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Obtain the complete power triangle for the following parallel-connected loads: load #1, 200 VA, pf 0:70 lagging; load #2, 350 VA, pf 0:50 lagging; load #3, 275 VA, pf 1:00 Ans: S 590 j444 VA, pf 0:799 lagging A 4500-VA load at power factor 075 lagging is supplied by a 60-Hz source at e ective voltage 240 V Determine the parallel capacitance in microfarads necessary to improve the power factor to (a) 090 lagging, (b) 090 leading Ans: a 61:8 mF; b 212 mF In Problem 1039, what percent reduction in line current and total voltamperes was achieved in part (a) What further reduction was achieved in part (b) Ans: 161 percent, none The addition of a 20-kvar capacitor bank improved the power factor of a certain load to 090 lagging.

3.57. Find (a) the variance, (b) the standard deviation of the number of points that will come up on a single toss of a fair die. 3.58. Let X be a random variable having density function f (x) Find (a) Var(X ), (b) sX. 3.59. Let X be a random variable having density function f (x) Find (a) Var(X ), (b) sX. 3.60. Find the variance and standard deviation for the random variable X of (a) Problem 3.43, (b) Problem 3.44. 3.61. A random variable X has E(X ) 2, E(X2) 8. Find (a) Var(X ), (b) sX. 1)2] 10, E[(X 2)2] 6 find (a) E(X ), (b) Var(X ), (c) sX. e e 0

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Determine the complex power before the addition of the capacitors, if the nal apparent power is 185 kVA Ans: S 166:5 j100:6 kVA A 25-kVA load with power factor 080 lagging has a group of resistive heating units added at unity power factor How many kW do these units take, if the new overall power factor is 085 lagging Ans: 4:2 kW A 500-kVA transformer is at full load and 060 lagging power faactor A capacitor bank is added, improving the power factor to 090 lagging After improvement, what percent of rated kVA is the transformer carrying Ans: 66:7 percent A 100-kVA transformer is at 80 percent of rated load at power factor 085 lagging How many kVA in additional load at 0.

5. Assume that FTR technique A requires 2 hours/KLOC preparation and allots 1 hour/KLOC review time and FTR technique B requires 1 hour/KLOC preparation time and 4 hours/KLOC review time. Also assume that in a controlled experiment with the same source code, technique A nds 12 errors/KLOC and B nds 14 errors/KLOC. Compare the two techniques for e ectiveness. Technique A took 80 percent of the time of technique B and found 85 percent of the errors that B found. So A is slightly more e cient than B. From the point of view of marginal improvement, it took 2 hours/KLOC more e ort to nd the last 2 errors/KLOC. 6. If the software had 5 failures in 100 tests during 10 days of testing, what would be a good estimate of the reliability of the software over the next day Week F 1 0:05 Next day Assume 10 tests per day (average from last 10 days). R 10 R 1 10 0:9510 0:598: Next week Assume 70 tests. R 10 R 1 70 0:9570 0:027: 7. Develop an SQA plan for the B&B problem ( 4, Problem 3). R 1 0:95

3.63. Find (a) the moment generating function of the random variable X and (b) the first four moments about the origin. e 1>2 1>2 prob. 1>2 prob. 1>2

60 lagging power factor will bring the transformer to full rated load Ans: 21:2 kVA A 250-kVA transformer is at full load with power factor 080 lagging a How many kvar of capacitors must be added to improve this power factor to 090 lagging (b) After improvement of the power factor, a new load is to be added at 050 lagging power factor How many kVA of this new load will bring the transformer back to rated kVA, and what is the nal power factor Ans: a 531 kvar (capacitive); (b) 3335 kVA, 0867 lagging A 65-kVA load with a lagging power factor is combined with a 25-kVA synchronous motor load which operates at pf 0:60 leading Find the power factor of the 65-kVA load, if the overall power factor is 085 lagging.

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