 0.05 A at 0.45 p.f. lagging. Determine (a) phase angle error on no load (b) phase angle error on load of 5 A at 0.85 p.f lagging and (c) VA burden at unity p.f to have zero phase angle. 5 m 10 m 7 m 3 a). Explain the use of copper shading bands in case of induction type energy meters? What is 8 m Creep? b). Describe in detail the working and construction of Trivector meter? 7 m 1 of 2

20 Code No: R31022 R10 Set No: 3 4 a). Describe the construction and working of a polar type potentiometer? Describe the procedure of standardization? b). During the measurement of a low resistance using a potentiometer the following readings were obtained. Voltage drop across the low resistance under test V voltage drop across the 0:1 standard resistance V. Calculate the value of un known resistance, Current and power lost in it 8 m 7 m 5 a). What are the important precautions to be taken when using Kelvin s double bridge? 5 m b). In a Carey-Foster bridge, a resistance of is compared with a standard resistance of 1, the slide wire has resistance of in 100 divisions. The ratio of arms normally 10 each are actually and 9.94 respectively. How far (in scale division) are the balance positions from those would obtain if arms ratio were true to their nominal value? The slide were is 100 cm long. 10 m 6 Describe how an unknown capacitance can be measured with the help of D sauty s bridge? What are the limitations of the bridge and how are they overcome by using a modified form of D stauty s bridge? 15 m 7 a). Describe the construction and working of flux meter? 8 m b). Describe a method of using an a.c. potentiometer for measuring the loss in an iron ring made 7m up of thin stampings? 8 a). Explain constructional details and working dual slope integrating type DVM? 8 m b). Explain constructional details and working digital tachometer? 7 m

21 Code No: R31022 R10 Set No: 4 ELECTRICAL MEASUREMENTS 1 a). Explain the principle of deflection torque production in moving coil and moving iron b). instruments? Obtain their expressions for spring controlled instruments? A 1 k resistance is connected in parallel with 500 resistance. This parallel resistance is connected with 100 V DC supply having 1 k series resistance. A 100 ammeter is used to measure the value of current in the 500 resistance. Calculate (i) actual value of current (ii) measured value of current (iii) the percentage error in the measurement? 8 m 7 m 2 a). Describe the effect of burden of secondary winding and power factor of secondary winding on the characteristics of potential transformer? b). A current transformer of nominal ratio 1000/5 A is operating with total secondary impedance of At rated current the components of the primary current associated with the core magnetizing and core loss effects are respectively 6 A and 1.5 A. The primary has 4 turns. Calculate the ratio error and phase angle at rated primary current if secondary has (a) 800 turns (b) 790 turns 8 m 7 m 3 a). Explain principle of working of single phase induction type energy meter? Derive the expression relating number of revolutions and energy? b). Explain errors caused due to pressure coil inductance and pressure coil capacitance in electro dynamometer watt meter? 8m 7m 1 of 2

22 Code No: R31022 R10 Set No: 4 4 a). Describe the steps for measurement of unknown resistance using Crompton s d.c. potentiometer? b). Calculate the inductance of a coil from the following measurements on a.c. potentiometer. The voltage drop across a 0.1 standard resistor connected in series with the coil. Voltage across test coil through a 100/1 voltage ratio box =, the frequency is 50 Hz. 5 a). Explain with the help of connection diagram how would you determine the value of low resistance by Carey-Foster bridge? Derive the formula used? b). The following results were obtained by loss of charge method of testing cable: discharged immediately after charging the deflection is 200 divisions. Discharged after 30 s after charging i) deflection of 125 divisions ii) when parallel with a resistance of 10 M, deflection of 100 divisions. Calculate the insulation resistance of the cable. 6 a). Describe working of Hay's bridge? Why is this bridge suited for measurement of inductance of high Q coils? b). The arms of a five node bridge are as follows: arm ab: an un known impedance (R1, L1) in series with a non-inductive variable resistor r1, arm bc: a non inductive resistor R3 = 100, arm cd: a non inductive resistor R4 = 200, arm da: a non inductive resistor R2 = 250, arm de: a non inductive variable resistor r, arm ec :a lossless capacitor C = 1 µf and arm be: a detector an A.C. supply is connected between a and c. Calculate the resistance and inductance R1, L1 when under balance conditions r1 = 43.1 and r = Describe a method of using an a.c. potentiometer for measuring the loss in an iron ring made up of thin stampings. Explain how the loss may be calculated in terms of the maximum density and state any assumptions made? 8m 7m 10 m 5 m 8 m 7 m 15 m 8 a). Describe how the digital frequency meter is used to measure period, frequency and time 8 m interval of a wave form? b) Explain the operation of digital multi meter with suitable diagram? 7 m

