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A low-pass RC circuit under no-load has R1 5 k . (a) Find C2 if jHv j 0:5 at 10 kHz. (b) Obtain Hv at 5 kHz. (c) What value of C2 results in jHv j 0:90 at 8 kHz (d) With C2 as in (a), nd a new value for R1 to result in jHv j 0:90 at 8 kHz. Ans: a 5:51 mF; (b) 0:756 40:898; (c) 1:93 mF; d 1749 A simple voltage divider would consist of R1 and R2 . If stray capacitance Cs is present, then the divider would generally be frequency-dependent. Show, however, that V2 =V1 is independent of frequency for the circuit of Fig. 12-51 if the compensating capacitance C1 has a certain value. Ans: C1 R2 =R1 Cs

F1(x)

1 96 5 v

Market analysis Project planning, cost estimating, requirement speci cation (may be done concurrently) Requirements review High-level design Low-level design Design review Implementation Unit testing Systems testing Acceptance testing 5. Draw a diagram that represents an iterative life cycle model. See Fig. 1-2.

CHAP. 12]

3 0 v

Fig. 12-51

For x 4, F1(x) 1; for x 0, F1(x)

F1(x)

Fig. 12-52

0 4 4

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Assume that a sinusoidal voltage source with a variable frequency and Vmax 50 V is applied to the circuit shown in Fig. 12-52. (a) At what frequency f is jIj a minimum (b) Calculate this minimum current. (c) What is jIC j at this frequency Ans: a 2:05 kHz; (b) 2.78 mA; (c) 10.8 mA A 20-mF capacitor is in parallel with a practical inductor represented by L 1 mHz in series with R 7 . Find the resonant frequency, in rad/s and in Hz, of the parallel circuit. Ans: 1000 rad/s, 159.2 Hz What must be the relationship between the values of RL and RC if the network shown in Fig. 12-53 is to be resonant at all frequencies Ans: RL RC 5

F2( y)

Fig. 1-2.

3 0 v

Fig. 12-53

F2( y)

Fig. 12-54

1 5 5

From Problem 2.11 it is seen that the joint density function for X and Y can be written as the product of a function of x alone and a function of y alone. In fact, f (x, y) f1(x)f2( y), where

For the parallel network shown in Fig. 12-54, (a) nd the value of R for resonance; (b) convert the RC branch to a parallel equivalent. Ans: a 6:0 ; b Rp 6:67 ; XCp 20 For the network of Fig. 12-55(a), nd R for resonance. Obtain the values of R 0 , XL , and XC in the parallel equivalent of Fig. 12-55(b). Ans: R 12:25 ; R 0 7:75 ; XL 25 ; XC 25

f1 (x)

A software process model (SPM) describes the processes that are done to achieve software development. A software process model usually includes the following: Tasks Artifacts ( les, data, etc.) Actors Decisions (optional)

Fig. 12-55 12.31 Branch 1 of a two-branch parallel circuit has an impedance Z1 8 j6 at ! 5000 rad/s. Branch 2 contains R 8:34 in series with a variable capacitance C. (a) Find C for resonance. (b) Sketch the admittance locus diagram. Ans: a 24 mF b See Fig. 12-56

f2(y)

and c1c2 c 1 > 96. It follows that X and Y are independent, so that their joint distribution function is given by F(x, y) F1(x)F2( y). The marginal distributions F1(x) and F2( y) were determined in Problem 2.12, and Fig. 2-9 shows the resulting piecewise definition of F(x, y).

Fig. 8-22

Fig. 2-9

Fig. 8-23

In Fig. 2-10 we have indicated the square region 0 x 4, 1 y 5 within which the joint density function of X and Y is different from zero. The required probability is given by

2 3 x 1

Obtain H s for the network shown in Fig. 8-23, where the excitation is the driving current I s and the response is the voltage at the input terminals.

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