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(c) If X is Y and _____ , then X is M. (d) If C is D and E is C, then _____ . (e) If squares (S) are rectangles (R) and rectangles are parallelograms (P), then _____ .

@vP vP @iP Q iP Q @i i Transconductance gm P P @vG Q vG Q Plate resistance rp

CHAP. 7]

Completing a syllogism Write the statement needed to complete each syllogism: Major Premise (General Statement) Minor Premise (Particular Statement) Fluffy is a cat. _____ / c and /d are vertical angles. A square is a rectangle. _____ Conclusion (Deducted Statement) _____ Jan must die. _____ A square has congruent diagonals. ^ABC has only one obtuse angle.

Fig. 7-5

7:9 7:10

(a) A cat is a domestic animal. (b) All people must die. (c) Vertical angles are congruent. (d) _____ (e) An obtuse triangle has only one obtuse angle.

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Fig. 7-6 Assume the switch S has been closed for a long time. The inductor current is then constant and its voltage is zero. The circuit at t 0 is shown in Fig. 7-6(b) with i 0 12=4 3 A. After the battery is disconnected, at t > 0, the circuit will be as shown in Fig. 7-6(c). For t > 0, the current decreases exponentially from 3 A to zero. The time constant of the circuit is L=R 1=100 s. Using the results of Example 7.3, for t > 0, the inductor current and voltage are, respectively, i t 3e 100t v t L di=dt 30e 100t i t and v t are plotted in Figs. 7-6(d) and (e), respectively. V

15.14. Construct a triangle given (a) two sides and the median to one of them; (b) two sides and the altitude to one of them; (c) an angle, the angle bisector of the given angle, and a side adjacent to the given angle. (15.5) 15.15. Construct angles of measure 15 and 165 . 15.16. Given an angle with measure A, construct angles with measure (a) A 60 ; (b) A 30 ; (c) A (15.6) 120 . (15.6)

Under the condition iG 0, (7.8) is simulated by the current-source equivalent circuit of Fig 7-9(a). The frequently used voltage-source model of Fig. 7-9(b) is developed in Problem 7.19.

If a dc source is suddenly applied to a series RL circuit initially at rest, as in Fig. 7-7(a), the current grows exponentially from zero to a constant value with a time constant of L=R. The preceding result is the solution of the rst-order di erential equation (8) which is obtained by applying KVL around the loop. The solution follows.

15.17. Construct a parallelogram, given (a) two adjacent sides and an angle; (b) the diagonals and the acute angle at their intersection; (c) the diagonals and a side; (d) two adjacent sides and the altitude to one of them; (e) a side, an angle, and the altitude to the given side. (15.7) 15.18. Circumscribe a triangle about a given circle, if the points of tangency are given.

_ K (a)

Fig. 7-7

(15.8)

for t > 0;

_ K (b)

15.19. Secant AB passes through the center of circle O in Fig. 15-39. Circumscribe a quadrilateral about the circle so that A and B are opposite vertices. (15.8)

i 0 0

(a) For the JFET ampli er of Example 4.2, use the drain characteristics of Fig. 4-6 to determine the small-signal equivalent-circuit constants gm and rds . (b) Alternatively, evaluate gm from the transfer characteristic.

Fig. 15-39

Since i ih t ip t , where ih t Ae Rt=L and ip t V0 =R, we have i Ae Rt=L V0 =R The coe cient A is found from i 0 A V0 =R 0 or A V0 =R. The current in the inductor and the voltage across it are given by (9) and (10) and plotted in Fig. 7-7(b) and (c), respectively. i t V0 =R 1 e Rt=L di v t L V0 e Rt=L dt for t > 0 for t > 0 9 10

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