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and the mean of the sampling distribution of means is mX illustrating the fact that mX sum of all sample means in (1) above 25 150 25 6.0

Two identical coupled coils have an equivalent inductance of 80 mH when connected series aiding, and 35 mH in series opposing. Find L1 , L2 , M, and k. Ans: 28:8 mH, 28.8 mH, 11.25 mH, 0.392 Two coupled coils, with L1 20 mH, L2 10 mH, and k 0:50, are connected four di erent ways: series aiding, series opposing, and parallel with both arrangements of winding sense. Obtain the equivalent inductances of the four connections. Ans: 44:1 mH, 15.9 mH, 9.47 mH, 3.39 mH Write the mesh current equations for the coupled circuit shown in Fig. 14-37. circuit and write the same equations. Ans: R1 R3 i1 L1 di1 R 3 i2 M dt di R2 R3 i2 L2 2 R3 i1 M dt di2 v dt di1 v dt Obtain the dotted equivalent

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2 (d) The variance sX of the sampling distribution of means is obtained by subtracting the mean 6 from each number in (1), squaring the result, adding all 25 numbers obtained, and dividing by 25. The final result is

1. Draw scenarios for the interaction between a customer trying to buy a particular music CD with cash and a clerk in the music store. Be sure to cover all possibilities. Use the state machine model with the events being the arcs. See Fig. 9-9.

Fig. 14-37 14.27 Write the phasor equation for the single-loop, coupled circuit shown in Fig. 14-38. Ans: j5 j3 j5:03 j8 10 I 50 08 Obtain the dotted equivalent circuit for the coupled circuit of Fig. 14-38. Ans: See Fig. 14-39. Obtain the equivalent

135 25

!5.40

14.28 14.29

This illustrates the fact that for finite populations involving sampling with replacement (or infinite 2 s2 >n since the right-hand side is 10.8>2 5.40, agreeing with the above value. For a populations), sX general proof of this, see Problem 5.7.

The three coupled coils shown in Fig. 14-40 have coupling coe cients of 0.50. inductance between the terminals AB. Ans: 239 mH

(c) There are 5C2 10 samples of size two which can be drawn without replacement (this means that we draw one number and then another number different from the first) from the population, namely, (2, 3), (2, 6), (2, 8), (2, 11), (3, 6), (3, 8), (3, 11), (6, 8), (6, 11), (8, 11).

The selection (2, 3), for example, is considered the same as (3, 2).

Obtain two forms of the dotted equivalent circuit for the coupled coils shown in Fig. 14-40. Ans: See Fig. 14-41. (a) Obtain the equivalent impedance at terminals AB of the coupled circuit shown in Fig. 14-42. Reverse the winding sense of one coil and repeat. Ans: a 3:40 41:668 ; b 2:54 5:378 (b)

Fig. 9-9.

The corresponding sample means are 2.5, 4.0, 5.0, 6.5, 4.5, 5.5, 7.0, 7.0, 8.5, 9.5

CHAP. 14]

and the mean of sampling distribution of means is mX 2.5 4.0 5.0 m. 6.5 4.5 10 5.5 7.0 7.0 8.5 9.5 6.0

(2.5

Fig. 14-38

6.0)2

Fig. 14-39

(4.0

2. Calculate Bieman and Ott s functional cohesion metrics for the following code segment. Draw a directed graph and show the ows. cin >> a >> b; int x,y,z; x=0; y=1; z=1; while (a > 0){ x = x + b; z = z * b; if (a > b){ y=y*a; } a=a-1; } cout << x << a << z << y; }

6.0)2

Fig. 14-40

(5.0 10

Fig. 14-41 14.32 In the coupled circuit shown in Fig. 14-43, nd V2 for which I1 0. What voltage appears at the 8 inductive reactance under this condition Ans: 141:4 458 V; 100 08 V (+ at dot)

6.0)2

Find the mutual reactance XM for the coupled circuit of Fig. 14-44, if the average power in the 5- resistor is 45.24 W. Ans: 4

(9.5

6.0)2

See Fig. 9-10.

Fig. 14-42

10.8 5 s2 N n n a N 1 b, since the right side equals 2 a 5 For a general proof of this result, see Problem 5.47.

Fig. 14-43

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