23 Code No: R31026 R10 Set No: 1 LINEAR & DIGITAL IC APPLICATIONS 1. a) Explain why level translator in an op-amp is a voltage follower. Also explain the operation of a level translator in an op-amp. b) Present the different packaging types for integrated circuits and discuss. (8+7) 2. a) Explain the term slew rate. Derive the expression for maximum frequency at which distortion sets in due to slew rate limitation. b) Explain lag compensation method. (8+7) 3. a) Explain the operation of a precision full wave rectifier using relevant equivalent circuits. b) For the integrator circuit shown in figure below show that v o = (1/RC)v i dt (10+5) 4. a) Explain the operation of a monostable multivibrator and derive the expression for pulse width. Use relevant diagram and waveforms. b) Discuss the application of PLL as an FM demodulator. (9+6) 5. a) Explain the operation of a weighted resistor DAC. b) Write the design requirements of a BPF. Also draw a typical diagram of such filter using op-amp. (9+6) 6. a) Design a combinational circuit to realize a half adder also present the block schematic to realize a full adder using two half adders. b) Explain the operation of a 4 bit ripple adder. (8+7) 7. a) Explain the operation of a SR flip-flop using a truth table. Also obtain its excitation table. b) Design and implement a mod 14 counter. (8+7) 8. a) Write short notes on internal structure of SRAM. b) Implement half adder using PLA. (7+8) 1 of 1

24 Code No: R31026 R10 Set No: 2 LINEAR & DIGITAL IC APPLICATIONS 1. a) Obtain differential mode gain of a differential amplifier using an ac equivalent circuit. b) Present the classification of integrated circuits based on scales of integration and discuss. (7+8) 2. a) Draw the high frequency model of an op-amp and explain its frequency response. b) An op-amp has a slew rate of 2 V/s. What is the maximum frequency of an output sinusoid of peak value 5V at which distortion sets in due to slew rate limitation. c) Explain the term input bias current. (7+4+4) 3. a) Explain the operation of antilog amplifier and obtain the expression for output voltage. b) Find output voltage for the circuit shown below for V 1 = 5V and V 2 = 3V. (9+6) 4. a) Explain the operation of Schmitt trigger using a 555 timer. (6+9) b) Discuss the applications of PLL in frequency division and also frequency translation. 5. a) Explain the operation of a R-2R ladder DAC. b) Write the design requirements of a band reject filter. Also draw a typical diagram of such filter using op-amp. (9+6) 6. a) Design a combinational circuit to realize a 4X1 multiplexer. b) Design a combinational circuit to perform 3 bit comparison. (7+8) 7. a) Explain the operation of a D flip-flop using a truth table. Also obtain its excitation table. b) Design and implement a mod 6 ring counter. (8+7) 8. a) Write short notes on internal structure of DRAM. b) Implement half subtractor using PLA. (7+8) 1 of 1

25 Code No: R31026 R10 Set No: 3 LINEAR & DIGITAL IC APPLICATIONS 1. a) Write the differences between the differential amplifiers used in first two stages of an op-amp. b) Present the properties of dual input unbalanced output differential amplifier configuration. (7+8) 2. a) Explain the term input offset voltage. For the non-inverting amplifier shown in figure below R 1 =1k and R f =10k. Calculate the maximum output offset voltage due to input offset voltage of 10mV and input bias current of 300nA. Also find the value of compensating resistor required to compensate the effect of input bias current. b) Explain the terms PSRR and drift. (10+5) 3. a) Explain the operation of a V-I converter using relevant diagrams. (8+7) b) For the circuit shown in figure below calculate the trigger points. Plot the output voltage v o vs t for two cycles if vi is a 100Hz triangular wave of magnitude ±10V. 1 of 2

26 Code No: R31026 R10 Set No: 3 4. a) Explain the operation of an AC inverting amplifier. (5+10) b) Draw the circuit of a Schmitt trigger using a 555 timer and explain its operation. 5. a) Explain the operation of counter type ADC. b) Write the design requirements of any 1 st order LPF. Also draw a typical diagram of such filter using op-amp. (9+6) 6. a) Design a combinational circuit to realize 4: 2 decoder. b) Implement a 16X1 multiplexer using 4X1 multiplexers. (7+8) 7. a) Explain the operation of a T flip-flop using a truth table. Also obtain its excitation table. b) Design and implement a mod 10 Johnson counter. (8+7) 8. a) Compare and contrast PAL, PLA and ROM. b) Implement full adder using ROM. (8+7) 2 of 2

