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Spheres A sphere is a solid such that every point on its surface is at an equal distance from the same point, its center. A sphere is formed by revolving a semicircle about its diameter as an axis. The outer end of the radius perpendicular to the axis generates a great circle, while the outer ends of other chords perpendicular to the diameter generate small circles. Thus, sphere O in Fig. 17-9 is formed by the rotation of semicircle ACB about AB as an axis. In the process, point C generates a great circle while points E and G generate small circles.

Fig. 7-23 (a) The small-signal equivalent circuit is given in Fig. 7-23(b), where the CD model of the JFET (see Problem 7.5) has been used. Since ib id and vgd vi , KVL yields rds vi id hie hfe 1 id R1 R2 1 1

resistors. The time constant of the circuit is 2 3 103 2 10 6 0:01 s. The currents and voltages are vC 8e 100t V mA

N (North Pole)

The switch in the circuit of Fig. 7-26 is closed on position 1 at t 0 and then moved to 2 after one time constant, at t 250 ms. Obtain the current for t > 0.

CHAP. 7]

B S (South Pole) Fig. 17-10

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It is simplest rst to nd the charge on the capacitor, since it is known to be continuous (at t 0 and at t ), and then to di erentiate it to obtain the current. For 0 t , q must have the form q Ae t= B

By Ohm s law, ve hfe 1 id R1 R2 Solving (1) for id , substituting the result into (2), and rearranging give Av hfe 1 R1 R2 ve vi rds 1 hie hfe 1 R1 R2 2

Fig. 17-9

CHAP. 7]

The way in which points on the earth s surface are located is better understood if we think of the earth as a sphere formed by rotating semicircle NQS in Fig. 17-10, which runs through Greenwich, England (near London), about NS as an axis. Point O, halfway between N and S, generates the equator, EQ. Points A and B generate parallels of latitude, which are small circles on the earth s surface parallel to the equator. Each position of the rotating semicircle is a semi-meridian, or longitude. (A meridian is a great circle passing through the North and South Poles.) The meridian through Greenwich is called the Prime Meridian. Using the intersection of the equator and the Prime Meridian as the origin, we would locate New York City r r at 40 481 North Latitude and 73 571 West Longitude. The heavy arc shown on the globe is an arc of a great 2 2 circle through New York City and London. Such an arc is the shortest distance between two points on the earth s surface. We could find this line by stretching a rubber band tightly between New York City and London on a globe.

(b) We replace R1 R2 with a driving-point source oriented such that vdp ve . With vi deactivated (short circuited), vgd 0. Then, by Ohm s law, ib and by KCL, idp hfe 1 ib Substituting (3) into (4) and rearranging give Ro vdp rds 1 hie idp 1 hfe 1 4 vdp hie rds = 1 3

Fig. 7-24

Regular polyhedra are solids having faces that are regular polygons, with the same number of faces meeting at each vertex. There are only five such solids, shown in Fig. 17-11. Note that their faces are equilateral triangles, squares, or regular pentagons.

Fig. 7-25

For a triode with plate characteristics given by Fig. 7-8, nd (a) the perveance and (b) the ampli cation factor .

Regular Tetrahedron (4 faces)

Fig. 7-26

(a) The perveance can be evaluated at any point on the vG 0 curve. Choosing the point with coordinates iP 15 mA and vP 100 V, we have, from (4.9), iP

Regular Hexahedron (6 faces)

20

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