Electric Circuits, 9th Edition P20 docx

193 1 Know and be able to use the equations for voltage, current, power, and energy in an inductor; understand how an inductor behaves in the presence of constant current, and the r

Figure P5.7 Figure P5.10

10 kfl AAV

Section 5.3

DESIGN

PROBLEM

5.8 a) Design an inverting amplifier using an ideal o p

a m p that has a gain of 3 Use a set of identical

resistors from A p p e n d i x H

b) If you wish to amplify a 5 V input signal using

the circuit you designed in part (a), what a r e t h e

smallest p o w e r supply signals you can use?

5.9 T h e o p a m p in the circuit in Fig P5.9 is ideal

MULTISIM a) ^ i n d the range of values for a in which the o p

a m p does not saturate

b) Find i () (in m i c r o a m p e r e s ) when a = 0.272

Figure P5.9

12 kfl

a50 kfl

1.6 kfl

-AAWW-50 k n

6

250 rnV 6.4 kfl

t t

l?n i io kn

5.10 a) T h e o p a m p in the circuit shown in Fig P5.10 is

PSPICE ideal T h e adjustable resistor R± h a s a m a x i

-m u -m value of 100 k f l , a n d a is r e s t r i c t e d to t h e

r a n g e of 0.2 < a < 1 C a l c u l a t e t h e r a n g e of

v n if v s = 40 m V

b) If a is n o t restricted, at what value of a will t h e

op a m p saturate?

10 kfl

Section 5.4 5.11 Refer to t h e circuit in Fig 5.12, where t h e o p a m p

PSPICE is assumed t o b e ideal Given that R a = 4 k f l , ULTISIM R h = 5 k l l i ^ = 2 Q k a ^ VA S 200 m V ,

v b = 150 m V , v c = 400 m V , and V cc = ±6 V, spec-ify the range of Rf for which t h e o p a m p o p e r a t e s

within its linear region

5.12 The o p a m p in Fig P5.12 is ideal

PSPICE a ) w h a t circuit configuration is shown in this figure?

b) Find v Q if

4 V

= I V , v h = 1.5 V, and

c) T h e voltages v a a n d v c remain at 1 V and - 4 V,

respectively W h a t a r e t h e limits on v b if t h e o p

a m p o p e r a t e s within its linear region?

Figure P5.12

44 k f l

• VA,

+ 27.5 k f l

220 kfl

AAA-0 a

• W ^

+ 80 kfl

5.13 Design an inverting-summing amplifier so that

v a = - ( 3 ¾ + 5v h + 4 ¾ + 2v d )

DE5IGN PROBLEM

MULTISIM Start by choosing a feedback resistor (Rf) from

Appendix H Then choose single resistors from

A p p e n d i x H or construct resistor neworks from resis-tors in A p p e n d i x H to satisfy the design values for /? a , /? b, R c , and i?d D r a w your final circuit diagram

5.14 a) T h e o p a m p in Fig P5.14 is ideal Find v a if

PSPICE ? ; a = 4 V , v b = 9 V, v c = \3 V, and v d = 8 V

4ULTISIM

b) A s s u m e v A v c , a n d v L \ retain their values as given

in ( a ) Specify the range of v x such that t h e o p

a m p o p e r a t e s within its linear region

Figure P5.17

Figure P5.14

40 kil

• VvV

+ 22kft

• VW

220 kil ' V W

ii,

T T

Okil

PSPICE

MULTISIM

5.15 Tlie 220 k i l feedback resistor in the circuit in

Fig P5.14 is replaced by a variable resistor Rf T h e

voltages v d - v d have t h e same values as given in

P r o b l e m 5.14(a)

a) W h a t value of Rf will cause t h e o p a m p to

satu-r a t e ? N o t e that 0 < R f < oo

b) W h e n Rf has the value found in (a), what is t h e

current (in m i c r o a m p e r e s ) into t h e output

ter-minal of the o p a m p ?

Section 5.5

5.16 T h e o p a m p in the circuit of Fig P5.16 is ideal

PSPICE a \ -yvhat 0 p a m p circuit configuration is this?

