EBK ELECTRIC CIRCUITS
10th Edition
ISBN: 9780100801790
Author: Riedel
Publisher: YUZU
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Question
Chapter 12, Problem 43P
(a)
To determine
Determine the inverse Laplace transform
(b)
To determine
Determine the inverse Laplace transform
(c)
To determine
Determine the inverse Laplace transform
(d)
To determine
Determine the inverse Laplace transform
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50mV and 10kHz from the function generator to the input. The mulitmeter postive is connected to the output and negative to a ground. Is the circuit connected correctly? Yes or No. Does the reading look correct? I don't need calculations but will take them. I just need to know if the connection is right.
Connect a signal generator to the input and set it for 50 mV Sine wave with a frequency of 10 kHz. Connect the output to a multimeter set to RMS voltage. Record the output voltage and frequency in the following table. Repeat the measurement for all given frequency values in the table.
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
Chapter 12 Solutions
EBK ELECTRIC CIRCUITS
Ch. 12.4 - Prob. 1APCh. 12.5 - Prob. 2APCh. 12.7 - Prob. 3APCh. 12.7 - Prob. 4APCh. 12.7 - Prob. 5APCh. 12.7 - Prob. 6APCh. 12.7 - Prob. 7APCh. 12.7 - Prob. 8APCh. 12.7 - Prob. 9APCh. 12.8 - Use the initial- and final-value theorems to find...
Ch. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Use step functions to write the expression for...Ch. 12 - Prob. 4PCh. 12 - Explain why the following function generates an...Ch. 12 - Find the area under the function shown in Fig....Ch. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - Prob. 10PCh. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - The switch in the circuit in Fig. P12.28LO has...Ch. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - Prob. 33PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - Prob. 45PCh. 12 - Use the initial-value theorem to find the initial...Ch. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Prob. 55PCh. 12 - Prob. 56P
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- 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).arrow_forward"I need an expert solution because the previous solution is incorrect." An antenna with a radiation impedance of 75+j10 ohm, with 10 ohm loss resistance, is connected to a generator with open-circuit voltage of 12 v and an internal impedance of 20 ohms via a 2/4-long transmission line with characteristic impedance of 75 ohms. (a) Draw the equivalent circuit (b) Determine the power supplied by the generator. (c) Determine the power radiated by the antenna. (d) Determine the reflection coefficient at the antenna terminals.arrow_forward--3/5- b) g(t) = 3 1441 g(t+mT) = g(t) -31 (i) Complex fourier coefficient Cn. (ii) Complex fourier coefficients - real fourier coefficient (the first 5 non-zero terms) of (iii) sketch the amplitude spectrum g(t) |Cal against n. n= -3 ⇒n=3 (labelling the axis).arrow_forward
- Q4) (i) Calculate the fourier transform of : h(t) 2T (is) h(t) 2T -T о T 2T ·(-++T). cos2t ost≤T (iii) hro (4) ((-++T). cos otherwisearrow_forwardQ2)a) consider the Circuit in figure 2 with initial conditions of Vc (o) = 5V, I₁ (o) = 1A, (i) redraw the circuit in the frequency domain using laplace Wansforms. (ii) using this circuit derive an equation for the Voltage across the inductor in the time domain.. 3.12 ww =V/3F ZH (figure 2) d) Solve the following second order differential equation using laplace transforms. d12 + 5 dx 3x=71 dt - with initial conditions x² (0) = 2, α(0) = 1arrow_forwardb) Another periodic waveform is defined by T c) g(t)= T with g(t+mT) = g(t) and m is an integer. (i) Sketch g(t) over two full cycles in the time domain, labelling the axes. (ii) Derive the formulae for the complex Fourier coefficients c₁ for g(t). For a periodic waveform h(t), if its complex Fourier coefficients are T T when n is odd T 2n²² T 4nn when n is even and not zero 4nn please derive the first five non-zero terms of the real Fourier series for h(t).arrow_forward
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