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2 25 > 64

x f (x)

From the impedance diagram, Fig. 9-23, 18:0 2 10 R 2 !L 2 11:2 2 R2 !L 2 where ! 2 60 377 rad/s. Solving simultaneously, R 4:92 L 26:7 mH

0 194,580 270,725

In the parallel circuit shown in Fig. 9-24, the e ective values of the currents are: Ix 18:0 A, I1 15:0 A, IT 30:0 A. Determine R and XL .

2 Show that the temperature scales of Celsius and Fahrenheit are an interval scale using the Celsius temperatures of 20, 30, and 40 degrees The Fahrenheit equivalents are 68, 86, and 104 degrees The di erence between the lowest and middle is 10 Celsius and 18 Fahrenheit The di erence between the bottom and the top is twice that, 20 Celsius and 36 Fahrenheit 3 Show that McCabe s cyclomatic number satis es the representational theory of measurement For the empirical system, consider the set of all control ow graphs The relation is that one CFG is less than or equal to the second CFG if the second CFG can be built out of the rst by adding nodes and arcs The numerical system (Answer Set) can be the integers The relation on the integers is the standard less than or equal The mapping is the formula e n 2.

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1 69,184 270,725

2 6768 270,725

CHAP. 9]

3 192 270,725

The problem can be solved in a manner similar to that used in Problem 9.14 but with the admittance diagram. The (e ective) voltage is V I1 4:0 60:0 V. Then Yx Ix 0:300 S V Yeq IT 0:500 S V Y1 1 0:250 S 4:0

4 1 270,725

x f (x)

Fig. 9-24 From the admittance diagram, Fig. 9-25, 0:500 2 0:250 G 2 B2 L 0:300 2 G2 B2 L which yield G 0:195 S, BL 0:228 S. Then R i.e., XL 4:39 . 1 5:13 G and jXL

0 1>8

There are only two operations, adding nodes and adding arcs Adding an arc means increasing the e value Adding a nodes means adding a node on an arc This means that both e and n increase by 1, so the value stays the same Thus, for any two CFGs x and y, if x is less than y, then y can be created from x by adding arcs and nodes Thus, the value of the mapping must either increase or stay the same Therefore, the less stringent representation condition is satis ed (The more stringent representation condition cannot be satis ed, since the order on the CFGs is a partial order) 4 Show that McCabe s cyclomatic number is an interval scale measure Since McCabe s cyclomatic number is one more than the number of decisions, every interval in the cyclomatic number is caused by that number of additional decisions.

Fig. 9-25

1 1>2

2 7>8

Obtain the phasor voltage VAB in the two-branch parallel circuit of Fig. 9-26.

2.46. (a)

By current-division methods, I1 4:64 120:18 A and I2 17:4 AYB may be considered. Choosing the former, VAB VAX VXB I1 20 I2 j6 92:8 120:18 104:4 30:18 A. Either path AXB or path 59:98 11:6 59:98 V

x f (x)

1 1>8

Fig. 9-26

So the di erence between 2 and 3 is the same as the di erence between 10 and 11 It is not a ratio scale measure because there is not a clear zero In fact, the cyclomatic number cannot be zero 5 Calculate McCabe s cyclomatic number on the following source code Draw a control ow graph Label the regions with Roman numerals read x,y,z; type = scalene ; if (x == y or x == z or y == z) type = isosceles ; if (x == y and x == z) type = equilateral ; if (x >= y+z or y >= x+z or z >= x+y) type = not a triangle ; if (x <= 0 or y <= 0 or| z <= 0) type = bad inputs ; print type;.

2 1>4

Fig. 9-27

3 3>8

4 1>4

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