(Solved): electrical machine Questions and answers will be written by hand. Any writing other than will not be ...

Questions and answers will be written by hand. Any writing other than will not be accepted. It will be used on A4 paper for homework. A4 paper borders will be as follows. \( 3 \mathrm{~cm} \) blank on left and right sides and bottom, page numbers will be written. In addition, your name and surname and number will be written on the front page. Grades: Question : Each of them is 5 puan Questions: 1. Consider the solid ferromagnetic core shown in below figure. The depth of the solid core is \( 5 \mathrm{~cm} \). Assume that the relative permeability of the core is 1000 and remains constant and that the current value in the coil is \( 4 \mathrm{~A} \). Ignore the fringing effects at the air gap and determine the following: (a) The equivalent circuit of the given core shown in Figure (b) The individual values of all reluctances (c) The value of the total reluetance of the core (d) The value of the total flux that exists in the core (e) The individual value of each flux that exists in each leg of the core. 2. A balanced, three-phase, delta-connected load is supplied by a balanced, wye-connected source over a balanced three-phase line. The source voltage data are given in \( a b c \) phase sequence in which \( V a n \) is \( 7.62 \angle 0^{\circ} \mathrm{kV} \) and the line impedance is \( I+j 7 \Omega \). If the balanced load consists of three equal impedances of \( 15+j 10 \Omega \), determine the following: (a) The line currents \( I a, I b \), and \( I c \) (b) The phase voltages \( V a b, V b c \), and \( V c a \) of the deltaconnected load (c) The phase currents Iab, \( \boldsymbol{I} b \), and \( \boldsymbol{I} c a \) of the delta-connected load (d) The phasor diagram of the phasors found in parts (a), (b), and (c) 3. The Secondary of a \( 500 \mathrm{kVA}, 44001500 \mathrm{~V}, 50 \mathrm{~Hz} \), singlephase transformer has 500 turns. Determine (i) emf per turn, (ii) primary turns, (iii) secondary full load current (iv) maximum flux (v) gross cross-sectional area of the core for flux density of \( 1.2 \) tesla and iron factor is \( 0.92 \) (vi) if the core is of square cross-section find the width of the limb. 4. A \( 230 \mathrm{~V}, 50 \mathrm{~Hz} \) transformer bas 200 primary tums. It draws \( 5 \mathrm{~A} \) at \( 0.25 \mathrm{p} \).f lagging at no-load. Determine: (i) Maximum value of flux in the core; (ii) Core loss; (iii) Magnetising current (iv) Exciting resistance 5. The furns ratio of \( 212 \mathrm{kVA} \) sitgle-phise trandormer is \( \mathrm{8} \). The resistance and reactance of the peimary is \( 0.85 \mathrm{otm} \) and \( 4.8 \) chm, respectively and the corresponding values for the secondary ate \( 0.012 \) ohm and \( 0.07 \) ohms, reyectively. The voltape to be appliad to the primary to obtain a current of 150 A in the secondary when the secondary terminal are short circuited. Ignore tbe magnetising cuarent. Determine 6. Sesondary resistance referred to primary, 7. Equivalent resistacce referred to primary 8. Secondary reactance referred to primary 9. Epuivalent neactance teferred to primary. 10. Equivalent impedance referred to primary. 11. Shart eircuit current sefersed to primary. 12. Woluge applied to the primary under shor eircuit condition 6. The armature and series field winding risistance of a \( 220 \mathrm{~V} \). four-pole DC serics motor is \( 0.75 \) ohm. It has 782 wave wound anmature conductors. If it draws \( 40 \mathrm{~A} \) from the supply mains and has a flux of \( 25 \mathrm{mWb} \), deternine its speed and induced torgae developed. shumt field resistance of a four-pole, lap wound DC shunt motor is \( 0.05 \) ohm andz5 ohm respectively. If is armature contains 500 conductors, find the speed of the moeor when it take \( 120 \mathrm{~A} \) froen a DC mains of \( 100 \mathrm{~V} \) supply. Flux per pole is \( 2,10-2 \mathrm{~Wb} \) 8. The electromagnetic toryue developed in a \( \mathrm{DC} \) machine is 80 Nin for an armatief current of \( 30 \mathrm{~A} \). What will be the tortyot for a current of \( 15 \mathrm{~A} \) ? Assurse constant fleck. What is the indoced emf at aqpeed of \( 900 \mathrm{~mm} \) and an armature current of \( 15 \mathrm{~A} \) ? 9. A \( 152 \mathrm{~V} \mathrm{DC} \) shant motor has an armature resistance of \( 0.3 \) othm, a brush voluge drop of \( 2 \mathrm{~V} \), the rated full lead current is \( 70 \mathrm{~A} \). Calculate (i) the current at the instant of saiting as a persentage of fill load current (iii) the valuc of starting resistance to limit the moter current at the instant of starting to 150 percent of the rated had cuirent. 