MULTISIM

b) Calculate v u

Figure P5.16

40 kH

—A/VV

80 kil -A<W

5.17 T h e o p a m p in t h e circuit of Fig P5.17 is ideal

a) W h a t o p a m p circuit configuration is this?

b) Find v a in terms of v s

c) Find t h e r a n g e of values for v s such that v n does

not s a t u r a t e and the o p a m p remains in its linear

region of o p e r a t i o n

28 kO

5.18 The op a m p in the circuit shown in Fig P5.18 is ideal

PSPI" a) Calculate v a when v., equals 4 V

MULTISIM ' " " n

b) Specify t h e range of values of v s so that t h e o p

a m p o p e r a t e s in a linear m o d e

c) A s s u m e that v„ equals 2 V a n d that the 63 kil

resistor is replaced with a variable resistor W h a t value of the variable resistor will cause the o p

a m p to s a t u r a t e ? Figure P5.18

63 kil

AAA-i.'„527kn

5.19 a) Design a n o n - i n v e r t i n g amplifier with a gain of

4 U s e resistors from A p p e n d i x H You might

n e e d t o c o m b i n e resistors in series a n d in p a r -allel t o get t h e d e s i r e d resistance D r a w your final circuit,

b) If you use ± 12 V p o w e r supplies for the o p a m p , what range of input values will allow the o p a m p

to stay in its linear operating region?

5.20 T h e o p a m p in the circuit of Fig P5.20 is ideal

PSPICE

MULTISIM a) W h a t o p a m p circuit configuration is this?

b) Find v <y in terms of v s

c) Find t h e range of values for v s such that v a does not saturate a n d the o p a m p remains in its linear region of o p e r a t i o n

Figure P5.20

60 kil

AA/V-5.21 The op amp in the circuit shown in Fig PAA/V-5.21 is

PSPICE ideal The signal voltages v and v b are 800 mV and

MULTISIM „ , ,

400 mv, respectively

a) What circuit configuration is shown in the figure?

b) Calculate v a in volts

c) Find /a and /b in microamperes

d) What are the weighting factors associated with

v a and v b ?

Figure P5.21

110 kO

' V W

»„£47kft

T T

5.22 The circuit in Fig P5.22 is a noninverting summing

PROBLEM amplifier Assume the op amp is ideal Design the

PSPICE circuit so that

MULTISIM

v <> = ya + 2«^ + 3v c a) Specify the numerical values of R a and R c

b) Calculate /a, /b, and /c (in microamperes) when

v a = 0.7 V, v b = 0.4 V, and uc = 1.1 V

Figure P5.22

loo kn

5.23 The op amp in the noninverting summing amplifier

of Fig P5.23 is ideal

a) Specify the values of Rf, R b , and R c so that

v 0 = 6v A + 3v h + 4v c

PSPICE

MULTISIM

b) Using the values found in part (a) for R ( , R h , and

JRC, find (in microamperes) ia, /b, i c , L, and /s

when v a = 0.5 V, % = 2.5 V, and v c = 1 V

Figure P5.23

« 3 3 kO

Section 5.6 5.24 a) Use the principle of superposition to derive

Eq 5.22

b) Derive Eqs 5.23 and 5.24

5.25 The resistors in the difference amplifier shown

PSPICE in Fig 5.15 are Ka = 2 4 k O , R b = 75 k l l ,

MULTISIM Rc = 1 3 0 k a a n d ^ - 120 kH The signal

volt-ages v d and v b are 8 and 5 V, respectively, and

V cc = ±20 V

a) Find v (>

b) What is the resistance seen by the signal source ya?

c) What is the resistance seen by the signal

source v b ?

5.26 The op amp in the circuit of Fig P5.26 is ideal What

value of R { will give the equation

v () = 5 - 4v u ,

for this circuit?

Figure P5.26

DESIGN

PROBLEM

PSPICE

MULTISIM

5.27 Design the difference-amplifier circuit in Fig P5.27

so that v (l = 10(¾¾ - v a ), and the voltage source v b

sees an input resistance of 220 kfi Specify the

val-ues of R a ,Rb» and R t using single resistors or

com-binations of resistors from Appendix H Use the

ideal model for the op amp

Figure P5.27

4.7 kft

DESIGN

PROBLEM

PSPrCE MULTISIM

5.30 Design a difference amplifier (Fig 5.15) to meet

the following criteria: v () = 3t>b — 4i>a The

resist-ance seen by the signal source v b is 470 kft, and

the resistance seen by the signal source v d is

22 kft when the output voltage v () is zero Specify

the values of R a , R b , R c , and R d using single resistors or combinations of resistors from Appendix H

5.31

»'„$22 kft

5.28 The op amp in the adder-subtracter circuit shown in

PSPICE pig P5.28 is ideal

MULTISIM

a) Find v 0 when v a = 1 V, v b = 2 V, v c = 3 V, and

V d = 4 V

b) If v a , v b , and v d are held constant, what values of

v c will not saturate the op amp?

