Strain Gages - Buku Electric circuits -10th edition

Changes in the shape of elastic solids are of great importance to engineers who design structures that twist, stretch, or bend when subjected to exter- nal forces. An aircraft frame is a prime example of a structure in which engineers must take into consideration elastic strain. The intelligent application of strain gages requires information about the physical structure of the gage, methods of bonding the gage to the surface of the structure, and the orientation of the gage relative to the forces exerted on the structure. Our purpose here is to point out that strain gage measurements are important in engineering applications, and a knowledge of electric circuits is germane to their proper use.

The circuit shown in Fig. 5.21 provides one way to measure the change in resistance experienced by strain gages in applications like the one

vref

V_CC V_CC Rf

R R

Figure 5.21 An op amp circuit used for measuring the change in strain gage resistance.

described in the beginning of this chapter. As we will see, this circuit is the familiar difference amplifier, with the strain gage bridge providing the two voltages whose difference is amplified. The pair of strain gages that are lengthened once the bar is bent have the values R + ¢R in the bridge

Practical Perspective 163

feeding the difference amplifier, whereas the pair of strain gages that are shortened have the values We will analyze this circuit to discover the relationship between the output voltage, and the change in resistance, experienced by the strain gages.

To begin, assume that the op amp is ideal. Writing the KCL equations at the inverting and noninverting input terminals of the op amp we see

(5.57)

(5.58)

Now rearrange Eq. 5.58 to get an expression for the voltage at the noninverting terminal of the op amp:

(5.59)

As usual, we will assume that the op amp is operating in its linear region, so and the expression for in Eq. 5.59 must also be the expression for . We can thus substitute the right-hand side of Eq. 5.59 in place of in Eq. 5.57 and solve for . After some algebraic manipulation,

(5.60)

Because the change in resistance experienced by strain gages is very small,

so and Eq. 5.60 becomes

(5.61)

where

NOTE: Assess your understanding of this Practical Perspective by trying Chapter Problem 5.49.

d = ¢R>R.

vo L Rf

R2dvref, R² - (¢R)² L R² (¢R)² V R²,

v_o =

Rf(2¢R) R² - (¢R)²v_ref. vo

vp = vn

v_p =

vref

(R - ¢R)¢ ¹ R + ¢R +

1 R - ¢R +

1 Rf≤

. vref - vp

R - ¢R = vp

R + ¢R + vp

R_f . vref - vn

R + ¢R = vn

R - ¢R +

vn - vo

R_f ,

¢R

v_o R - ¢R.

Summary

• The equation that defines the voltage transfer charac- teristic of an ideal op amp is

where A is a proportionality constant known as the open-loop gain, and represents the power supply voltages. (See page 147.)

• A feedback path between an op amp’s output and its inverting input can constrain the op amp to its linear operating region where . (See page 147.)

• A voltage constraint exists when the op amp is con- fined to its linear operating region due to typical values of and A. If the ideal modeling assumptions are made—meaning Ais assumed to be infinite—the ideal op amp model is characterized by the voltage constraint

(See page 147.)

• A current constraint further characterizes the ideal op amp model, because the ideal input resistance of the op amp integrated circuit is infinite. This current constraint is given by

(See page 148.)

• We considered both a simple, ideal op amp model and a more realistic model in this chapter. The differences between the two models are as follows:

Simplified Model More Realistic Model Infinite input resistance Finite input resistance Infinite open-loop gain Finite open-loop gain Zero output resistance Nonzero output resistance

(See page 159.)

ip = in = 0.

vp = vn. VCC

vo = A(vp - vn) VCC

vo = _d

-VCC, A(vp - vn) 6 -VCC,

A(vp - vn), -VCC … A(vp - vn) … + VCC, + VCC, A(vp - vn) 7 + VCC,

• An inverting amplifier is an op amp circuit producing an output voltage that is an inverted, scaled replica of the input. (See page 150.)

• A summing amplifier is an op amp circuit producing an output voltage that is a scaled sum of the input voltages.

(See page 152.)

