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A balanced -connected load, with impedances 10:0 36:98 , and a balanced Y-connected load are supplied by the same three-phase, ABC system having VCA 141:4 2408 V. If IB 40:44 13:418 A, what are the impedances of the Y-connected load Ans: 5:0 53:38 A three-phase, ABC system, with e ective line voltage 500 V, has a -connected load for which ZAB 10:0 308 ZBC 25:0 08 ZCA 20:0 308

4.13. If area refers to that under the standard normal curve, find the value or values of z such that (a) area between 0 and z is 0.3770, (b) area to left of z is 0.8621, (c) area between 1.5 and z is 0.0217.

(a) In the table in Appendix C the entry 0.3770 is located to the right of the row marked 1.1 and under the column marked 6. Then the required z 1.16. By symmetry, z 1.16 is another value of z. Therefore, z 1.16 (Fig. 4-8). The problem is equivalent to solving for z the equation

Obtain the line currents. Ans: IA 106:1 90:08 A; IB 76:15 68:208 A; IC 45:28 128:658 A 11.26 A three-phase, ABC system, with VBC 294:2 08 V, has the -connected load ZAB 5:0 08 ZBC 4:0 308 ZCA 6:0 158

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(b) Since the area is greater than 0.5, z must be positive. Area between 0 and z is 0.8621 0.5 0.3621, from which z

Obtain the line currents. Ans: IA 99:7 99:78 A; IB 127:9 43:3 A; IC 77:1 172:18 A 11.27 A three-phase, four-wire, CBA system, with e ective line voltage 100 V, has Y-connected impedances ZA 3:0 08 ZB 3:61 56:318 ZC 2:24 26:578

5. Draw a use case diagram for the B&B problem (see Problem 4.3). See Fig. 8-12.

1.09 (Fig. 4-9).

Fig. 4-8

Obtain the currents IA ; IB ; IC ; and IN . Ans: 27:2 908 A; 22:6 26:38 A; 36:4 176:68 A; 38:6 65:38 A 11.28 A three-phase, four-wire, ABC system, with VBC 294:2 08 V, has Y-connected impedances ZA 12:0 458 ZB 10:0 308 ZC 8:0 08

Fig. 4-9

Obtain the currents IA ; IB ; IC ; and IN Ans: 14:16 458 A; 16:99 608 A; 21:24 1508 A; 15:32 90:48 A 1129 A Y-connected load, with ZA 10 08 , ZB 10 608 , and ZC 10 608 , is connected to a threephase, three-wire, ABC system having e ective line voltage 1414 V Find the load voltages VAO , VBO , VCO and the displacement neutral voltage VON Construct a phasor diagram similar to Fig 11-18 Ans: 173:2 908 V; 100 08 V; 100 1808 V; 57:73 908 V A Y-connected load, with ZA 10 608 , ZB 10 08 , and ZC 10 608 , is connected to a threephase, three-wire, CBA system having e ective line voltage 1471 V Obtain the line currents IA , IB , and IC .

(c) If z were positive, the area would be greater than the area between must be negative. Case 1 z is negative but to the right of Area between 0.0217 1.5 (Fig. 4-10). (area between

1.5 and 0)

Ans: 20:8 608 A; 0; 20:8 1208 A A three-phase, three-wire, ABC system with a balanced load has e ective line voltage 200 V and (maximum) Ans: 2887 W line current IA 13:61 608 A Obtain the total power Two balanced -connected loads, with impedances 20 608 and 18 458 , respectively, are connected to a three-phase system for which a line voltage is VBC 212:1 08 V Obtain the phase power of each load After using the single-line equivalent method to obtain the total line current, compute the total power, and compare with the sum of the phase powers Ans: 562:3 W; 883:6 W; 4337:5 W 3 562:3 W 3 883:6 W In Problem 115, a balanced -connected load with Z 20 458 resulted in line currents 865 A for line voltages 100 V, both maximum values.

1.5 (Fig. 4-11). 1.5 (area between z and 0) (area between 1.5 and 0) 0.4332 1.694 by using linear interpolation;

Fig. 8-12.

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