The resistor R £ in the circuit in Fig P5.31 is adjusted until the ideal op amp saturates Specify

R t in kilohms

Figure P5.31

1.6 kO

18 V

5.6 kH

Figure P5.28

20 kft

V W W/

180 kH

^vw-<v

18 kft

- A W

30 kO

v B 147 kfi

20 kH

5.29 Select the values of R a and R{ in the circuit in

DESIGN Fig P5.29 so that

PROBLEM °

PSPICE

MULTISIM

5.32 The op amp in the circuit of Fig P5.32 is ideal

a) Plot v„ versus a when Rf = 4R-[ and v g =* 2 V Use increments of 0.1 and note by hypothesis

thatO < a < 1.0

b) Write an equation for the straight line you plot-ted in (a) How are the slope and

inter-cept of the line related to v g and the ratio Rf/Ri? c) Using the results from (b), choose values for v g

and the ratio Rf/R\ such that v a = - 6 a + 4

Figure P5.32

v a = 5000(;b - Q

Use single resistors or combinations of resistors

from Appendix H.The op amp is ideal

Figure P5.29

»«t*L

t ) %**

5.33 In the difference amplifier shown in Fig P5.33, what

range of values of R x yields a CMRR > 1000?

Figure P5.33

5 0 k i l

' W W

5.34 In the difference amplifier shown in Fig P5.34,

compute (a) the differential mode gain, (b) the

common mode gain, and (c) the CMRR

Figure P5.34

1 kO

^ L

<b x

i

vJ

i k n

) <

i

25kfl

r ^ f 10V

^ " S - i o v

124 kO

1

+

»„

r

Sections 5.1-5.6

5.35 Assume that the ideal op amp in the circuit seen in

Fig P5.35 is operating in its linear region

a) Show that v 0 = [(/?, + R 2 )/R x \v s

b) What happens if R 1 —• oo and R 2 - » 0?

c) Explain why this circuit is referred to as a

volt-age follower when Z?j = oo and R 2 = 0

Figure P5.35

5.36 The voltage v g shown in Fig P5.36(a) is applied to

PSPICE t n e inverting amplifier shown in Fig P5.36(b)

Sketch v„ versus f, assuming the op amp is ideal

Figure P5.36

v

0.5 V

-0.5 V

(a)

120 kO

7.5 kO

—AMs

(b)

5.37 Tlie signal voltage v g in the circuit shown in Fig P5.37

PSPICE js described by the following equations:

MULTISIM *•

v g = 10 sin(ir/3)/ V, 0 < / < oo

Sketch v a versus r, assuming the op amp is ideal

Figure P5.37

15 kO 75 kH

»,, f 6.8 kfi

5.38 a) Show that when the ideal op amp in Fig P5.38 is

operating in its linear region,

*• =

-R-b) Show that the ideal op amp will saturate when

R(±V CC ~ 2v g )

g

Figure P5.38

5.39 A s s u m e that t h e ideal o p a m p in t h e circuit in

PSPICE Fig P5.39 is operating in its linear region

MULTISIM

a) Calculate t h e p o w e r delivered t o the 16 k O

resistor

b) R e p e a t (a) with t h e o p a m p r e m o v e d from t h e

circuit, that is, with t h e 16 kfit resistor connected

in t h e series with t h e voltage source a n d t h e

48 k f t resistor

c) Find t h e ratio of the p o w e r found in ( a ) to that

found in (b)

d) D o e s t h e insertion of t h e o p a m p b e t w e e n t h e

source a n d t h e load serve a useful p u r p o s e ?

