Answers to Problems for Electrical Machines

Chapter 1: Magnetic Circuits

1.1 (a) 50000 At/m, 0.062832 T; (b) 308.43 µH1.3 1.2096 A

1.5 0.392 ×10−3 Wb and 0.627 Wb/m2, 0.196 ×10−3 and 0.3135 Wb/m

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1.6 (b) 1302.5 At/pole; (c) 0.044 Wb1.7 0.628 T1.8 4.5 mm1.9 (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 T1.15 (a) -2.53 A; (b) 0.18 mWb.1.16 (a) 193.6 mH; (b) 0.2513 A; (c) 0.377 A1.17 Ph(60)/Ph(50) = 1.008, Pe(60)/Pe(50) = 1.211.18 2.88 W1.19 79.92 V1.22 0.5 × 10−3 Wb1.23 1

180 s1.24 1.16 T1.25 (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 Ω2.4 (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 kΩ,Xm1 = 60.32 kΩ, Req1 = 13 Ω,Xeq1 = 60.32 Ω;

(b) Rc2 = 5 kΩ,Xm2 = 2.4128 kΩ, Req2 = 0.52 Ω,Xeq2 = 2.4128 Ω2.9 (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 kΩ,Xm(HV ) = 20 kΩ, Req(HV ) = 2.55 Ω,Xeq(HV ) = 8.5 Ω;

(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 kVA2.19 (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) 1.522.23 (a) HV side: 200 kVA, 2100 V, 95.24 A, 22.05 Ω; LV side: 200 kVA, 210 V, 952.4 A, 0.2205 Ω2.24 (a) 97.14%; (b) 3.4%2.25 (a) RC(LV ) = 375 Ω,Xm(LV ) = 125 Ω, Req(LV ) = 0.0938Ω,Xeq(LV ) = 0.375Ω;

(b) 270.2 V, 54.04 A, -7.48%

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Chapter 4: DC Machines

4.1 (a) Lap (120 V), Wave (240 V); (b) 120, 120; (c) 2.4 kW4.3 (a) 0.907 V/rad/s; (b) 114 V, 51.82 A; (c) 47 Nm, 5370.6 W4.4 (a) 0.907 V/rad/s; (b) 76 V, 34.55 A; (c) 31.33 Nm, 2387.41 W4.5 (a) 0.64 A; (b) 87.5 Ω4.6 (a) Ea(max) = 125 V, Ea(min) = 92 V;

(b) Rfc = 20 Ω, Vt = 110 V (No AR), Vt = 107.5 (V ) (With AR)4.7 (a) 156.25 V, 115 V; (b) 124.72 Ω, 110 V, 94.75 V4.9 (a) 126 V, 8 V; (b) 20 Ω, (bi) 170 A, 60 V, (bii) 80 A, 74 V4.10 (a) Ea(res.) = 10 V; (b) 400 Ω; (c) 23.25 Ω; (d) 192 V; (e) 816.3 rpm4.11 (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/pole4.13 (1a) 222 V; (b) 10 Ω; (c) 21 kW, 111.41 Nm; (d) 0.09 A; (e) 250 A; (2b) 4.08 turns/pole4.15 (a) 100 V; (b) 172 V; (c) 190 V4.17 (a) 1895.2 rpm; (b) 2064.9 rpm4.19 (a) 1568.8 rpm; (b) 1743.1 rpm4.21 (a) 1800 rpm; (b) 2176.5 rpm4.23 (a) motor; (b) 0.25 Ω; (c) 400 W, 9200 W; (d) 73.19 Nm; (ei) 1252.2 rpm, (eii) 1127 rpm4.25 1862.1 rpm4.27 (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 V4.29 (a) 240 V, 9600 W, 76.37 Nm; (bi) 996 W, (bii) 1245 rpm, (biii) 1131.82 rpm4.30 (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 Ω; (c) 1687.5 rpm4.33 (a) 1410 A; (b) 33000 rpm4.34 (a) 50 Nm; (b) 4.72 Ω4.35 (a) 8640 W, 68.76 Nm; (b) 2477.8 rpm, 17.19 Nm, 4460 W4.37 (a) 0.103 A < Ifg < 1.2 A; (b) 2420 rpm4.39 (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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