27 Code No: R31026 R10 Set No: 4 LINEAR & DIGITAL IC APPLICATIONS 1. a) Explain how level shifter can be used as a buffer to isolate high gain stages from the output stage. b) Explain the use of a constant current circuit in a differential amplifier. (8+7) 2. a) Draw the block diagram of op-amp and describe the functionality of each block. b) Explain the term output offset voltage. A 741 op-amp is used as an inverting amplifier shown in figure below with R 1 =1k and R f =100k. What is the maximum output offset voltage caused by the input offset voltage of 6mV. (7+8) 3. a) Explain the operation of a square wave generator using op-amp using relevant diagram and wave forms. Also derive the expression for frequency of the waveform generated. b) Find R1 and R2 in figure shown below if V o is the average of V 1 and V 2 and R f = 10K (9+6) 1 of 2

28 Code No: R31026 R10 Set No: 4 4. a) Explain the application of monostable multivibrator as a missing pulse detector. b) Explain the operation of astable multivibrator using 555 timer also derive the expression for frequency of wave form generated. (6+9) 5. a) Explain the operation of an inverted R-2R ladder DAC. b) Write the design requirements of any 1 st order HPF. Also draw a typical diagram of such filter using op-amp. (9+6) 6. a) Design a combinational circuit to realize a 1X4 demultiplexer. b) Explain the working of a 4 bit parallel binary adder. (8+7) 7. a) Explain the operation of a JK flip-flop using a truth table. Also obtain its excitation table. b) Explain the operation of a 4 bit parallel- in parallel- out shift register. (8+7) 8. a) Write short notes on synchronous DRAMS. b) Implement full subtractor using PAL. (8+7) 2 of 2

29 Code No: R31024 POWER ELECTRONICS 1. a) What is power MOSFET? What are the types of power MOSFETs? Write the difference between general purpose MOSFET and power MOSFET? b) Describe the different methods, of triggering SCR. 2. a) Define String efficiency. What is the derating factor of a series connected thyristors? Prove that string efficiency of two series connected SCRs is less than unity or 1. b) Describe the basic behavior of thyristor using a two- transistor model. 3. Draw the circuit diagram of single- phase full wave controlled rectifier using centre tap transformer with RL load and free wheeling diode. (b) Prove that the average output 2V voltage at firing angle is V o = (1 + cos α ) π 4. a) A single phase fully controlled bridge converter with RLE load is supplied from 230 V, 50 Hz ac supply. The average load current is 5 A which is constant over the working range. Determine the firing angle for (i) E = 100 V (ii) E = V. Assume R = 4 and L= 5 mh b) Explain how a free wheeling diode improves power factor in a converter. 5. a) Draw the circuit diagram of a three phase mid point six pulse controlled rectifier with R load. Discuss its working principle b) A three phase half wave controlled rectifier is connected to a 3, 220 V, 50 Hz ac supply and it is also connected with a resistive load of 5. If the firing angle of thyristor is 60 o, calculate (i) dc output voltage, (ii) rms value of output voltage, (iii) average output. 6. a) What is ac voltage controller? What are the types of ac voltage controllers? b) A single phase full wave ac voltage controller is connected with a load of R = 10 with an input voltage of 230 V, 50 Hz. When the firing angle of thyristors is 45 o, determine (i) power output at load, ( ii) average value of thyristor current and ( iii) rms value of thyristor current. 7. A step down chopper has a load resistance of 20 and input dc voltage is 200 V, When the chopper switch is ON, the voltage across semiconductor switch is 2 V. If the chopping frequency is 1.5 k Hz and duty ratio is 40%, determine (a) average dc output voltage, ( b) rms output voltage and ( c) efficiency of chopper. 8. a) What is an inverter. What are the types of inverters? What are the applications of inverter circuit? What are the switching devices used in inverter circuit? b) A 3-phase bridge inverter is fed with 600 V dc supply. If the semiconductor switches(transistors) which are used in inverter conducts for 120 degrees duration and the inverter is supplying a star connected resistive load of 10, determine i) rms value of per phase voltage and line voltage ii) rms value of load current and iii) power delivered to load. 1 of 1 R10 Set No: 1

