Delmar's Standard Textbook of Electricity (MindTap Course List)
6th Edition
ISBN: 9781285852706
Author: Stephen L. Herman
Publisher: Cengage Learning
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Chapter 20, Problem 4RQ
In what form is the energy of a capacitor stored?
Expert Solution & Answer
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Students have asked these similar questions
The input reactance of an infinitesimal linear dipole of length A/60 and radius a=A/200
is given by
Xin = – 120
[In(€/a) — 1]
tan(ke)
Assuming the wire of the dipole is copper with a conductivity of 5.7 x 10' S/m,
determine at f = 1 GHz the
(a) loss resistance
(b) radiation resistance
(c) radiation efficiency
(d) VSWR when the antenna is connected to a 50-ohm line
Example
Solve the octic polynomial
2x⁸-9x⁷+20x⁶-33x⁵+46x⁴-66x³+80x²-72x+32=0
Solution
Divide by x⁴
2x⁴-9x³+20x²-33x+46-66/x + 80/x² - 72/x³ + 32/x⁴=0
Combine and bring terms
2(x⁴+16/x⁴) - 9(x³+8/x³) +20(x²+4/x²)-33(x+2/x) + 46= 0
Let use substitution
Let x+2/x =u
(x+2/x)²= u²
x²+2x*2/x + 4/x² = u²
x²+4/x²= u²-4
(x+2/x)³= x³+8/x³+3x*2/x(x+2/x)
u³= x³+8/x²+6u
x³+8/x³= u³-6u
(x²+4/x²)²= x⁴+2x²*4/x² + 16/x⁴
(u²-4)²= x⁴+16/x⁴ + 8
x⁴+16/x⁴ = (u²-4)²-8
x⁴+16/x⁴ = u⁴-8u²+8
2(u⁴-8u²+8)-9(u³-6u)+20(u²-4)-33u+46=0
Expand and simplify
2u⁴-9u³+4u²+21u-18=0
After checking
(u-1)(u-2) Are factors
Then
2u²-3u-9=0
u=3, u=-3/2
Assignment question
Solve the octic polynomial
2s⁸+s⁷+2s⁶-31s⁴-16s³-32s²-160=0 using the above example question, please explain in detail
b)
Another waveform g(t) is defined by
=0
t≥0, α>0
otherwise
g(t)= At exp(-at)
and is plotted in Figure 1 (for representative values of 4 = 1 and α = 1).
g(t)
0.4T
0.3+
0.2
0.1+
2
0
2
Figure 1
8
c)
Show that its amplitude spectrum is |G(@)| = -
A
(a²+0²)²
Describe briefly, with the aid of labelled sketches, how changing a affects
the waveform in both the time and frequency domains.
d) Deduce the Fourier transform H(@) of h(t) = g(t)+g(t+b)+g(t-b) and
calculate its DC amplitude H(0).
Chapter 20 Solutions
Delmar's Standard Textbook of Electricity (MindTap Course List)
Ch. 20 - 1. What is the dielectric?
Ch. 20 - List three factors that determine the capacitance...Ch. 20 - A capacitor uses air as a dielectric and has a...Ch. 20 - 4. In what form is the energy of a capacitor...Ch. 20 - Four capacitors having values of 20 F, 50 F, 40 F,...Ch. 20 - f the four capacitors in Question 5 were to be...Ch. 20 - A 22-F capacitor is connected in series with a...Ch. 20 - 8. A 450-pF capacitor has a total charge time of...Ch. 20 - Can a nonpolarized capacitor be connected to a DC...Ch. 20 - Explain how an AC electrolytic capacitor is...
Ch. 20 - What type of electrolytic capacitor will be...Ch. 20 - A 500-nF capacitor is connected to a 300-k...Ch. 20 - A film-type capacitor is marked 253 H. What are...Ch. 20 - A postage stamp mica capacitor has the following...Ch. 20 - A postage stamp capacitor has the following color...Ch. 20 - You are changing the starting relay on a central...Ch. 20 - You are an electrician working in an industrial...Ch. 20 - You find that a 25-F capacitor connected to 480...Ch. 20 - Fill in all the missing values. Refer to the...Ch. 20 - Two capacitors having values of 80 F and 60 F are...Ch. 20 - Three capacitors having values of 120 F, 20 F, and...Ch. 20 - Three capacitors having values of 2.2 F, 280 F,...Ch. 20 - A 470-F capacitor is connected in series with a...
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