ENGINEERING CIRCUIT...(LL)>CUSTOM PKG.<
9th Edition
ISBN: 9781260540666
Author: Hayt
Publisher: MCG CUSTOM
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Chapter 7, Problem 18E
To determine
Sketch the voltage across
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Introduction
The circuit of Fig. 1 is required to be modeled using a state - space representation, where 2
states will be used, based on the number of the energy - storing elements of the circuit, the
capacitor and the inductor.
u(t)
+
ΙΩ
www
13
F
5 Ω it (t)
www
vc(t) 1 H
Figure 1: LCR circuit
The input signal to the circuit is the voltage u(t) in Volts and the output signal is the voltage
across the capacitor, vc(t).
Questions
1. Choice of system states:
Choose appropriate signals for the 2 states of the
system.
x₁(t) = i₁(t)
x₂ (t) =
5. State transition matrix:
(t), which is defined as,
Calculate analytically the state transition matrix
(t) = et = L¯¹{(sI – A)¯¹}
Show that the answer is the following,
1
e-4t cos(√2t) -
e-4 sin(√2 t)
1
e
-4t
√2
(t) = et
-3
1
-4t sin (√2 t)
e
COS
-4t cos (√2t) + -
e
sin(√2 t)
2-4t sin(√2 t)|
Calculate the following:
(SI - A)-1=
Use the completion - in - the-square technique (CASE 3) to calculate the inverse Laplace:
L¯¹{(SI - A)¯¹} =
A single-core cable working on 66 kV has a conductor diameter of 2 cm and the sheath of inside diameter
is 10 cm. If two metallic intersheaths of diameters 5 cm, 8 cm respectively are used for grading the cable.. If
the maximum electric stress is the same for each layers.
1- Find the voltage of each metallic intersheaths.
2- Find the thickness of each layers.
Chapter 7 Solutions
ENGINEERING CIRCUIT...(LL)>CUSTOM PKG.<
Ch. 7.1 - Determine the current flowing through a 5 mF...Ch. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.2 - 7.4 The current through a 200 mH inductor is shown...Ch. 7.2 - The current waveform of Fig. 7.14a has equal rise...Ch. 7.2 - Prob. 6PCh. 7.2 - Let L = 25 mH for the inductor of Fig. 7.10. (a)...Ch. 7.3 - Find Ceq for the network of Fig. 7.23. FIGURE...Ch. 7.4 - If vC(t) = 4 cos 105t V in the circuit in Fig....Ch. 7.5 - Derive an expression for vout in terms of vs for...
Ch. 7.6 - Prob. 11PCh. 7 - Making use of the passive sign convention,...Ch. 7 - Prob. 2ECh. 7 - (a) If the voltage waveform depicted in Fig. 7.42...Ch. 7 - A capacitor is constructed from two brass plates,...Ch. 7 - Prob. 5ECh. 7 - Prob. 6ECh. 7 - Design a capacitor whose capacitance can be varied...Ch. 7 - Design a capacitor whose capacitance can be varied...Ch. 7 - Prob. 9ECh. 7 - Assuming the passive sign convention, sketch the...Ch. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Calculate the power dissipated in the 40 resistor...Ch. 7 - Prob. 15ECh. 7 - Design a 30 nH inductor using 28 AWG solid soft...Ch. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Calculate vL and iL for each of the circuits...Ch. 7 - The current waveform shown in Fig. 7.14 has a rise...Ch. 7 - Determine the inductor voltage which results from...Ch. 7 - Prob. 24ECh. 7 - The voltage across a 2 H inductor is given by vL =...Ch. 7 - Calculate the energy stored in a 1 nH inductor if...Ch. 7 - Determine the amount of energy stored in a 33 mH...Ch. 7 - Making the assumption that the circuits in Fig....Ch. 7 - Calculate the voltage labeled vx in Fig. 7.52,...Ch. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Determine an equivalent inductance for the network...Ch. 7 - Using as many 1 nH inductors as you like, design...Ch. 7 - Compute the equivalent capacitance Ceq as labeled...Ch. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Reduce the circuit depicted in Fig. 7.59 to as few...Ch. 7 - Refer to the network shown in Fig. 7.60 and find...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Let vs = 100e80t V with no initial energy stored...Ch. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Interchange the location of R1 and Cf in the...Ch. 7 - For the integrating amplifier circuit of Fig....Ch. 7 - Prob. 53ECh. 7 - For the circuit shown in Fig. 7.73, assume no...Ch. 7 - A new piece of equipment designed to make crystals...Ch. 7 - An altitude sensor on a weather balloon provides a...Ch. 7 - One problem satellites face is exposure to...Ch. 7 - The output of a velocity sensor attached to a...Ch. 7 - A floating sensor in a certain fuel tank is...Ch. 7 - (a) If Is = 3 sin t A, draw the exact dual of the...Ch. 7 - Draw the exact dual of the simple circuit shown in...Ch. 7 - (a) Draw the exact dual of the simple circuit...Ch. 7 - (a) Draw the exact dual of the simple circuit...Ch. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - For the circuit of Fig. 7.28, (a) sketch vout over...Ch. 7 - (a) Sketch the output function vout of the...Ch. 7 - For the circuit of Fig. 7.72, (a) sketch vout over...
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