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In the parallel circuit shown in Fig. 9-27, VAB 48:3

(d) 1

308 V.

0 0 1 2 3 3

Fig. 5-6.

2.50. F (x)

j4 1 j8:66 V V VBX V 4 j4 1 j 5 j8:66 1 j8:66 1 V V VBX 1 j 5 j8:66 0:268 j1 1058 48:3 308 50:0 1358 V

2.51. (a) 1/27 (b) f (x)

V 0:268 j1 VAB 1:035

x 2/9 0

Fig. 12-56

(b) 1 > 2 (c) 3 > 4 (d) F(x)

2.54. (a) 1 > 36 (b) 1 > 6 (c) 1 > 4 (d) 5 > 6 (e) 1 > 6 (f) 1 > 6 (g) 1 > 2 2.55. (a) f1(x) e x>6 0 x 1, 2, 3 (b) f2( y) other x

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The number of regions is 5, so the cyclomatic number is 5. It can also be counted with decisions. There is a decision about which way to exit nodes a, c, e, and g. Thus, there are 4 decisions. The cyclomatic number is the number of decisions plus 1, so it is 5. It can also be counted using the formula e n 2. Here, e 12, and n 9, so e n 2 5. 6. Calculate McCabe s cyclomatic number from the control ow graph shown in Fig. 5-5. Note that the graph is not planar (that is, drawn without crossing lines). Removing arcs until the graph is planar and then counting an additional region for each removed arc can calculate the cyclomatic number. In this graph (see Fig. 5-7), the arc e-g was removed, the regions were counted, and then region VIII was added for arc e-g. The count of decisions is seven (two decisions each on nodes a and c, one decision each on b, e, and f). The e n 2 16 10 2 8.

Fig. 12-57

2.57. (a) F1(x)

Find R for resonance of the network shown in Fig. 12-57. Sketch the admittance locus diagram. Ans: Resonance cannot be achieved by varying R. See Fig. 12-58.

(b) F2( y)

0 1 1

Fig. 12-58

2.58. (a) f (x u y) (b) f ( y u x) 2.59. (a) f (x u y) (b) f ( y u x)

In Problem 12.32, for what values of the inductive reactance will it be possible to obtain resonance at some value of the variable resistance R Ans: XL 8:2 (a) Construct the admittance locus diagram for the circuit shown in Fig. 12-59. resistance in the RL branch is resonance possible for only one value of XL Ans: a See Fig. 12-60. b 6:25 : (b) For what value of

1, 2, 3 (see Problem 2.55) 1, 2, 3 (see Problem 2.55)

Fig. 5-7.

1 2)

Fig. 12-59 12.35

1 3)

Fig. 12-60

1 2)

2.60. (a) f (x u y) (b) f ( y ux)

Determine the value(s) of L for which the circuit shown in Fig. 12-61 is resonant at 5000 rad/s. Ans: 2:43 mH, 66.0 mH A three-branch parallel circuit has xed elements in two branches; in the third branch, one element is variable. The voltage-current phasor diagram is shown in Fig. 12-62. Identify all the elements if ! 5000 rad/s.

1 3)

7. Calculate Halstead s basic measures on the triangle code from Problem 5. operators 1 == 2 or 7 and 6 >= 5 <= 4 + 4 print operands 5 6 1 3 3 3 1 string x y z 0 5 9 8 8 3

CHAP. 12]

0 (b) f (y u x) 0 2.64. (2p)

2.66. 1>p for 2.68. (a) g( y)

Fig. 12-61

y) 1)

Fig. 12-62 Ans: Branch 1: R 8:05 ; L 0:431 mH Branch 2: R 4:16 ; C 27:7 mF Branch 3: L 2:74 mH, variable R

2.70. ve v >(1

2.73. g(z)

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