• A noninverting amplifier is an op amp circuit producing an output voltage that is a scaled replica of the input voltage. (See page 153.)

• A difference amplifier is an op amp circuit producing an output voltage that is a scaled replica of the input voltage difference. (See page 155.)

• The two voltage inputs to a difference amplifier can be used to calculate the common mode and difference mode voltage inputs, and . The output from the difference amplifier can be written in the form

where is the common mode gain, and is the differential mode gain. (See page 157.)

• In an ideal difference amplifier, To measure how nearly ideal a difference amplifier is, we use the common mode rejection ratio:

An ideal difference amplifier has an infinite CMRR.

(See page 159.)

CMRR = 2^A^dm A_cm2.

A_cm = 0.

A_dm A_cm

vo = Acmvcm + Admvdm, vdm

vcm

Problems 165

Problems

Sections 5.1–5.2

5.1 The op amp in the circuit in Fig. P5.1 is ideal.

a) Label the five op amp terminals with their names.

b) What ideal op amp constraint determines the value of ? What is this value?

c) What ideal op amp constraint determines the value of ? What is this value?

d) Calculate Figure P5.1

5.2 a) Replace the 2 V source in the circuit in Fig. P5.1 and calculate for each of the following source values: 6 V, 3.5 V, 1.25 V, 2.4 V, 4.5 V, 5.4 V.

b) Specify the range of voltage source values that will not cause the op amp to saturate.

5.3 Find (in milliamperes) in the circuit in Fig. P5.3.

Figure P5.3

5.4 The op amp in the circuit in Fig. P5.4 is ideal.

a) Calculate if and

b) Calculate if and

c) Calculate if and

d) Calculate if v_o v_a = 2.5 Vand v_b = 1 V.

vb = 2.5 V.

va = 1 V vo

v_b = 0 V.

v_a = -0.5 V v_o

vb = 0 V.

va = 1.5 V vo

6 k

5 k 10 k 3 k

6 V 5 V

20 V

8 k 20 V

i_L

- -

- v_o

12 k 4 k

2 V 6 k

15 V

v_o. (vp - vn) i_n

e) Calculate if and

f) If , specify the range of such that the amplifier does not saturate.

Figure P5.4

5.5 Find in the circuit in Fig. P5.5 if the op amp is ideal.

Figure P5.5

5.6 The op amp in the circuit in Fig. P5.6 is ideal.

Calculate the following:

a) b) c) d) Figure P5.6

20 k 8 k

240 mV

15 V

60 k 30 k

i_o

i_a 40 k

i_o vo

v_a ia

i_o 10 k

6 V

2.5 k 5 k 0.5 mA

16 V 40 k

10 k 16 V

2 k 5 k

Áo

Áb

Áa

vb = 2 V

v_b = 0 V.

v_a = 2.5 V v_o

PSPICE MULTISIM

5.7 A voltmeter with a full-scale reading of 10 V is used to measure the output voltage in the circuit in Fig. P5.7. What is the reading of the voltmeter?

Assume the op amp is ideal.

Figure P5.7

Section 5.3

5.8 a) Design an inverting amplifier with a gain of 4.

Use an ideal op amp, a resistor in the feedback path, and 12 V power supplies.

b) Using your design from part (a), determine the range of input voltages that will keep the op amp in its linear operating region.

c) Suppose you wish to amplify a 2 V signal, using your design from part (a) with a variable feedback resistor. What is the largest value of feedback resistance that keeps the op amp in its linear operation region? Using this resistor value, what is the new gain of the inverting amplifier?

5.9 a) Design an inverting amplifier using an ideal op amp that has a gain of 2.5. Use a set of identical resistors from Appendix H.

b) If you wish to amplify signals between 2 V and 3 V using the circuit you designed in part (a), what are the smallest power supply voltages you can use?

5.10 a) The op amp in the circuit shown in Fig. P5.10 is ideal. The adjustable resistor has a maximum value of and is restricted to the range of Calculate the range of

b) If is not restricted, at what value of will the op amp saturate?

a a

vg = 40 mV.

