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It can be shown that the inductance L of an N-turn coil is proportional to N 2 . wound on the same core, 2 L1 N1 L2 N2

4.90. If 3% of the electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs, (a) 0, (b) 1, (c) 2, (d) 3, (e) 4, (f) 5 bulbs will be defective. 4.91. In Problem 4.90, find the probability that (a) more than 5, (b) between 1 and 3, (c) less than or equal to 2, bulbs will be defective. 4.92. A bag contains 1 red and 7 white marbles. A marble is drawn from the bag, and its color is observed. Then the marble is put back into the bag and the contents are thoroughly mixed. Using (a) the binomial distribution, (b) the Poisson approximation to the binomial distribution, find the probability that in 8 such drawings, a red ball is selected exactly 3 times. 4.93. According to the National Office of Vital Statistics of the U.S. Department of Health and Human Services, the average number of accidental drownings per year in the United States is 3.0 per 100,000 population. Find the probability that in a city of population 200,000 there will be (a) 0, (b) 2, (c) 6, (d) 8, (e) between 4 and 8, (f) fewer than 3, accidental drownings per year. 4.94. Prove that if X1 and X2 are independent Poisson variables with respective parameters 1 and 2, then X1 X2 has a Poisson distribution with parameter 1 2. (Hint: Use the moment generating function.) Generalize the result to n variables.

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The ux common to both windings in Fig. 14-10 is the mutual ux, m 12 21 . induces the coil emfs by Faraday s law,

4.95. A fair die is tossed 6 times. Find the probability that (a) 1 one , 2 twos and 3 threes will turn up, (b) each side will turn up once.

4.96. A box contains a very large number of red, white, blue, and yellow marbles in the ratio 4:3:2:1. Find the probability that in 10 drawings (a) 4 red, 3 white, 2 blue, and 1 yellow marble will be drawn, (b) 8 red and 2 yellow marbles will be drawn. 4.97. Find the probability of not getting a 1, 2, or 3 in 4 tosses of a fair die.

CHAP. 14]

4.98. A box contains 5 red and 10 white marbles. If 8 marbles are to be chosen at random (without replacement), determine the probability that (a) 4 will be red, (b) all will be white, (c) at least one will be red. 4.99. If 13 cards are to be chosen at random (without replacement) from an ordinary deck of 52 cards, find the probability that (a) 6 will be picture cards, (b) none will be picture cards. 4.100. Out of 60 applicants to a university, 40 are from the East. If 20 applicants are to be selected at random, find the probability that (a) 10, (b) not more than 2, will be from the East.

A use case diagram is part of the UML set of diagrams. It shows the important actors and functionality of a system. Actors are represented by stick gures and functions by ovals. Actors are associated with functions they can perform.

De ning the turns ratio, a N1 =N2 , we obtain from these the basic equation of the linear transformer: e1 a 11 e2 In the frequency domain, E1 =E2 a. The relationship between the mutual ux and the mutual inductance can be developed by analysis of the secondary induced emf, as follows: e2 N2 d m d 12 d 21 d 12 d k 2 N2 N2 N2 N2 dt dt dt dt dt di1 di di M di2 kL2 2 M 1 a dt dt dt dt

1 2 ).

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