Electric Circuits (10th Edition)
10th Edition
ISBN: 9780133760033
Author: James W. Nilsson, Susan Riedel
Publisher: PEARSON
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Question
Chapter 6, Problem 21P
a.
To determine
Derive the expression for the voltage across the capacitor at the interval
b.
To determine
Derive the expression for the voltage across the capacitor at the interval
c.
To determine
Derive the expression for the voltage across the capacitor at the interval
d.
To determine
Derive the expression for the voltage across the capacitor at the interval
e.
To determine
Sketch the voltage
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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 6 Solutions
Electric Circuits (10th Edition)
Ch. 6.1 - The current source in the circuit shown generates...Ch. 6.2 - Prob. 2APCh. 6.2 - The current in the capacitor of Assessment Problem...Ch. 6.3 - The initial values of i1 and i2 in the circuit...Ch. 6.3 - Prob. 5APCh. 6.4 - Write a set of mesh-current equations for the...Ch. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - The current in a 200 mH inductor is
The voltage...Ch. 6 - Evaluate the integral
for Example 6.2. Comment on...
Ch. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Initially there was no energy stored in the 5 H...Ch. 6 - The voltage across a 5 μF capacitor is known to...Ch. 6 - The triangular voltage pulse shown in Fig. P6.15...Ch. 6 - Prob. 16PCh. 6 - The expressions for voltage, power, and energy...Ch. 6 - The initial voltage on the 0.5 μF capacitor shown...Ch. 6 - Prob. 21PCh. 6 - Use realistic inductor values from Appendix H to...Ch. 6 - Prob. 24PCh. 6 - For the circuit shown in Fig. P6.24, how many...Ch. 6 - Prob. 27PCh. 6 - Use realistic capacitor values from Appendix H to...Ch. 6 - Derive the equivalent circuit for a series...Ch. 6 - Derive the equivalent circuit for a parallel...Ch. 6 - Prob. 31PCh. 6 - The four capacitors in the circuit in Fig, P6.32...Ch. 6 - For the circuit in Fig. P6.32, calculate
the...Ch. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Show that the differential equations derived in...Ch. 6 - Prob. 37PCh. 6 - Let υg represent the voltage across the current...Ch. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 44PCh. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - Prob. 47PCh. 6 - Prob. 48PCh. 6 - Prob. 49PCh. 6 - The self-inductances of two magnetically coupled...Ch. 6 - Prob. 51PCh. 6 - Prob. 52PCh. 6 - Prob. 53P
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