This document contains solutions to problems from chapters 1-4 of a textbook on electrical machines. Chapter 1 covers magnetic circuits and includes problems on flux, inductance, reluctance and properties of magnetic materials. Chapter 2 involves transformer problems related to equivalent circuits, efficiency, regulation and performance calculations. Chapter 3 discusses synchronous machines. Chapter 4 provides DC machine calculations for generated voltages, torque, speed and efficiency. The document was authored by S. Z. Sayed Hassen from the University of Mauritius in November 2005.

1. Answers to Problems for Electrical Machines
Chapter 1: Magnetic Circuits
1.1 (a) 50000 At/m, 0.062832 T; (b) 308.43 μH
1.3 1.2096 A
1.5 0.392 ×10−3 Wb and 0.627 Wb/m2, 0.196 ×10−3 and 0.3135 Wb/m2
1.6 (b) 1302.5 At/pole; (c) 0.044 Wb
1.7 0.628 T
1.8 4.5 mm
1.9 (a) 2.51 A; (b) 1.51 × 10−3 Wb; (c) 12.06 A.
1.11 (b) 6.2832 × 10−3 Wb, 1.257 T; (c) 1.6756 H.
1.13 0.1257 mm.
1.14 (a) 1.41 and 3.54 A; (b) 34.6 and 6.35 mH; (c) 0.5 T
1.15 (a) -2.53 A; (b) 0.18 mWb.
1.16 (a) 193.6 mH; (b) 0.2513 A; (c) 0.377 A
1.17 Ph(60)/Ph(50) = 1.008, Pe(60)/Pe(50) = 1.21
1.18 2.88 W
1.19 79.92 V
1.22 0.5 × 10−3 Wb
1.23 1
180 s
1.24 1.16 T
1.25 (a) 0.45 T, -350 kA/m; (b) 0.7276 cm, 4.4444 cm2; (c) Vsamarium/Valnico = 0.2535
Chapter 2: Transformers
2.1 (a) 1.41 to 1; (b) 50 V to 70.7 V; (c) 5000 W.
2.3 (a) 10 kVA; (b) 1.21 − 36.87
2.4 (a) VH(rated) = 1000V, IH(rated) = 100A, VL(rated) = 100V, IL(rated) = 1000A; (c) -2.56%
2.5 (a) Rc = 38.46,Xm = 12.58,Req = 0.0405,Xeq = 0.0779 pu; (b) 8 %
2.7 (a) Rc1 = 125 k
,Xm1 = 60.32 k
,Req1 = 13
,Xeq1 = 60.32
;
(b) Rc2 = 5 k
,Xm2 = 2.4128 k
,Req2 = 0.52
,Xeq2 = 2.4128
2.9 (a) -0.95%; (b) 141.75 A, 283.5 A.
2.10 (ai) 2.57%; (aii) 2100 W; (aiii) 0.27 lagging; (aiv) 2070 W; (b) 2.17%
2.11 (a) RC(HV ) = 60 k
,Xm(HV ) = 20 k
,Req(HV ) = 2.55
,Xeq(HV ) = 8.5
;
(b) 0.0255 pu; (ci) 201.7 V; (cii) 1314.7 W; (di) 11255 V; (dii) -2.2667%
2.13 3.03%
2.14 (a) 97.3%; (b) Loading = 49.9%, Efficiency = 97.8%
2.15 (a) 95.92%; (b) 0.6455, 96.67%; (c) 95.93%
2.17 (b) 48.33 kVA; (c) 99.2%
2.18 (b) 4.5 kVA
2.19 (b) I2 = 69.4 A, I1 = 18.12 A; (c) 454.5; (d) -1.2%
2.20 (c) Vl−l = 2593.5 V; (d) I1 = 130.42 A, I2 = 652.17 A.
2.21 (a) 543.48 A; (b) P1 = 248.205 kW, P2 = 98.205 kW; (c) 1086.95 A; (d) 73.2%
2.22 (bi) 10; (bii) 10; (c) 1.52
2.23 (a) HV side: 200 kVA, 2100 V, 95.24 A, 22.05
; LV side: 200 kVA, 210 V, 952.4 A, 0.2205
2.24 (a) 97.14%; (b) 3.4%
2.25 (a) RC(LV ) = 375
,Xm(LV ) = 125
,Req(LV ) = 0.0938
,Xeq(LV ) = 0.375
;
(b) 270.2 V, 54.04 A, -7.48%
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2. Chapter 4: DC Machines
4.1 (a) Lap (120 V), Wave (240 V); (b) 120, 120; (c) 2.4 kW
4.3 (a) 0.907 V/rad/s; (b) 114 V, 51.82 A; (c) 47 Nm, 5370.6 W
4.4 (a) 0.907 V/rad/s; (b) 76 V, 34.55 A; (c) 31.33 Nm, 2387.41 W
4.5 (a) 0.64 A; (b) 87.5
4.6 (a) Ea(max) = 125 V, Ea(min) = 92 V;
(b) Rfc = 20
, Vt = 110 V (No AR), Vt = 107.5 (V ) (With AR)
4.7 (a) 156.25 V, 115 V; (b) 124.72
, 110 V, 94.75 V
4.9 (a) 126 V, 8 V; (b) 20
, (bi) 170 A, 60 V, (bii) 80 A, 74 V
4.10 (a) Ea(res.) = 10 V; (b) 400
; (c) 23.25
; (d) 192 V; (e) 816.3 rpm
4.11 (a) 258 V; (b) 98.55 Nm; (c) 1.86 A; (d) 88.12%
4.12 (a) 237 V, 226.43 Nm; (b) 3 V; (c) 2.4 turns/pole
4.13 (1a) 222 V; (b) 10
; (c) 21 kW, 111.41 Nm; (d) 0.09 A; (e) 250 A; (2b) 4.08 turns/pole
4.15 (a) 100 V; (b) 172 V; (c) 190 V
4.17 (a) 1895.2 rpm; (b) 2064.9 rpm
4.19 (a) 1568.8 rpm; (b) 1743.1 rpm
4.21 (a) 1800 rpm; (b) 2176.5 rpm
4.23 (a) motor; (b) 0.25
; (c) 400 W, 9200 W; (d) 73.19 Nm; (ei) 1252.2 rpm, (eii) 1127 rpm
4.25 1862.1 rpm
4.27 (a) 190 V; (b) 298.4 Nm; (c) 80.71%
4.28 (1a) 220 V; (1b) 3%; (2a) 240 V; (2b) 1614.6 rpm; (2c) 247.6 V
4.29 (a) 240 V, 9600 W, 76.37 Nm; (bi) 996 W, (bii) 1245 rpm, (biii) 1131.82 rpm
4.30 (a) 1674.6 rpm; (b) 12.66 A, 2763.1 W, 86%
4.31 T = 11.244 Nm, (a) 1700 rpm; (b) 9.27 A, 2002 W, 83.24%
4.32 (a) 1000 A; (b) 1.958
; (c) 1687.5 rpm
4.33 (a) 1410 A; (b) 33000 rpm
4.34 (a) 50 Nm; (b) 4.72
4.35 (a) 8640 W, 68.76 Nm; (b) 2477.8 rpm, 17.19 Nm, 4460 W
4.37 (a) 0.103 A Ifg 1.2 A; (b) 2420 rpm
4.39 (a) 1959 rpm, 1827.8 rpm; (b) 28.8◦; (c) 2.18%.
S. Z. Sayed Hassen
University of Mauritius
November 11, 2005
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