Explain

Figure P5.39

320 mV

5.40 The circuit inside the shaded area in Fig P5.40 is a con-PSPICE st a n t current source for a limited range of values of R f

MULTISIM

a) Find t h e value of i L for R L = 4 k f t

b) Find t h e m a x i m u m value for R L for which i L will have t h e value in (a)

c) Assume that R L = 16 k f t Explain the operation

of t h e circuit You can assume that i n = i p ~ 0

u n d e r all operating conditions

d) Sketch i L versus R L for 0 < R L < 16 k f t

Figure P5.40

50 kfl

'v© , -20V [ IA R L ( t Jh l t-\:

:4 left

5.41 T h e t w o o p a m p s in t h e circuit in Fig P5.41 a r e

PSPICE ideal C a l c u l a t e v„\ a n d v o2

MULTISIM

Figure P5.41

15 V

15 V

10 V

«4,2 f 5 k f t

5.42 T h e o p a m p s in t h e circuit in Fig P5.42 are ideal

PSPICE a) F i n d / a

ULTISIM

b) Find t h e value of t h e left source voltage for which / n = 0

Figure P5.42

10 k n i—vvv—4

47 kD

- v w 220 kH A A A

-I V ©

33 kH

AA/v—i

6 150 mV

Section 5.7

5.43 Repeat Assessment Problem 5.6, given that the

PSPICE inverting amplifier is loaded with a 500 ft resistor

MULTISIM

5.44 Assume the input resistance of the op amp in

PSPKE Fig P5.44 is infinite and its output resistance is zero

MULTISIM

a) Find v 0 as a function of v g and the open-loop

gain A

b) What is the value of v 0 if v g - 1 V and A = 150?

c) What is the value of v 0 if v g = 1 V and A - oo?

d) How large does A have to be so that v {) is 99% of

its value in (c)?

Figure P5.44

10 kfl

'VW-5.46

PSPICE MULTISIM

a) Find the Thevenin equivalent circuit with respect to the output terminals a,b for the inverting amplifier of Fig P5.46 The dc signal source has a value of 880 mV The op amp has

an input resistance of 500 kft, an output resistance of 2 kft and an open-loop gain

of 100,000

b) What is the output resistance of the inverting amplifier?

c) What is the resistance (in ohms) seen by the

sig-nal source v s when the load at the terminals a,b

is 330 ft?

Figure P5.46

24 kO

A W

-5.45 The op amp in the noninverting amplifier circuit of

PSPICE Fig P5.45 has an input resistance of 560 kft, an

out-WLTISIM pU t r e s{sta n c e 0f § k O , and an open-loop gain of

50,000 Assume that the op amp is operating in its

linear region

a) Calculate the voltage gain (v () /v g )

b) Find the inverting and noninverting input

volt-ages v n and v p (in millivolts) if v g — 1 V

c) Calculate the difference (v p - v n ) in microvolts

when Vg ~ 1 V

d) Find the current drain in picoamperes on the

signal source v R when v g = 1 V

e) Repeat (a)-(d) assuming an ideal op amp

5.47 Repeat Problem 5.46 assuming an ideal op amp

Figure P5.45

200 kft

20 kCL

PSPICE MULTISIM

5.48 Derive Eq 5.60

Sections 5.1-5.7

5.49 Suppose the strain gages in the bridge in Fig 5.21

PRACTICAL have the value 120 ft ± 1% The power supplies

PERSPECTIVE r r r

to the op amp are ± 1 5 V , and the

refer-ence voltage, v rc{ , is taken from the positive

power supply

a) Calculate the value of Rf so that when the strain

gage that is lengthening reaches its maximum length, the output voltage is 5 V

b) Suppose that we can accurately measure

50 mV changes in the output voltage What change in strain gage resistance can be detected in milliohms?

5.50

PRACTICAL

PERSPECTIVE

a) For the circuit shown in Fig P5.50, show that if

AR « R, the output voltage of the op amp is

approximately

show that the percent error in the

approxima-tion of v„ in Problem 5.50 is

R 2 (R + 2R t ) (~AR)v h

AR (R + Re)

% error = — 7½ TTTT X 100

R (R + 2R { )

b) Find v () if R f = 470 kfl, R = 10 kf>, AR = 95 ft,

and v in = 15 V

c) Find the actual value of v a in (b)

Figure P5.50

5.51 a) If percent error is defined as

PRAOICAL

PERSPECTIVE

PSPICE

MULTISIM

% error = approximate value true value - 1 x 100,

b) Calculate the percent error in v a for Problem 5.50 5.52 Assume the percent error in the approximation of

PRACTICAL v t) in the circuit in Fig P5.50 is not to exceed 1%

PERSPECTIVE " °

PSPICE What is the largest percent change in R that can be

MULTisiM tolerated?

