Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 15, Problem 25P
Let
- (a) Use the initial and final value theorems to find f(0) and f(∞).
- (b) Verify your answer in part (a) by finding f(t), using partial fractions.
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Problem 4:
Use Initial value theorem and final value theorem to find f(0) and f() for the following rational functions
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Introduction
The Riemannian Sum is a discrete-time approximation of integration (which is a continuous
time operation). The discrete-time approximation is useful because it allows integration to be
performed on computer systems which are based on digital electronics. Digital electronics
can only have discrete states (1s and Os) therefore all continuous-time signals are
represented as a discrete-time signals on a computer system.
Knowledge of the following topics is required to complete this assessment:
Sampling - Converting x(t) to x[n]
Converting between sample number (n) and time taken to reach that sample. This is
discussed in Lecture 1.
Nyquist Sampling Theorem - Discussed in Lecture 1.
Overall Objective
The objective for this assessment is for the student to write a C/C++ program that will
generate a signal x[n]. The values
(t) will be sent to a text file. This text file will then be used in MS Excel to plot the signal.
each sample of the signal and the value of the time
The area…
Use only DeMorgan's relationships and Involution to find the complement of the following
function:
(b) f(A, B, C, D) = AB'C + (A' + B + D)(ABD' + B')
Chapter 15 Solutions
Fundamentals of Electric Circuits
Ch. 15.2 - Prob. 1PPCh. 15.2 - Prob. 2PPCh. 15.3 - Prob. 3PPCh. 15.3 - Prob. 4PPCh. 15.3 - Prob. 5PPCh. 15.3 - Prob. 6PPCh. 15.3 - Obtain the initial and the final values of...Ch. 15.4 - Prob. 8PPCh. 15.4 - Find f(t) if F(s)=48(s+2)(s+1)(s+3)(s+4)Ch. 15.4 - Obtain g(t) if G(s)=s3+2s+6s(s+1)2(s+3)
Ch. 15.4 - Find g(t) given that G(s)=20(s+1)(s2+4s+13)Ch. 15.5 - Graphically convolve the two functions in Fig....Ch. 15.5 - Given g(t) and f(t) in Fig. 15.20, graphically...Ch. 15.5 - Use convolution to find vo(t) in the circuit of...Ch. 15.6 - Prob. 15PPCh. 15.6 - Prob. 16PPCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - If F(s) = 1/(s + 2), then f(t) is (a) e2t u(t) (b)...Ch. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Find F(s) if: (a) ft=6etcosh2t (b) ft=3te2tsinh4t...Ch. 15 - If g(t) = 4e 2t cos 4t, find G(s).Ch. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Design a problem to help other students better...Ch. 15 - Let F(s)=18(s+1)(s+2)(s+3) (a) Use the initial and...Ch. 15 - Determine the initial and final values of f(t), if...Ch. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - Find f(t) for each F(s): (a) 10ss+1s+2s+3 (b)...Ch. 15 - Prob. 32PCh. 15 - Prob. 33PCh. 15 - Prob. 34PCh. 15 - Obtain f(t) for the following transforms: (a)...Ch. 15 - Prob. 36PCh. 15 - Prob. 37PCh. 15 - Prob. 38PCh. 15 - Determine f(t) if: (a)...Ch. 15 - Show that...Ch. 15 - Prob. 41PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - Given h(t) = 4e2tu(t) and x(t) = (t) 2e 2tu(t),...Ch. 15 - Given the following functions...Ch. 15 - A system has the transfer function...Ch. 15 - Find f(t) using convolution given that: (a)...Ch. 15 - Prob. 49PCh. 15 - Prob. 50PCh. 15 - Given that v(0) = 5 and dv(0)/dt = 10, solve...Ch. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Design a problem to help other students better...Ch. 15 - Prob. 55PCh. 15 - Solve for v(t) in the integrodifferential equation...Ch. 15 - Prob. 57PCh. 15 - Given that dvdt+2v+50tv()d=4u(t) with v(0) = 1,...Ch. 15 - Solve the integrodifferential equation...Ch. 15 - Prob. 60P
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- Calculate the convolution for the continuous time signal h (t) shown in the figure below.and draw. (*:convolution) h(t) * h(t) * h(t)arrow_forwardNow consider the following continuous-time system with input and output specified sepa- rately, where u(t) is the unit step function and 8(t) is the Dirac delta function: r(t) = u(t)-3u(t-1) y(t) = 56(t)- 156(t-1)+u(t)- 2e-u(t)- 3u(t-1)+6e-u(t-1) (d) Is this system linear, and why?arrow_forward5 H(S) x(S) = ! %3D s+3 a. Find the output in the time domain (y(t) with a value for t :5r b. Picture of the first order step function response curve.arrow_forward
- Required information Consider the CTFT pair. u (t + 5) – u (t – 7) → A sinc (bf) eicf The numerical values of the literal constants are A = b = and c=arrow_forward3. A discrete time signal x(n) is shown in figure below x(n)t -2 -1 0 1 2 3 4 Sketch the signal x(n)u(2 – n) 1/2arrow_forwardLet x(t) = u(cos (2nt)) (u(t)-u(t-2)) and h(t) = eu(t), and let y (t) = x(t) * h(t). What is the value of y (2) ? Hint: u(x) is the unit step function None of the choices O y(2) = 0.1198 O y(2) = 0.27662 %3D O y(2) = 0.037437 O y(2) = 0.10177 O y(2) = 0.32569arrow_forward
- Waveform synthesis Below, use the symbol r(t) for the ramp function and u(t) for the step function. Write the expression of æ1 (t) below in terms of ramp and step functions:|| x1 (t) 2 -3 -2 -1 0 1 2 3arrow_forwardConsider the signal: x(t) = exp(-rt) cos(t) u(t) where u(t) is a step function. The signal x(t) will have Finite-energy signal when r>0 Finite-energy when r<0 Finite-energy for all values of r Infinite-energy regardless of the r valuearrow_forwardFind the mathematical expression for iC(t) on the interval t0 < t < t1. Provide your answer in amps (A). Response format: Use the following "Picture 1"arrow_forward
- Calculate and plot each convolution for the continuous time signal h (t) shown in the figure below. (u (t): continuous time unit step function) a) h(t) * h(t) b) h(t) * h(t) * h(t)arrow_forwardCompute the convolution between signal F(t) and G(t) by shifting F(t), i.e., use the following equation to compute your convolution F(t) * G(t) = | F(t – t)G(t) dr - 00 F(T) = U(T-155)-U(t+155) G() 100+ 50 -100 100 Recommended steps to follow while solving 1. Draw the signal F(t) by properly labelling the axis 2. Draw the signal G(t) by properly labelling the axis 3. Draw the signal F(t – t) by properly labelling the axis and mentioning the condition of t 4. Draw the signal G(t) by properly labelling the axis 5. Compute the convolution now by properly defining ranges of t for which two signals do not overlap, partially overlap or full overlap.arrow_forwardThe following shows the discrete-time state equations of the continuous-time state equations given above for T = 0.1 seconds.arrow_forward
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