10. A 10 b.h.p. \( (7.46 \mathrm{~kW} \), \( 200-\mathrm{V} \) shunt motoe has full-load sfficiency of \( 85 \% \). The ammature has a resistance of \( 0.238 \) Calculate the value of the starting resistance necessary so limit the starling current io \( 1.5 \) times the fall-load eursent ai the moment of first switching on. The shuat curtent may be meglocted. Find also the back emf of the nootoc, when the eurrent has fallen to ies full-load value, assuming that the whole of the starting resistance is still in circuit. 11. A 1-phase \( 60 \mathrm{KVA}, 220 \mathrm{~V}, 50 \mathrm{~Hz} \), allernasor has an effective armafure leakage reactanes of 0- 07 ohm and negligible armature resistance. Calculate the voltage induced in the armature when the alternator is delivering rated currest at a load proce factor of \( 0.7 \) lagging. 12. A three-phase, star-6onnested, \( 10 \mathrm{kVA}, 400 \mathrm{~V} 50 \mathrm{H} z \) alternator has armature resistance of \( 0.5 \mathrm{ohm} \) phase and synchronous reactance 10 ohm/phase. Detemuine is torque anyle and volage regulation ubich if supplics rated load at \( 0.8 \) pf lagging. 13 A 3.petase, \( 10 \mathrm{HP} \) squirel cage indoction motor is wound for 6 poles. When the motot is coenscted b \( 230 \mathrm{~V}, 50 \mathrm{Hi} \). supply, at full-load, it operaies at \( 4 \% \) slip. Deternine (i) full loud speed, (ii) fual load norque in Newtoe-metre, (iii) frequency of rotor current under this coobition and ( \( \mathrm{w} \) ) spoed of cotation of the stator minn 14 An \( 8 \mathrm{HP}, 3 \)-phase, 4-pole squirncl cage induction motor is connected to \( 400 \mathrm{~V}, 50 \mathrm{Fiz} \) srpply. The motor is operating at full-load with \( 5 \% \) slip. Calculate the following: (i) The speed of the revolving field relative to the stator structureriii) The frequency of the rotor currents; (iii) The speed of the rotor menf relative to the rotor structure; (iv) The speed of the rotor \( \mathrm{mmf} \) relative to the stator structurc; (v) The speed of the rotor mmf relative to the stator field distribution; (vi) Are the conditions right for the development of the net unidirectional torque? 15. The resistance and stand-still reactance per phase of a 3. phase, 4-pole, \( 50 \mathrm{~Hz} \) induction motor is \( 0.2 \mathrm{ohm} \) and \( 2 \mathrm{obm} \) respectively. The rotor is connected in star and emf induced between the sliprings at start is \( 80 \mathrm{~V} \). If at full-load motor is running at a speed of \( 1440 \mathrm{~mm} \), calculate (i) the slip, (ii) rotor induced emf per phase, (iii) the rotor current and power factor under running condition and (iv) rotor current and p.f. at standstill when the slip rings are short circuited. 16. A 3-phase, 6-pole induction motor is supplied from a 3phase, \( 400 \mathrm{~V}, 50 \mathrm{~Hz} \) supply. If it is operating at full-lood with \( 0.04 \) slip, determine: (i) The speed of the revolving ficld relative to the stator structure. (ii) The frequency of the rotor currents. (iii) The speed of the rotot mmf relative to the rotor structure. (iv) The speed of the rotor mmf relative to the stator structure. (v) The speod of the rotor mmf relative to the stator field distribution. (w) Are the conditions night for the development of the net unidirectional torque?." 17. A single.phase induction motor draws a current of \( 0.6 \mathrm{~A} \) at \( 230 \mathrm{~V} \) and \( 0.6 \) lagging \( p \).f. If in runs at a speed of 100 radian per second and develops an eutput loryec of \( 0.25 \mathrm{Nm} \), find its outpoit power and efficiency. 18 The main winding of a \( 110 \mathrm{~N}, 60 \mathrm{~Hz}, 0.25 \mathrm{hp} \), single phase capacitor start motor carries a current of 6-ampere which lags behind the applied voltage by \( 42^{\circ} \). The starting winding carries a current of \( 4 \mathrm{~A} \) which leads the voltage vector by \( 40^{\circ} \), Calculate (i) the voeal starting current and the power factor. (ii) the phase angle between the main winding current and starting winding current. 19. The main winding of a \( 230 \mathrm{~V}, 0.5 \mathrm{HP} \) single-phase induction motor (split-phase) draw a current of \( 6 \mathrm{~A} \) which lags behind the voltage vector by \( 45^{*} \) " whereas the starting winding draw a current of \( 4 . A \) which lags being the voltage by \( 15^{\circ} \). Determine (i) Current drawn by the motor at stant and its pf. (ii) Current draw by the modor during running and its pf. (iii) Phase angle between the current drawn by the main winding and starting winding. (iv) Power drawn by the motor during starting and running. 20. a) What is an ideal transformer? b) Even at no-load, a transformer draws cument from the mains. Wby? c) What are the various types of I-phase motors? d) What are the starting methods of single-phave motor