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Draw a directed graph showing the dependencies between the variables in the code in Example 9.7. Use solid lines for data dependencies and dashed lines for control dependencies. From the graph in Fig. 9-6, we can see that the output slice will start from the only output, z. The tokens z, z, y , z, and 0 from the statements z=z+y and z=0 are added to the slice. Next, the tokens x and 0 are added from the statement while x> 0. Next, the tokens, x , x , and 1 from the statement x=x+1 are added. This exhausts the statements, so everything in this program is in the output slice for the variable z.

4.90. (a) 0.04979 (b) 0.1494 (c) 0.2241 (d) 0.2241 (e) 0.1680 (f) 0.1008 4.92. (a) 0.05610 (b) 0.06131

EXAMPLE 14.7 The three-winding transformer shown in Fig. 14-14 has turns N1 20, N2 N3 10. given that I2 10:0 53:138 A, I3 10:0 458 A. With the dots and current directions as shown on the diagram, Find I1

4.91. (a) 0.0838 (b) 0.5976 (c) 0.4232

Fig. 14-14 N1 I1 N2 I2 N3 I3 0 from which 20I1 10 10:0 53:138 10 10:0 458 I1 6:54 j7:54 9:98 49:068 A

4.93. (a) 0.00248 (b) 0.04462 (c) 0.1607 (d) 0.1033 (e) 0.6964 (f) 0.0620 4.95. (a) 5 > 3888 (b) 5 > 324 4.97. 1> 16 4.99. (a) a 4.96. (a) 0.0348 (b) 0.000295

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4.98. (a) 70 > 429 (b) 1> 143 (c) 142 > 143 13 39 52 b a b^a b 6 7 13 40 20 60 b a b^a b 10 10 20 (b) a 13 39 52 b a b^a b 0 13 13

An autotransformer is an electrically continuous winding, with one or more taps, on a magnetic core. One circuit is connected to the end terminals, while the other is connected to one end terminal and to a tap, part way along the winding. Referring to Fig. 14-15(a), the transformation ratio is V1 N1 N2 a 1 V2 N2 which exceeds by unity the transformation ratio of an ideal two-winding transformer having the same turns ratio. Current I1 through the upper or series part of the winding, of N1 turns, produces the ux 1 . By Lenz s law the natural current in the lower part of the winding produces an opposing ux

(b) [(40C0)(20C20)

Fig. 14-15

(40C1)(20C19)

Fig. 9-6 An input slice can start with the input variable x . The tokens x , 0, x , x , and 1 from the statements while x>0 and x=x-1 are added to the slice. Next, the tokens, z, z, and y from the statement z=z+y are added. No other tokens can be added. Thus, the input slice is everything except z=0. An input slice for the variable y will only contain the initial y token and the tokens z and y from the statement z=z+y.

4.101. (a) 3> 4 (b) 3> 4 4.103. (a) 0 (b) 9> 5 4.105. (a) 3/4 (b) 1/3

2 . Therefore, current In leaves the lower winding by the tap. The dots on the winding are as shown in Fig. 14-15(b). In an ideal autotransformer, as in an ideal transformer, the input and output complex powers must be equal.

13 e 8

That is, the currents also are in the transformation ratio. Since IL Iab Icb , the output complex power consists of two parts:

5 e 2

4.109. (a) 21.0 (b) 26.2 (c) 23.3

The rst term on the right is attributed to conduction; the second to induction. Thus, there exist both conductive and magnetic coupling between source and load in an autotransformer.

4.111. (a) 20.1 (b) 36.2 (c) 48.3 (d) 63.7

James Bieman and Linda Ott, Measuring Functional Cohesion, IEEE TOSE, 20:8 August 1994, 644 657.

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