Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 15.2, Problem 1PP
To determine
Calculate the Laplace transform for the given functions
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Find the transforms of the following waveforms
a) f(t) = [2+2sin2t – 2cos2t] u(t)
b) f(t) = 3[1- e 10] u(t)
c) f(t) = -58(t) + 50u(t)
Find the inverse z-transform for each of the following functions:
4z
a. X(z) = 2+
%3D
Z-1
Z-0.5
5z
2z
b. X(z)
%3D
(z - 1)2
(z - 0.5)?
Q1
Find the z transform for each of the following sequences:
a) 3u(n-4)
b) 2(-0.5)nu(n)
c) 4e-2nu(n)
d) 4(0.8) "cos (0.1лn)u(n)
Q2
Given the two sequences
x₁(n)= -28(n)+58(n-2) and x2(n)= 48(n-4)
a) Let x3(n) = x₁(n) * x2 (n)
Determine the Z transform of x3(n)
b) Find x3(n) using the inverse transform of X3(z).
Q3
Using the Z-transform properties and the Z-transform table find the inverse Z-
transform for each of the following sequences
a) 5- (7z/z+1) - (3z/z-0.5)
b) (-3z/(z-0.5)) +[ 8z/(z−0.8)]+ [2z/(z-0.8)²]
c)
3z/(z²+1.414z+1)
d) (5z %/z-1)-[ z^²/(z−1)²] + [z −¹⁰0] + [z ³/z-0.75]
Q4
Use partial fraction expansion, Find the inverse Z-transform of the following:
a) [1/(z²+0.5z+0.06)]
b) z/[(z+0.3)(z-0.5)]
c) 5z/[(z-0.75) (z²-z+0.5)]
d) 2z(z-0.4)/[(z-0.2)²(z+0.8)]
Q5
A system is described by the following difference equation
y(n)-0.5y(n-1) +0.06y(n-2)= (0.4)n-1u(n-1)
Determine the solution when the initial conditions are y(-1) = 1 and y(-2)=2.
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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- Q) Find the z-transform f(z) and sketch the pole-zero plot with the ROC for the following sequence. f(n) = (0.25)" u(n)+ (-0.5)" u(n)arrow_forwardQ.1 Find the z-transform f(z) and sketch the pole-zero plot with the ROC for each of the following sequences?arrow_forwardDerive the Laplace transform for the full-rectified waveform fFR (t) in figure 2 belowarrow_forward
- Determine the z-transforms of: i. x(n) = (-"u(n – 1) + 3(-2)"u(-n-1) ii. x(n) = )" nu(n + 1) – ()" u(n – 2)arrow_forwarda) A siganl x (1) =te u (t) +P (t-3) find its frequency transform b. Signal: y(t) =ae e-u(t) +"u(t-3) find its Laplas transform Hint: use trandform pairs and propertiesarrow_forwardA system defined by ℎ(t)=5e−5tu(t) is driven by a sinusoidal signal with frequency 5 rps and amplitude 4 V. How much is the amplitude of the output signal in volt? (hint: use L-transform of h(t))arrow_forward
- 6. Sequences are generated by sampling a causal continuous-time signal u(t) (t > 0) at uniform intervals T. Write down an expression for uk, the general term of the sequence, and calculate the corresponding z transform when u(t) = sin t. z sin T z2 – 2z cos T+1 z Cos T' z2 – 2z sin T+1 z Cos 2T z2 + 2z sin 2T – 1 z sin T z2 + 2z cos T 1arrow_forwardQIB) Determine the z-transform for the following sequences, sketch the pole-zero plot and indicate the ROC. x(n)= (0.5)" [u(n)-u(n-10)] n=0, 1, 2,..., 9arrow_forward2- Find the z transform of the following two functions: (a) x₁(n) = n(0.5)"-2u(n) (b) x2 (n) = (0.5)"u(n-2)arrow_forward
- From the first order system in the picture kv = 0.5 kp = 1.5 and ka = 4 using laplace transforms derive an expression to show how the output (angular displacement) will vary with time when a step input of 10v is appliedarrow_forwardExpress the function below using window and step functions and compute its Laplace transform. 2190 Q 0- 5x 16 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. A. g(t)= (sin 8t)u t-- (sin 8t)u (1-56) OB. 9(t)=11 sin (81) OC, 9(t) = (sin 8t)II 5x (t) + (sin 8t)u t- 0.7 16 salt) 0.16 I OD. g(t)=(cos 8t)u t-- : 8tu (1-556) 16 Compute the Laplace transform of g(t). L(g) = (Type an expression using s as the variable.)arrow_forwardDetermine the Z Transform for the foNowing sequence Sketch the pole-zero plot and indicate the ROC 7T (n) = 4"cos(n + -)u(-n – 1) 3 %3Darrow_forward
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