5.53 Assume the resistor in the variable branch of the

PRACTICAL bridge circuit in Fig P5.50 is R

R + AR

AR instead of

PSPICE

MULTISIM

a) What is the expression for v () if AR « R?

b) What is the expression for the percent error in

v a as a function of R, i?f, and AR1

c) Assume the resistance in the variable arm of the bridge circuit in Fig P5.50 is 9810 fi and the

values of R, R ( , and v m are the same as in Problem 5.50(b) What is the approximate value

of v a '?

d) What is the percent error in the approximation

of v (} when the variable arm resistance is

9810 a ?

• t _•< a B n i r i r

6.1 The Inductor p 176

6.2 The Capacitor p 182

6.3 Series-Parallel Combinations of Inductance

and Capacitance p 187

6.4 Mutual Inductance p 189

6.5 A Closer Look at Mutual Inductance p 193

1 Know and be able to use the equations for

voltage, current, power, and energy in an

inductor; understand how an inductor behaves

in the presence of constant current, and the

requirement that the current be continuous in

an inductor

2 Know and be able to use the equations for

voltage, current, power, and energy in a

capacitor; understand how a capacitor behaves

in the presence of constant voltage, and the

requirement that the voltage be continuous in a

capacitor

3 Be able to combine inductors with initial

conditions in series and in parallel to form a

single equivalent inductor with an initial

condition; be able to combine capacitors with

initial conditions in series and in parallel to

form a single equivalent capacitor with an

initial condition

4 Understand the basic concept of mutual

inductance and be able to write mesh-current

equations for a circuit containing magnetically

coupled coils using the dot convention

correctly

174

Inductance, Capacitance, and Mutual Inductance

We begin this chapter by introducing the last two ideal circuit

elements mentioned in Chapter 2, namely, inductors and capaci-tors Be assured that the circuit analysis techniques introduced in Chapters 3 and 4 apply to circuits containing inductors and capac-itors Therefore, once you understand the terminal behavior of these elements in terms of current and voltage, you can use Kirchhoff s laws to describe any interconnections with the other basic elements Like other components, inductors and capacitors are easier to describe in terms of circuit variables rather than electromagnetic field variables However, before we focus on the circuit descriptions, a brief review of the field concepts under-lying these basic elements is in order

An inductor is an electrical component that opposes any change in electrical current It is composed of a coil of wire wound around a supporting core whose material may be mag-netic or nonmagmag-netic The behavior of inductors is based on phe-nomena associated with magnetic fields The source of the magnetic field is charge in motion, or current If the current is varying with time, the magnetic field is varying with time A time-varying magnetic field induces a voltage in any conductor linked

by the field The circuit parameter of inductance relates the

induced voltage to the current We discuss this quantitative rela-tionship in Section 6.1

A capacitor is an electrical component that consists of two conductors separated by an insulator or dielectric material The capacitor is the only device other than a battery that can store electrical charge The behavior of capacitors is based on phenom-ena associated with electric fields The source of the electric field

is separation of charge, or voltage If the voltage is varying with time, the electric field is varying with time A time-varying electric field produces a displacement current in the space occupied by

the field The circuit parameter of capacitance relates the

dis-placement current to the voltage, where the disdis-placement current

is equal to the conduction current at the terminals of the capaci-tor We discuss this quantitative relationship in Section 6.2

Proximity Switches

The electrical devices we use in our daily lives contain many

switches Most switches are mechanical, such as the one used

in the flashlight introduced in Chapter 2 Mechanical switches

use an actuator that is pushed, pulled, slid, or rotated,

caus-ing two pieces of conductcaus-ing metal to touch and create a

short circuit Sometimes designers prefer to use switches

without moving parts, to increase the safety, reliability,

con-venience, or novelty of their products Such switches are

called proximity switches Proximity switches can employ a

variety of sensor technologies For example, some elevator

doors stay open whenever a light beam is obstructed

Another sensor technology used in proximity switches

detects people by responding to the disruption they cause in

electric fields This type of proximity switch is used in some

desk lamps that turn on and off when touched and in elevator

buttons with no moving parts (as shown in the figure) The

switch is based on a capacitor As you are about to discover in

this chapter, a capacitor is a circuit element whose terminal

characteristics are determined by electric fields When you

touch a capacitive proximity switch, you produce a change in

the value of a capacitor, causing a voltage change, which acti-vates the switch The design of a capacitive touch-sensitive switch is the topic of the Practical Perspective example at the end of this chapter

175