0.2 … a … 1.

a 100 kÆ,

R^¢ +

;

30 kÆ

vo vm

3.5 mA

2.2 M 10 V

10 V

Figure P5.10

5.11 The op amp in the circuit in Fig. P5.11 is ideal.

a) Find the range of values for in which the op amp does not saturate.

b) Find (in microamperes) when Figure P5.11

Section 5.4

5.12 The op amp in Fig. P5.12 is ideal.

a) What circuit configuration is shown in this figure?

b) Find if and

c) The voltages and remain at 1 V and V, respectively. What are the limits on if the op amp operates within its linear region?

-4 vc

-4 V.

vc=

1.5 V, vb =

1 V, va =

50 k s50 k

10 k 5 V

5 V

250 mV

1.6 k

12 k

6.4 k

i_o

s = 0.272.

i_o

10 k 7 V

7 V

2 k

50 k

aR R

PSPICE MULTISIM

DESIGN PROBLEM

b) Suppose 2 V and 1 V. What range of values for will keep the op amp in its linear operating region?

5.17 Design an inverting-summing amplifier so that

Start by choosing a feedback resistor ( ) from Appendix H. Then choose single resistors from Appendix H or construct resistor neworks from resistors in Appendix H to satisfy the design

values for and Draw your final

circuit diagram.

Section 5.5

5.18 The op amp in the circuit of Fig. P5.18 is ideal.

a) What op amp circuit configuration is this?

b) Calculate Figure P5.18

5.19 The op amp in the circuit of Fig. P5.19 is ideal.

a) What op amp circuit configuration is this?

b) Find in terms of

c) Find the range of values for such that does not saturate and the op amp remains in its linear region of operation.

Figure P5.19

5.20 The op amp in the circuit shown in Fig. P5.20 is ideal, a) Calculate when equals 4 V.

b) Specify the range of values of so that the op amp operates in a linear mode.

12 V

15 V 7 k

32 k

56 k

vs 8 k

12 k vo

v_s. v_o

16 V

25 k

150 k

2 V vo.

Rd. Rc,

Rb, Ra,

vo = -(8va + 4vb + 10vc + 6vd).

- vc = va =

Figure P5.12

5.13 Refer to the circuit in Fig. 5.12, where the op amp is assumed to be ideal. Given that

and specify the range of for which the op amp operates within its linear region.

5.14 a) The op amp in Fig. P5.14 is ideal. Find if and

b) Assume , and retain their values as given in (a). Specify the range of such that the op amp operates within its linear region.

Figure P5.14

5.15 The feedback resistor in the circuit in Fig. P5.14 is replaced by a variable resistor The voltages have the same values as given in Problem 5.14(a).

a) What value of will cause the op amp to saturate? Note that

b) When has the value found in (a), what is the current (in microamperes) into the output terminal of the op amp?

5.16 a) Design an inverting-summing amplifier using a 120 resistor in the feedback path so that

Use 15 V power supplies.;

vo = -(8va + 5vb + 12vc).

kÆ Rf

0 … R_f … q. R_f

va-vd

Rf . 180 kÆ

10 V

10 V vo

16 k 60 k

20 k 36 k

180 k

270 k

v_c vd

6 V.

vd = 5 V, vc= 9 V, vb= 3 V, va =

;6 V, VCC =

400 mV, vc=

150 mV, vb =

200 mV, va =

20 kÆ, Rc =

5 kÆ, Rb =

4 kÆ, Ra =

10 V

10 V vo

3.3 k 44 k

27.5 k 80 k

220 k

PSPICE MULTISIM

DESIGN PROBLEM

PSPICE MULTISIM

Problems 167

c) Assume that equals 2 V and that the resistor is replaced with a variable resistor. What value of the variable resistor will cause the op amp to saturate?

Figure P5.20

5.21 a) Design a non-inverting amplifier (see Fig. 5.13) with a gain of 6, using a 75 resistor in the feedback path. Draw your final circuit diagram.

b) Suppose you wish to amplify input signals in the

range What are the mini-

mum values of the power supplies that will keep the op amp in its linear operating region?

