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A cubic unit is a cube whose edge measures 1 unit. Thus, a cubic inch is a cube whose edge is 1 in long. A parallelepiped is a prism bounded by six parallelograms (Fig. 17-5). Hence, the rectangular solid and cube are special parallelepipeds. The table that follows shows some relationships among polygons in plane geometry and the corresponding relationships among polyhedra in solid geometry. Plane Geometry Solid Geometry Polyhedron Polygon Quadrilateral Prism Parallelogram Parallelepiped Rectangle Square Rectangular solid Cube Pyramids A pyramid is a polyhedron whose base is a polygon and whose other faces meet at a point, its vertex. The base (B in Fig. 17-6) may have any number of sides. However, the other faces must be triangles. The distance from the vertex to the base is equal to the measure of the altitude or height h, a line from the vertex at a right angle to the base.

(2) (3)

Fig. 7-23 i t i 0 i 0 1 A For t > 0, the current source is replaced by an open circuit and the 50-V source acts in the RL series circuit R 20

B Regular Pyramid (square base)

. Consequently, as t ! 1, i ! 50=20 2:5 A. Then, by Sections 6.10 and 7.3, i t i 0 i 1 e Rt=L i 1 3:5e 100t 2:5 A By means of unit step functions, the two formulas may be combined into a single formula valid for all t: i t u t 3:5e 100t 2:5 u t A

Fig. 17-6

(b) Realizing that RG1 R11 kR12 , we have Ai where Av is given by (3). iL v =R R o L Av G1 ii vi =RG1 RL

Find iR , iC ,

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A regular pyramid is a pyramid whose base is a regular polygon and whose altitude joins the vertex and the center of the base. A frustum of a pyramid is the part of a pyramid that remains if the top of the pyramid is cut off by a plane parallel to the base. Note in Fig. 17-6 that its lateral faces are trapezoids. Cones A circular cone (Fig. 17-7) is a solid whose base is a circle and whose lateral surface comes to a point. (A circular cone is usually referred to simply as a cone.)

For the JFET-BJT Darlington ampli er of Fig. 7-23(a), nd (a) the voltage-gain ratio Av ve =vi and (b) the output impedance Ro . Assume hre hoe 0 and that RG ) R1 ; R2 .

10 V. For t > 0, the time constant is RC 10 ms and iR 0 0; iR 1 2 mA, and iR 2 1 e 100t mA

Fig. 17-7

[See Fig. 7-24 b : [See Fig. 7-24 c : [See Fig. 7-24 e :

rds m+1 + m L m + 1 gd _ D (b)

A right circular cone is formed by revolving a right triangle about one of its legs. This leg becomes the altitude h of the cone, and the other becomes the radius r of the base. A frustum of a cone is the part of a cone that remains if the top of the cone is cut off by a plane parallel to the base. Cylinders A circular cylinder (Fig. 17-8) is a solid whose bases are parallel circles and whose cross-sections parallel to the bases are also circles. (A circular cylinder is usually referred to simply as a cylinder.) A right circular cylinder is a circular cylinder such that the line joining the centers of the two bases is perpendicular to the radii of these bases. The line joining the centers is the height h of the cylinder, and the radius of the bases is the radius r of the cylinder.

10 V, and vC 10 1 e 100t V iC 0 2 mA; iC 1 0, and iC 2e 100t mA [See Fig. 7-24 d : V vs 0 0; vs 1 2 mA 5 k

_ Ro (a)

Fig. 17-8

For t < 0, the circuit is at steady state with iR 6 4 = 4 2 4 mA, iC 0, and vC vs 4 2 8 V. During the switching at t 0, the capacitor voltage remains the same. After the switch is opened, at t 0 , the capacitor has the same voltage vC 0 vC 0 8 V. For t > 0, the capacitor discharges in the 5-k

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