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An RC transient identical to that in Problems 7.1 and 7.2 has a power transient pR 360e t=0:00001 Obtain the initial charge Q0 , if R 10

Q2 =2C, 0

Given: Regular polygon ABCDE . . . having center O, apothem of length r, perimeter p 1 To Prove: Area of ABCDE . . . 2rp Plan: By joining each vertex to the center, congruent triangles are obtained, the sum of whose areas equals the area of the regular polygon.

Prb7_15.CIR vs 1 0 SIN(0V 0.25V 10kHz) VDD 5 0 DC 15V CC1 1 2 100uF CC2 3 6 100uF CS 4 0 100uF R1 2 0 200kohm R2 5 2 600kohm RD 5 3 2kohm RS 4 0 2kohm RL 6 0 3kohm M 3 2 4 4 NMOSG .MODEL NMOSG NMOS (Vto=-4V Kp=0.0008ApVsq + Rd=1ohm Rg=1kohm) .TRAN 1us 0.1ms .PROBE .END

The switch in the RL circuit shown in Fig. 7-21 is moved from position 1 to position 2 at t 0. Obtain vR and vL with polarities as indicated.

PROOF:

Execute hPrb7_15.CIRi and use the Probe and FFT features of PSpice to plot the instantaneous waveforms of vS and vL along with their Fourier spectra as shown by Fig. 7-20. The voltage gain follows from ratio of

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Fig. 7-21 The constant-current source drives a current through the inductance in the same direction as that of the transient current i. Then, for t > 0, i I0 e Rt=L 2e 25t vR Ri 200e

Statements 1. Draw OA, OB, OC, OD , OE, . . . . 2. r is the altitude of each triangle formed. 3. Area of ^AOB ^BOC

25t

CHAP. 7]

Reasons 1. A straight line segment may be drawn between two points. 2. Apothems of a regular polygon are congruent. 3. The area of a triangle equals one-half the product of the length of its base and altitude.

25t

5. p

Fig. 7-20

50t

A solid is an enclosed portion of space bounded by plane and curved surfaces. Thus, the pyramid , the cube , the cone , the cylinder , and the sphere are solids. A solid has three dimensions: length, width, and thickness. Practical illustrations of solids include a box, a brick, a block, and a ball. These are not, however, the pure or ideal solids that are the concern of solid geometry. In solid geometry we study the geometric properties of perfect solids, such as their shape, their size, the relationships of their parts, and the relationships along solids; physical properties such as their color, weight, or smoothness are disregarded.

the marked spectra magnitudes with the negative sign accounting for the 1808 phase shift observed from inspection of the instantaneous waveforms. Av vL 0:621 2:48 0:250 vS

Negative power for the inductance is consistent with the fact that energy is leaving the element. this energy is being transferred to the resistance, pR is positive.

Polyhedra A polyhedron is a solid bounded by plane (flat) surfaces only. Thus, the pyramid and cube are polyhedrons. The cone, cylinder, and sphere are not polyhedra, since each has a curved surface. The bounding surfaces of the polyhedron are its faces; the lines of intersection of the faces are its edges, and the points of intersection of its edges are its vertices. A diagonal of a polyhedron joins two vertices not in the same face. Thus, the polyhedron shown in Fig. 17-1 has six faces. Two of them are triangles (ABC and CFG), and the other four are quadrilaterals. Note AF is a diagonal of the polyhedron. The shaded polygon HJKL is a section of the polyhedron formed by the intersection of the solid and a plane passing through it.

CHAP. 7]

In the cascaded MOSFET ampli er of Fig. 7-21, CC ! 1. Av vL =vi and (b) the current-gain ratio Ai iL =ii .

Fig. 17-1

and C 20 mF has a constant-voltage source of 100 V applied at t 0; there is no initial charge on the capacitor. Obtain i, vR , vC , and q, for t > 0.

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