5.22 a) Design a non-inverting amplifier (see Fig. 5.13) with a gain of 2.5. Use resistors from Appendix H. You might need to combine resistors in series and in parallel to get the desired resistance. Draw your final circuit.

b) If you use power supplies for the op amp, what range of input values will allow the op amp to stay in its linear operating region?

5.23 The op amp in the circuit of Fig. P5.23 is ideal.

a) What op amp circuit configuration is this?

b) Find in terms of

c) Find the range of values for such that does not saturate and the op amp remains in its linear region of operation.

Figure P5.23

10 V

10 V 24 k

96 k

16 k 24 k

5 V vo

10 k

vs . vo

;16 V

… 1.5 V.

-2.5 V …

kÆ

12 V

12 V vg

30 k

63 k

12 k

68 k

vo 27 k

63 kÆ

vg 5.24 The circuit in Fig. P5.24 is a noninverting summing

amplifier. Assume the op amp is ideal. Design the circuit so that

a) Specify the numerical values of and

b) Calculate and (in microamperes) when and

Figure P5.24

Section 5.6

5.25 a) Use the principle of superposition to derive Eq. 5.22.

b) Derive Eqs. 5.23 and 5.24.

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

a) What op amp circuit configuration is this?

b) Find an expression for the output voltage in terms of the input voltage .

c) Suppose 2 V. What value of R_fwill cause the op amp to saturate?

Figure P5.26

10 V

10 V 5 k

8 k

R_f = 20 k

5 V va

2 k

27 k v_a =

5 V

vo 4.7 k Ra

20 k

R_b 15 k R_c

100 k

i_b i_c

vc = 1.1 V.

vb = 0.4 V, va = 0.7 V,

ib, ia,

R_c. R_a

vo = va + 2vb + 3vc.

PSPICE MULTISIM

DESIGN PROBLEM

5.27 The resistors in the difference amplifier shown in Fig. 5.15 are

and The signal volt-

ages and are 8 and 5 V, respectively, and a) Find

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

c) What is the resistance seen by the signal source ?

5.28 The resistor in the circuit in Fig. P5.28 is adjusted until the ideal op amp saturates. Specify

in kilohms.

Figure P5.28

5.29 Design a difference amplifier (Fig. 5.15) to meet the following criteria: The resistance seen by the signal source is and the resistance seen by the signal source is when the output voltage is zero. Specify

the values of and using single

resistors or combinations of resistors from Appendix H.

5.30 The op amp in the adder-subtracter circuit shown in Fig. P5.30 is ideal.

a) Find when and

b) If and are held constant, what values of will not saturate the op amp?

Figure P5.30

20 V

47 k

20 k va

18 k 20 k

20 k vc

30 k

180 k v_c

v_d v_b, v_a,

4 V.

vd =

3 V, vc = 2 V, vb = 1 V, va = vo

Rc , Rb , Ra ,

22 kÆ

470 kÆ, vb

vo = 3vb - 4va. 9 V

9 V 1.6 k

7.5 k

1.5 k 5.6 k

R_f

18 V

vo. VCC = ;20 V.

Rd = 120 kÆ. Rc = 130 kÆ

Rb = 75 kÆ, Ra = 24 kÆ,

5.31 Select the values of and in the circuit in Fig. P5.31 so that

Use single resistors or combinations of resistors from Appendix H. The op amp is ideal.

Figure P5.31

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

a) Plot versus when and

Use increments of 0.1 and note by hypothesis that

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 and the ratio ? c) Using the results from (b), choose values for

and the ratio such that Figure P5.32

5.33 In the difference amplifier shown in Fig. P5.33, compute (a) the differential mode gain, (b) the common mode gain, and (c) the CMRR.

Figure P5.33

1 k 10 V

10 V 1 k

24 k 25 k

10 V

10 V R₁ R_f

R_L vo

aR_g

vo = -6a + 4.

Rf >R1

0 … a … 1.0.

vg = 2 V.

Rf = 4R1

vo a

⫹

⫺ 15 V

⫺15 V

⫺

⫹ Rf

R_b i_a

i_b 2 k⍀

vo = 8000(ib - ia).