30 Code No: R31024 R10 Set No: 2 POWER ELECTRONICS 1. a) Explain the safe operating area (SOA) of a power MOSFET. What is the effect of pulse width on SOA. b) What are the different turning ON methods of a thyristor? Explain each method. 2. a) Explain the common technique for current sharing of parallel connected thyristors. Prove that string efficiency of two parallel connected SCRs is less than unity or 1. b) Distinguish between the following :i)voltage commutation and ii)current commutation 3. a) Write the advantage of free wheeling diode in single phase half wave controlled rectifier with RL load. b) A single phase 220 V, 1 k W heater is connected to a half- wave controlled rectifier fed from a 220 V, 50 Hz ac supply, Determine the power absorbed by the heater when the firing angle is (i) = 30 o and (ii) = 90 o. 4. a) What is the effect of source inductance in single phase full wave controlled bridge rectifier with RL load? and explain the operation of the bridge. b) Draw the voltage and current waveforms of the above circuit. 5. A three phase converter is fed to a RLE load and draw the output voltage and current wave forms. Derive the expression of current flow through load. 6. a) Define power factor. Derive an expression for power factor of a bidirectional ac voltage controllers with R load. b) Explain the operating principle of mid-point-type single phase to single phase step up cycloconverter. Mention the conduction of various thyristors in the waveforms. 7. a) State the current limit control? Explain the difference between current limit control and time ratio control. Why current limit control is proffered over any other control strategies? b) Discuss the principle of operation of BUCK-Boost converter. 8. Explain the operating principle of inverter with a suitable diagram. Draw the voltage and current waveforms of inverter. Derive the expression for rms output voltage. 1 of 1

31 Code No: R31024 R10 Set No: 3 POWER ELECTRONICS 1. a) Draw the V-I characteristics of a thyristor and explain different operating regions. What is the effect of gate current on the V-I characteristics of a thyristor? b)compare Power MOSFET and IGBT 2. a) What do you mean by the following terns in a UJT: (i) UJT triggering circuit (ii) Synchronised UJT triggering circuit (iii) Ramp and pedestal triggering circuit. b) Distinguish between the following: i)natural commutation and ii)forced commutation 3. Draw the circuit diagram of a single phase full wave controlled rectifier using centre tap transformer with R load and find (a) dc output voltage (b) average d.c. load current (c) rms output voltage (d) rms load current (e) Ripple factor (g) efficiency 4. What are the different modes of operation of single phase full wave controlled rectifier using centre tap transfer with RL load? Draw voltage and current waveform in each operating mode. 5. Draw the circuit diagram of three phase half wave controlled rectifier with R load and explain its operating principle with voltage and current waveforms. Determine the following parameters for R load with firing angle = 60 o : (a) dc output voltage (b) Average dc load current (c) rms output voltage (d) rms load current 6. a) Discuss the operating principle of single phase to single phase step down cycloconverter using bridge converters. Mention the conduction of various thyristors in the wave forms. b) Draw the single phase bidirectional ac voltage controller with R load and explain its working principle with waveforms. 7. a) What are the different control strategies of DC Choppers? b) A 100 V dc chopper operates using current limit control (CLC) strategy, the maximum value of load current is 250 A and the lower limit of current is 50 A. The ON- time and OFF time of chopper are 20 ms and 30 ms respectively. Determine ( i) the limit of current pulsation, (ii) chopping frequency, (iii) duty cycle and (iv) output voltage. 8. a) What are pulse width modulated inverters? What are the different PWM techniques used in inverter? b) A single-phase PWM inverter is fed from a 220 V dc supply and it is connected to a RL load with R=10 ohms and L=10 mh. Determine the total harmonic distortion in the load current.assume width of each pulse is /2 and the output frequency is 50 Hz. 1 of 1

32 Code No: R31024 R10 Set No: 4 POWER ELECTRONICS 1. a) Explain the turn ON and turn OFF time of SCR b) Draw the switching characteristics of IGBT. Define turn ON delay time, rise time, turn- ON time, turn-off delay time, first fall time, final fall time and turn OFF time. 2. a) What is commutation? What are the types of commutation? Explain any one commutation circuit with a diagram and waveforms. b) Thyristors with a rating of 1250 V and 200 A are used in a string to handle 10 k V and 1 k A. Determine the number of series and parallel connected thyristors in case derating factor is (i) 0.2, (ii) a) What is phase angle controlled technique? Explain the operation of single phase angel controlled rectifier. Derive the expression for average dc output voltage. b) A Single phase half wave controlled rectifier with R load is supplied from a 230 V, 50 Hz ac source, When average dc output voltage is 50% of maximum possible average dc output voltage, determine (i) firing angle of thyristor, (ii) average dc output, (iii) rms output voltage, Assume R = a) A single phase full wave controlled rectifier using centre tap transformer is fed from a 230 V, 50 Hz ac source and it is connected a resistive load R = 10. Determine (i) the output voltage, ( ii) form factor, ( iii) efficiency, at = 30 o. Turn ratio of transformer is 1:1. b)write the applications of phase controlled rectifiers. 5. A three phase full converter is connected to a load resistance of 5 and it is supplied form a 220 V, 50 H ac supply, If the firing angel of thyristor is = 30 o, determine (a) average output voltage, (b) average output current, (c ) rms output voltage and (d) rms output current. 6. a) What are the advantage and disadvantage of phase control? b) Explain the working of TRIAC as voltage controller with RL loads and draw the output voltage waveform. 7. Explain the operating principle of dc chopper with a suitable diagram. Draw the voltage and current waveforms of chopper. Derive expressions for average output voltage and rms output voltage. 8. a) Explain the operation of a basic Single Phase Series Inverter. b) A Single-Phase transistorized full bridge bipolar PWM inverter is operated from a 120 V dc battery and it is connected with a RL load. If the modulation index is 0.9, determine i) rms output voltage, ii) fundamental output voltage iii) distortion factor of output voltage waveform. 1 of 1

