Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 6, Problem 6.6P
A parallel-plane capacitor is made using two circular plates of radius a, with the bottom plate on the xy plane, centered at the origin. The top plate is located at z = d, with its center on the 2 axis. Charge Q is on the top plate; -Q is on the bottom plate. Dielectric having z-dependent permittivity fills the region between plates. The permittivity is given by (z) = đ�œ–0(l + z2/d2 ). Find (a) D; (b) E; (c) V0 : (d) C.
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Q2. Figure Q2 shows a block diagram with an input of C(s) and an output R(s).
a)
C(s)
K₁
R(s)
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Figure Q2. Block diagram of control system.
Simply the block diagram to get the transfer function of the system C(s)/R(s).
b)
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c)
What is the gain of the system?
d) Determine the values of K₁ and K₂ to obtain a natural frequency w of
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e) What is the rise time and overshoot of the system with a unit step input?
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a) A purely derivative controller (i.e. with a zero at the origin only) is defined
by an improper transfer function. Considering its asymptotic behaviour,
explain why a purely derivative controller is difficult to implement in
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performance.
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frequency. Relate your discussion to the implications on system
performance.
c)
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S
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(ii) Clearly describe the asymptotic behaviour of each individual
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Module Code: EN2058
Q1. a) List the advantages and disadvantages of a closed loop system compared to
an open loop system.
b)
c)
What is the procedure for designing a control system for a bread toaster?
An RC circuit is given in Figure Q1. vi(t) and v(t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
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time response of the circuit.
R1 R2
v₁(t)
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vo(t)
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Figure Q1. RC circuit.
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Chapter 6 Solutions
Engineering Electromagnetics
Ch. 6 - Prob. 6.1PCh. 6 - Let S = 100 mm2. d= 3 mm, and er = 12 for a...Ch. 6 - Capacitors tend to be more expensive as their...Ch. 6 - Prob. 6.4PCh. 6 - Prob. 6.5PCh. 6 - A parallel-plane capacitor is made using two...Ch. 6 - For the capacitor of Problem 6.6, consider the...Ch. 6 - Prob. 6.8PCh. 6 - Prob. 6.9PCh. 6 - A coaxial cable has conductor dimensions of a =...
Ch. 6 - Prob. 6.11PCh. 6 - (a) Determine the capacitance of an isolated...Ch. 6 - With reference to Figure 6.5, let b=6m, h=15m, and...Ch. 6 - Two=16 copper conductor (1.29 mm diameter) are...Ch. 6 - Prob. 6.15PCh. 6 - Prob. 6.16PCh. 6 - Construct a curvilinear-square map for a coaxial...Ch. 6 - Prob. 6.18PCh. 6 - Construct a curvilinear- square map of the...Ch. 6 - Prob. 6.20PCh. 6 - The inner conductor of the transmission line shown...Ch. 6 - Prob. 6.22PCh. 6 - Prob. 6.23PCh. 6 - A potential field in free space is given in...Ch. 6 - A capacitor is formed from concentric spherical...Ch. 6 - Given the spherical symmetric field in free space,...Ch. 6 - Let V=z(x,y)=4e2xf(x)3y2 in a region of free space...Ch. 6 - Show that in a homogeneous medium of conductivity...Ch. 6 - What total charge must be located within a unit...Ch. 6 - Prob. 6.30PCh. 6 - For the parallel-plate capacitor shown in Figure...Ch. 6 - Prob. 6.32PCh. 6 - The functions V1 (p, , z) and V2(p, , z) both...Ch. 6 - Prob. 6.34PCh. 6 - Prob. 6.35PCh. 6 - Prob. 6.36PCh. 6 - Prob. 6.37PCh. 6 - Prob. 6.38PCh. 6 - Prob. 6.39PCh. 6 - Prob. 6.40PCh. 6 - Prob. 6.41PCh. 6 - Prob. 6.42PCh. 6 - Prob. 6.43PCh. 6 - Prob. 6.44PCh. 6 - Prob. 6.45PCh. 6 - By appropriate solution of Laplaces and Poissons...
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