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Question 1

(a) A two-legged magnetic core has dimensions as follows:Cross-sectional area Ac=1.8x10

-3 m2

Mean core length lc=0.6 m

Single gap length g=2.3x10-3

m on the right-hand leg of the coreN=83 turns on the left-hand leg of the core

Neglect fringing fields at the air gap and the leakage flux. Assume that the core is of infinite

permeability. Calculate(i) the reluctance of the core and the air gap. [3

Marks]

(ii) the coil current which will result in a core flux density of 1.0 T. [3 Marks]

(b)A two-legged magnetic core with an air gap is shown in Figure Q1-b(i).The depth of the core is 5 cm, the length of the air gap in the core is 0.06cm, and the number of turns on the coil is 1000. The magnetization curve

of the core material is shown in Figure Q1-b(ii). Assume a 5 percentincrease in effective air-gap area to account for fringing. (i) Determinethe current required to produce an air-gap flux density of 0.5 T? (ii)Determine the flux densities of the four sides of the core at that current?

[19 Marks]

Figure Q1-b(i)

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Continued..

Figure Q1-b(ii)

Question 2

(a) For the -Y 3-phase system shown in Figure Q2-a:

(i) Find the voltage across each phase of the load. [6 Marks](ii) Find the magnitude of the line voltages. [4 Marks]

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+

+

a

c

n

Ibn

ICc

= 2 A 120

IBb

= 2 A -120

33

3

EBC

Ian

IAa

= 2 A 0

44

3-phase

-connected

generator

Phase

sequence:ABC

4

ECA

EAB

Figure Q2-a

Icn b

+

A

B

C

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Continued..

(b) A star-connected load having an impedance of (180 13.53 ) per phase is connected

in parallel with s delta-connected load having an impedance of (32.45 69.33 ) perphase. With both the loads being balanced, and fed from a three-phase voltage of 230

0 V, find the following:

(i) magnitude of the line current [7 Marks](ii) power factor [2 Marks]

(iii) total real power [2 Marks]

(iv) total reactive power [2 Marks]

(v) total volt-amperes (VA) [2 Marks]

Question 3

(a) What are the functions of potential transformer and current transformers? With a schematic

diagram, show how these are used. [10 Marks]

(b) A 100-kVA, 1100/230-V, 50-Hz transformer has a primary winding resistance of 0.1 and a

leakage reactance of 0.4 . The secondary winding has a resistance of 0.006 and a leakagereactance of 0.01 . Find the following:

(a) The equivalent circuit of the transformer referred to the low voltage side.

[7.5 Marks](b) The voltage regulation at rated condition and at 0.8 pf lagging. [7.5 Marks]

Question 4

(a) A 400-V, 3-phase, 1500-rpm, Y-connected induction motor has the following parameters:R1= 1.5 , R2 = 1.2 , Xe=X1+X2 = 8

Assume that the magnetizing branch is neglected. If a reactor of X= 4 is connected in

series with the line, draw the equivalent circuit and calculate the starting torque, and themaximum torque developed. [10 Marks]

(b) Sketch with a proper labeling a typical torque-speed characteristic curve. [6 Marks]

(c) A 50-kW, 440-V, 50-Hz, six-pole induction motor has a slip of 6 percent when operating at

full-load conditions. At full-load conditions, the friction and windage losses are 300-W, andthe core losses are 600-W. Find the load and induced torques for full-load conditions.

[9 Marks]

Question 5

(a) On which part of the synchronous machine are the armature and the field windings normally

mounted? State the reasons. [8 Marks]

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(b) A three-phase, 9-kVA, 415-V, two-pole, 50-Hz, Y-connected synchronous machine has

negligible stator winding resistance and a three-phase synchronous reactance of 30 at rated

terminal voltage. The machine is first operated as a generator in parallel with a three-phase,415-V, 50-Hz power supply.

(i) Determine the excitation voltage and the power angle when the machine is deliveringrated kVA at 0.85 pf lagging. [5 Marks]

(ii) If the field excitation current is now increased by 20% (without changing the prime-

mover power), find the stator current, power factor, and reactive kVA supplied by

the machine. [7 Marks](iii) With the field current as in (i), the prime-mover power is slowly increased. What

is the steady-state stability limit? Find the corresponding values of the stator current,

power factor, and real power at this maximum power transfer condition?[5 Marks]

Question 6

(a) Explain the meaning of regulation curve? With the help of sketches explain the

regulation curves of an alternator. [7 Marks]

(b) List out the advantages of parallel operation of synchronous generators and explain the

synchronizing procedure. [12 Marks]

(c) A 3-phase synchronous generator has a direct-axis synchronous reactance of 0.6 p.u.

and a quadrature-axis synchronous reactance of 0.4 p.u. The generator is supplying a

full-load current of 1.0 p.u at 0.8 lagging power factor and 1.0 p.u terminal voltage.

Calculate the power angle and the no-load voltage if the excitation remains unchanged.

Draw the phasor diagram for this condition. [6 Marks]

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