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A pure inductance, L 10 mH, has an applied voltage with the waveform shown in Fig. 17-60, where ! 200 rad/s. Obtain the current series in trigonometric form and identify the current waveform. Ans: i 20 1 1 sin !t 1 sin 3!t 25 sin 5!t 49 sin 7!t A ; triangular 9

Since t0.975 2.23 for 12 2 10 degrees of freedom, the 95% confidence limits for yp are y0 where y0 35.82 2.23 2n sy.x n 2 A 1 n(x0 s2 x 2.66 (Problem 8.43), and n 12. x)2 #

12.2.3 METRIC 3: NUMBER OF CHILDREN (NOC)

Figure 17-61 shows a full-wave-recti ed sine wave representing the voltage applied to the terminals of an LC series circuit. Use the trigonometric Fourier series to nd the voltages across the inductor and the capacitor.

65.0, y0 66.76 inches. Also, (x0 2.23 (1.28) 12 A !10 x)2 # 1 (65.0 12(2.78) (2.66)2 800>12)2 2.78. Then 95% confidence limits

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i.e., we can be about 95% confident that the sons heights are between 63.0 and 70.6 inches. (b) If x0 70.0, y0 69.14 inches. Also, (x0 x)2 (70.0 800>12)2 11.11. Then the 95% confidence # limits are computed to be 69.14 5.09 inches, i.e., we can be about 95% confident that the sons heights are between 64.1 and 74.2 inches. Note that for large values of n, 95% confidence limits are given approximately by y0 1.96 sy.x or y0 2sy.x provided that x0 x is not too large. This agrees with the approximate results mentioned on # page 269. The methods of this problem hold regardless of the size of n or x0 x, i.e., the sampling methods # are exact for a normal population.

7 4Vm 6 4!L 6 2!L cos 2!t cos 4!t 7 5 1 1 4 3 2!L 15 4!L 2!C 4!C 2 4Vm 61 6 42

8.46. In Problem 8.11, find 95% confidence limits for the mean heights of sons whose fathers heights are (a) 65.0, (b) 70.0 inches.

Fig. 17-61

Since t0.975 2.23 for 10 degrees of freedom, the 95% confidence limits for yp are # y0 where y0 35.82 2.23 sy.x 1 !20 A (x0 s2 x x)2 #

1.28 (Problem 8.43).

in series with a parallel combination of L and C. At Find the total current if the applied voltage is given by ! 500 rad/s, XL 2

Not only is the depth of the inheritance tree signi cant, but the width of the inheritance tree. The number of children metric is the number of immediate subclasses subordinated to a class in the inheritance hierarchy. This metric is calculated for each class.

(a) If x0 65.0, we find [compare Problem 8.45(a)] the 95% confidence limits 66.76 1.07 inches, i.e., we can be about 95% confident that the mean height of all sons whose fathers heights are 65.0 inches will lie between 65.7 and 67.8 inches. (b) If x0 70.0, we find [compare Problem 8.45(b)] the 95% confidence limits 69.14 1.45 inches, i.e., we can be about 95% confident that the mean height of all sons whose fathers heights are 70.0 inches will lie between 67.7 and 70.6 inches.

. v 50 20 sin 500t 10 sin 1000t (V). Ans: i 10 3:53 sin 500t 28:18 (A)

Sampling theory of correlation 8.47. A correlation coefficient based on a sample of size 18 was computed to be 0.32. Can we conclude at a significance level of (a) 0.05, (b) 0.01 that the corresponding population correlation coefficient is significantly greater than zero

We wish to decide between the hypotheses (H0: r t r !n !1 2 r2 0) and (H1: r 0.32 !18 2 !1 (0.32)2 0). 1.35

A1 p A complex number z is a number of the form x jy, where x and y are real numbers and j 1. We write x Re z, the real part of z; y Im z, the imaginary part of z. Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. COMPLEX NUMBERS

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