33 Code No: R31023 R10 Set No: 1 POWER SYSTEMS II 1. (a) Show that the inductance per unit length of an overhead line due to internal flux linkages is constant and is independent of size of conductor. (b)discuss how transmission helps in equalizing the capacitances in an unsymmetrically spaced 3-phase overhead transmission line. 2. (a) What is the purpose of an overhead transmission lines? How are these lines classified? (b) A balanced 3-phase load of 20MW is supplied at 132kV, 50Hz and 0.8 p.f. lagging by means of a transmission line. The series impedance of a single conductor is ( j45) ohms and the total phase-neutral admittance is mho. Using nominal- method, find: (i) The A, B, C and D constants of the line, (ii) Sending end voltage and (iii) Regulation of the line 3. (a) What do you understand by long transmission lines? How capacitance effects are taken into account in such lines? (b) A 400kV, 3-phase transmission line has an impedance per phase of (40+j90)ohms and an admittance of 0+j0023mho. Using the convergent series method, find (i) the sending end voltage and(ii) the sending end current when the receiving end current is 160Amps at 0.85 p.f lagging 4. (a) Show that a travelling wave moves with a velocity of light on the over head line and 1 its speed is proportional to on a cable with dielectric material of permittivity ε r. ε r (b) An 510kV, 3µSec rectangular surge travels along the line terminated by an capacitance of 2400pF. Determine the voltage across the capacitance and reflected voltage wave if the surge impedance of the line is 350 ohms. 5. (a) Explain the Ferranti effect and derive an expression for power loss in an open circuited line. (b) A 132 kv, 3 Phase, 50 Hz transmission line, 200 km long consists of three 1.2 cm diameter stranded copper conductors spaced in 3.5 m delta arrangement. Temperature taken at 26 0 C and barometric pressure as 73 cm. Assume surface irregularity factor m= 0.85 (Roughness factor) m v for local corona= 0.72 and m v for general corona=0.82. Calculate the following (i) Disruptive voltage (ii) Visual corona voltage for local corona (iii) Visual corona voltage for general corona and (iv) Power loss due to corona using Peek s formula under fair weather and wet conditions 1 of 2

34 Code No: R31023 R10 Set No: 1 6. (a) What is a stringing chart? Explain clearly the procedure adapted for stringing the power conductors on the supports. (b) Find the erection sag and tension of the line use particulars as follows: nominal span = 2. 5 m conductor data : Size = /2.79 mm steel cored aluminum Nominal copper area = 115mm 2 Weight per metre = kg Ultimate strength 7960 kg Coefficient of linear expansion per degree centigrade = Modulus of elasticity kg/mm 2 3 = The factor of safety based on worst loading conditions (radial ice thickness 0.95cm and wind pressure 39kg/m 2 of projected area at 5.5 C ) is to be 2. The line is to be erected at 50 C in still air, weight of ice of 913 kg/m (a) Why are insulators used with overhead lines? Discuss the desirable properties of insulators. (b) A three phase over head transmission line is suspended by a suspension type insulator which consists of three units. The potential across top unit and middle unit are 5 kv and 9 kv respectively. Determine the following (i) The ratio of capacitance between pin and earth to the self capacitance of the each unit (ii) The line voltage (iii) String efficiency 8. (a) Explain the importance of voltage control in the modern power systems. (b) A 450 HP, 50 Hz, 6 kv, star-connected 3-φ induction motor has: F.L. efficiency = 90 %, F.L. power factor = 80% lagging is connected to a feeder. DEtermine the rating of capacitor bank to improve load p.f. to 95% by connecting the bank at induction motor load. When (i) capacitors in star and (ii) capacitors in delta 2 of 2