Engineering Electromagnetics
Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Chapter 5, Problem 5.30P

Consider a composite material made up of two species: having number densities N1 and N2 molecule s/m3, respectively. The two materials are uniformly mixed, yielding a total number density of N = N1 +N2- The presence of an electric field E induces molecular dipole moments p1 and p2 within the individual species, whether mixed or not. Show that the dielectric constant of the composite material is given by ε r = f ε r 1 + ( 1 f ) ε r 2 , where f is the number fraction of species 1 dipoles in the composite, and where ε r 1 and ε r 2 are the dielectric constants that the unmixed species would have if each had number density N.

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consider the circuit below. Assume it uses ideal diodes with the details specified above. the left side of the circuit is basically a wheatstone bridge, hooked to the right side, which is a differential op amp. a) what is the voltage between junctions "A" and "B" if R2 is 201 ohms? b) what are the minimum and maximum values of R2 can be without the op amp hitting saturation?remember that for the diodes to be ideal you they have to have a turn on voltage of 0.6 volts.
The capacitors in the circuit shown below have no energy stored in them and then switch “S1” closes at time t=0. Assume the ideal op amp does not saturate. As stated above assume the diodes are ideal with parameters specified above. Diodes are at 0.6 Volts Show the derivations of the mathematical equations for v(t) at Locations A and B for t≥ 0
Phase (deg) Magnitude (dB) -20 -40 -60 -80 -100 ° -90 -180 -270 10-1 (i) ° Problem 5 Consider a unity (negative) feedback system with a proportional controller. The Bode plot of the plant transfer function G(s) is given as below. System: sys Frequency (rad/s): 1 Magnitude (dB): 13.9 System: sys Frequency (rad/s): 14.9 Magnitude (dB): 6.58 System: sys Frequency (rad/s): 1 Phase (deg): -9.76 10° System: sys Frequency (rad/s): 25.6 Magnitude (dB): -0.0703 System: sys Frequency (rad/s): 41.3 Magnitude (dB): -8.06 System: sys Frequency (rad/s): 200 Magnitude (dB): -44.4 System: sys Frequency (rad/s): 14.9 Phase (deg): -110 System: sys Frequency (rad/s): 25.6 Phase (deg): -148 System: sys Frequency (rad/s): 41.3 Phase (deg): -180 System: sys Frequency (rad/s): 200 Phase (deg): -247 101 Frequency (rad/s) 102 Find the gain crossover frequency, phase crossover frequency, gain margin and phase margin of the system. Is the closed-loop system stable? (ii) What is the steady-state error of the…

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