Ra PSPICE

MULTISIM

PSPICE MULTISIM

DESIGN PROBLEM

PSPICE MULTISIM

DESIGN PROBLEM

Problems 169

5.34 In the difference amplifier shown in Fig. P5.34, what range of values of yields a

Figure P5.34

Sections 5.1–5.6

5.35 The voltage shown in Fig. P5.35(a) is applied to the inverting amplifier shown in Fig. P5.35(b).

Sketch versus t, assuming the op amp is ideal.

Figure P5.35

5.36 The signal voltage in the circuit shown in Fig. P5.36 is described by the following equations:

Sketch versus vo t, assuming the op amp is ideal.

vg = 4 cos(p>4)t V, 0 … t … q. vg = 0, t … 0,

8 V

8 V vo

15 k 15 k

75 k

(b) 2

2 V 2 V

4 6 8 10 12 14 t (s)

(a) vg

etc.

16 v_o

v_g

3 k 10 V

10 V Rx

6 k 6 k

vb va

CMRR Ú 1500?

Figure P5.36

5.37 a) Show that when the ideal op amp in Fig. P5.37 is operating in its linear region,

b) Show that the ideal op amp will saturate when

Figure P5.37

5.38 Assume that the ideal op amp in the circuit seen in Fig. P5.38 is operating in its linear region.

a) Show that

b) What happens if and ?

c) Explain why this circuit is referred to as a voltage follower when R1 = qand R2 = 0.

R2:0 R1:q

vo = [(R1 + R2)>R1]vs .

V_CC

VCC

R R

R_a i_a

Ra =

R(;V_CC - 2v_g) 3vg

. i_a =

3vg

R .

10 V

10 V vg

20 k 60 k

1.8 k

5.4 k

vo 5 k

PSPICE MULTISIM

5.41 The op amps in the circuit in Fig. P5.41 are ideal.

a) Find

b) Find the value of the left source voltage for which ia = 0.

i_a. Figure P5.38

5.39 The two op amps in the circuit in Fig. P5.39 are ideal. Calculate and

Figure P5.39

5.40 Assume that the ideal op amp in the circuit in Fig. P5.40 is operating in its linear region.

a) Calculate the power delivered to the resistor.

b) Repeat (a) with the op amp removed from the circuit, that is, with the resistor connected in the series with the voltage source and the

resistor.

c) Find the ratio of the power found in (a) to that found in (b).

d) Does the insertion of the op amp between the source and the load serve a useful purpose?

Explain.

Figure P5.40

48 k

Source Load

16 k 320 mV

48 kÆ

16 kÆ

16 kÆ 15 V

15 V

15 V vo1

15 V

500

400 2 k

5 k

1 k

10 V vo2

vo2. vo1

R_s

R₂

Figure P5.41

1 V

150 mV

6 V

6 V 10 k

47 k

1 k

220 k 33 k 6 V

6 V

i_a

5.42 The circuit inside the shaded area in Fig.P5.42 is a constant current source for a limited range of values of a) Find the value of for

b) Find the maximum value for for which will have the value in (a).

c) Assume that Explain the operation of the circuit. You can assume that

under all operating conditions.

d) Sketch versus for Figure P5.42

Section 5.7

5.43 Derive Eq. 5.60.

5.44 Repeat Assessment Problem 5.6, given that the inverting amplifier is loaded with a resistor.

5.45 a) Find the Thévenin equivalent circuit with respect to the output terminals a, b for the inverting amplifier of Fig. P5.45. The dc signal source has a value of 880 mV. The op amp has an input resistance of an output resistance of and an open-loop gain of 100,000.

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

2 kÆ

500 kÆ, 500 Æ 20 V

20 V 50 k

4 k

R_L

i_L i_g i_L R_L

8 V

0 … R_L … 16 kÆ. R_L

i_L

ip L 0 in =

16 kÆ. RL =

i_L R_L

RL = 4 kÆ. iL

R_L.

PSPICE MULTISIM

Problems 171

c) What is the resistance (in ohms) seen by the signal source when the load at the terminals a, b is ?

