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Each of the 6 ways in which the first die can fall can be associated with each of the 6 ways in which the second die can fall, so there are 6 6 36 ways in which both dice can fall. These are: 1 on the first die and 1 on the second die, 1 on the first die and 2 on the second die, etc., denoted by (1, 1), (1, 2), etc. Of these 36 ways, all equally likely if the dice are fair, a total of 9 occurs in 4 cases: (3, 6), (4, 5), (5, 4), (6, 3). Then the probability of a total of 9 in a single toss of a pair of dice is p 4 >36 1 >9, and the probability of not getting a total of 9 in a single toss of a pair of dice is q 1 p 8 >9. (a) P(two 9s in 6 tosses) (b) P(at least two 9s)

61,440 531,441

The diode of Example 2.4 operates within the range 10 < i < 20 mA. Within that range, approximate its terminal characteristic by a straight line i v , by specifying and . Ans. i 630 v 4407 mA, where v is in V

P(four 9s)

The diode of Example 2.4 operates within the range of 20 < i < 40 mA. Within that range, approximate its terminal characteristic by a straight line connecting the two operating limits. Ans. i 993:33 v 702:3 mA, where v is in V

P(two 9s)

P(three 9s)

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Program slices can be calculated from either direction. An output slice nds every statement that a ects the value of the speci ed output. An input slice nds every statement that is a ected by the value of the speci ed input. It is easier to calculate the program slices from a directed graph that has a set of nodes, n, where each node is an input, an output, or a statement in the code. The arcs, e, are the dependencies. James Bieman and Linda Ott4 have used variable de nitions and references as the basic units instead of program statements. These de nitions and references are called tokens. Thus, every constant reference, variable reference, and variable de nition is a separate token.

Within the operating range of 20 < i < 40 mA, model the diode of Example 2.4 by a resistor R in series with a voltage source V such that the model matches exactly with the diode performance at 0.72 and 0.75 V. Find R and V. Ans. R 1:007 ; V 707 mV

P(five 9s) 1

3.1 INTRODUCTION An electric circuit or network consists of a number of interconnected single circuit elements of the type described in 2. The circuit will generally contain at least one voltage or current source. The arrangement of elements results in a new set of constraints between the currents and voltages. These new constraints and their corresponding equations, added to the current-voltage relationships of the individual elements, provide the solution of the network. The underlying purpose of de ning the individual elements, connecting them in a network, and solving the equations is to analyze the performance of such electrical devices as motors, generators, transformers, electrical transducers, and a host of electronic devices. The solution generally answers necessary questions about the operation of the device under conditions applied by a source of energy.

P(six 9s)

61,440 531,441 Another method P(at least two 9s)

For any closed path in a network, Kirchho s voltage law (KVL) states that the algebraic sum of the voltages is zero. Some of the voltages will be sosurces, while others will result from current in passive elements creating a voltage, which is sometimes referred to as a voltage drop. The law applies equally well to circuits driven by constant sources, DC, time variable sources, v t and i t , and to circuits driven by sources which will be introduced in 9. The mesh current method of circuit analysis introduced in Section 4.2 is based on Kirchho s voltage law.

10,240 531,441

EXAMPLE 3.1. Write the KVL equation for the circuit shown in Fig. 3-1.

960 531,441

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