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VTH = 35 V Req = 600
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If the conditions for maximum power transfer exist, determine: a The value of RL b The power developed in RL c The ef ciency of the circuit
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[V0 ,I0 ]
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356 A nonideal voltage source can be modeled as an
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ideal voltage source in series with a resistance representing the internal losses of the source as shown in Figure P356 A load is connected across the terminals of the nonideal source VS = 12 V RS = 03
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a Plot the power dissipated in the load as a function of the load resistance What can you conclude from your plot b Prove, analytically, that your conclusion is valid in all cases
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where [V0 , I0 ] is the operating point of the circuit a For the circuit of Figure P358, nd the operating point of the element that has the characteristic curve shown b Find the incremental resistance of the nonlinear element at the operating point of part a c If VT were increased to 20 V, nd the new operating point and the new incremental resistance
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VT + _ I RS + + V _ S R I VT = 15 V
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Nonlinear element
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RT = 200
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Figure P356
I = 00025V 2
Section 5: Nonlinear Circuit Elements 357 Write the node voltage equations in terms of v1 and
v2 for the circuit of Figure P357 The two nonlinear resistors are characterized by ia = ib =
3 2va 3 vb +
Figure P358
10vb
359 The device in the circuit in Figure P359 is a
temperature sensor with the nonlinear i-v characteristic shown The remainder of the circuit in
Do not solve the resulting equations
Part I
Circuits
which the device is connected has been reduced to a Th venin equivalent circuit with: e VTH = 24 V Req = 192
R + + V _ S
iD + vD NL
Determine the current through the nonlinear device
i (ma)
R eq + VTH
i + N v L D
i D (ma)
1 v (V) (b)
05 vD (V) (b) 10 15
Figure P359
Figure P361
360 The device in the circuit in Figure P360 is an
induction motor with the nonlinear i-v characteristic shown Determine the current through and the voltage across the nonlinear device VS = 450 V R=9
362 The resistance of the nonlinear device in the circuit
in Figure P362 is a nonlinear function of pressure The i-v characteristic of the device is shown as a family of curves for various pressures Construct the DC load line Plot the voltage across the device as a function of pressure Determine the current through the device when P = 30 psig VS = VTH = 25 V R = Req = 125
R iD + N vD L D
40 i D (a)
STALL
+ + _ VS
R + + _ VS
iD N VD L D +
150 vD (V) (b)
30 40 30 25
Figure P360
i D (ma)
361 The nonlinear device in the circuit shown in Figure
P361 has the i-v characteristic given VS = VTH = 15 V R = Req = 60
10 10 psig 10 v D (V) (b) 20 30
Determine the voltage across and the current through the nonlinear device
Figure P362
3
Resistive Network Analysis
363 The resistance of the nonlinear device in the
circuits shown in Figure P363 is a nonlinear function of pressure The i-v characteristic of the device is shown as a family of curves for various pressures Construct the DC load line and determine the current through the device when P = 40 kPa VS = VTH = 25 V R = Req = 125
R + + _ VS iD + N vD L D
364 The nonlinear device in the circuit shown in Figure
P364 has the i-v characteristic: iD = Io evD /VT Io = 10 15 A VT = 26 mV VS = VTH = 15 V R = Req = 60 Determine an expression for the DC load line Then use an iterative technique to determine the voltage across and current through the nonlinear device
+ + _ VS
30 25
iD + vD NL
30 40
Figure P364
20 i D (ma) 20
10 10 psig 10 v D (V) (b) 20 30
Figure P363
AC Network Analysis
n this chapter we introduce energy-storage elements and the analysis of circuits excited by sinusoidal voltages and currents Sinusoidal (or AC) signals constitute the most important class of signals in the analysis of electrical circuits The simplest reason is that virtually all of the electric power used in households and industries comes in the form of sinusoidal voltages and currents The chapter is arranged as follows First, energy-storage elements are introduced, and time-dependent signal sources and the concepts of average and rootmean-square (rms) values are discussed Next, we analyze the circuit equations that arise when time-dependent signal sources excite circuits containing energystorage elements; in the course of this discussion, it will become apparent that differential equations are needed to describe the dynamic behavior of these circuits The remainder of the chapter is devoted to the development of circuit analysis techniques that greatly simplify the solution of dynamic circuits for the special case of sinusoidal signal excitation; the more general analysis of these circuits will be completed in 5 By the end of the chapter, you should have mastered a number of concepts that will be used routinely in the remainder of the book; these are summarized as follows:
De nition of the i-v relationship for inductors and capacitors Computation of rms values for periodic waveforms
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