Figure P5.45

5.46 Repeat Problem 5.45 assuming an ideal op amp.

5.47 Assume the input resistance of the op amp in Fig. P5.47 is infinite and its output resistance is zero.

a) Find as a function of and the open-loop gain A.

b) What is the value of if and ? c) What is the value of if and ? d) How large does Ahave to be so that is 99% of

its value in (c)?

Figure P5.47

5.48 The op amp in the noninverting amplifier circuit of Fig. P5.48 has an input resistance of an output resistance of and an open-loop gain of 50,000. Assume that the op amp is operating in its linear region.

a) Calculate the voltage gain ( ).

b) Find the inverting and noninverting input voltages and (in millivolts) if

c) Calculate the difference ( ) in microvolts when

d) Find the current drain in picoamperes on the signal source when

e) Repeat (a)–(d) assuming an ideal op amp.

vg = 1 V.

v_g = 1 V.

v_p - v_n vg = 1 V.

v_o>v_g 8 kÆ,

560 kÆ,

2 k 6 V

6 V

10 k

A = q vg = 1 V

A = 150 vg = 1 V

15 V

a 1.6 k

24 k

b 330 Æ

Figure P5.48

Sections 5.1–5.7

5.49 Suppose the strain gages in the bridge in Fig. 5.21 have the value The power supplies to the op amp are and the refer- ence voltage, , is taken from the positive power supply.

a) Calculate the value of 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 a) For the circuit shown in Fig. P5.50, show that if the output voltage of the op amp is approximately

b) Find if and

c) Find the actual value of in (b).

Figure P5.50

vin

R_f

R R

R vo

15 V.

vin=

95 Æ,

¢R 10 kÆ, R =

470 kÆ, Rf =

vo L R_f R²

(R + R_f)

(R + 2R_f)(- ¢R)vin.

¢R V R,

vref

;15 V, 120 Æ ; 1%.

16 k 15 V

15 V

20 k 240 k

200 k

PSPICE MULTISIM

PRACTICAL PERSPECTIVE

PSPICE MULTISIM PRACTICAL PERSPECTIVE

5.51 a) If percent error is defined as

show that the percent error in the approximation of in Problem 5.50 is

b) Calculate the percent error in for Problem 5.50.

5.52 Assume the percent error in the approximation of in the circuit in Fig. P5.50 is not to exceed 1%.

What is the largest percent change in Rthat can be tolerated?

% error =

¢R R

(R + Rf)

(R + 2Rf) * 100.

% error = Bapproximate value

true value - 1R ^* ^100,

5.53 Assume the resistor in the variable branch of the bridge circuit in Fig. P5.50 is instead of a) What is the expression for if ? b) What is the expression for the percent error in

as a function of R, , and ?

c) Assume the resistance in the variable arm of the bridge circuit in Fig. P5.50 is and the values of R, , and are the same as in Problem 5.50(b). What is the approximate value of ?

d) What is the percent error in the approximation of when the variable arm resistance is

? 9810 Æ

v_o

v_in R_f

9810 Æ

¢R Rf

¢R V R v_o

R + ¢R.

R - ¢R

PRACTICAL PERSPECTIVE PSPICE MULTISIM

PRACTICAL PERSPECTIVE

PSPICE MULTISIM

PRACTICAL PERSPECTIVE

PSPICE MULTISIM

Problems 173

We begin this chapter

by introducing the last two ideal circuit elements mentioned in Chapter 2, namely, inductors and capacitors. Be assured that the circuit analysis techniques introduced in Chapters 3 and 4 apply to circuits containing inductors and capacitors. 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 magnetic or nonmagnetic. 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 relationship 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 displacement current to the voltage, where the displacement current is equal to the conduction current at the terminals of the capacitor. We discuss this quantitative relationship in Section 6.2.

C H A P T E R C O N T E N T S

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

C H A P T E R O B J E C T I V E S

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.

Inductance, Capacitance, and Mutual Inductance

6 6

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Dalam dokumen Buku Electric circuits -10th edition (Halaman 186-200)