Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 15, Problem 8RQ
To determine
Choose the correct option to find the initial value of
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Given R = 3.1 Ω, C=92 mF in the equation
Vs (t) = Ri (t) + 1/C ∫ i (r) dr Note: Integral goes from 0 to t
Apply Lapace transform, we can have
I(s) = (Ys/ s + X ) Vs (s)
What is the value of Y?
Apply the initial- and final-value theorems to each transform pair
1. F(s)=8s2+37s+32(s+1)(s+2)(s+4).
2. F(s)=8s3+89s2+311s+300s(s+2)(s2+8s+15).
3. F(s)=22s2+60s+58(s+1)(s2+4s+5).
4. F(s)=250(s+7)(s+14)s(s2+14s+50).
The inverse Laplace transform of the following function is:
6.
F(s) =
(s+5)4
%3D
O a. He-5tu(t-5)
Ob Be-5tu(t)
6e-5tsin(t)u(t)
|
O d. None of the answers
6e-5tcos(t)u(t)
e.
N
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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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- • What is the inverse transform of 10(6* +119 ) 2 F (s) = (s +5 s? +10s +169 ) 2 • Solution approach: Separate into 1 term for each root: * A F (s) = K K + + (s +5)" (s+5 – j12)" (s +5+ j12)arrow_forward4. In the circuit below, i(t) is given by the following waveform. Solve for the voltage across the capacitor in the s-Domain. Your answer should be reduced and simplified; there is no need to calculate the inverse transform. i(A) 1kQ ↑)i(t) 3μH + V I 2μF 10+ 5 10°t (sec)arrow_forwardQ5: If the F.T of f (t) is: 10 F(@) = 2+ jw)(5 + jw) Determine the transform of the following: f(-3t) f(2t - 1) f(t) cos2t d. f(t) dt t f(t)dt -00arrow_forward
- i. Determine from first principles the Laplace Transform of t+2e=t -6s+85-56 ii. Show that f (t) = {4sin (2t) – 6e“} =F+4)(3-4)arrow_forward4- Find the z transform of the following functions: (a) x₁(n)= (-1)"2"u(n) (b) x2 (n) = na" sin(won)u(n) (c) x3 (n) = (n²+ n)an-lu(n-1) (d) x4(n) = (0.5)" [u(n) - u(n = 5)] -arrow_forwardxpress each of the waveforms in terms of step functions and then determine its Laplace transform. [Recall that the ramp function is given by r(t -T) = (t -T) u(t -T)]. Assume that all waveforms are zero for t < 0. fi(1) 4 2 0 A. f₁(t) = 2 t(s) fs(1) 10+ 0 -10+ B. f5(t) = 2 -t (s)arrow_forward
- (c) Suppose f(t) = u(t – 2) and g(t) = u(t + 2). Using the convolution integral, derive an expression for y(t) = f(t) * g(t). In your work, you must flip and shift f(t).arrow_forwardThe Laplace transform of the following function is: f(t) = 8u(t-1) + 2u(t − 5) – u(t) - Select one: a. F(s) = §els b. O ○ c. F(s) = F(s) = O d. F(s) = = els es 90/0000100 e - - + / e-8 2 - e+e- ³ + 3/2e - 1 8² e + ²/e-58-1 8 Sarrow_forwardQuestion The Laplace transform of f (t) = 5 cos(7t)- 7e2t +t³ is: 5s F(s) , * 2 6. F(s) = s2+4 S-2 s+3 This option O This option 7 F(s) = +: 4. F(s) $2+49 S-2 s2+4 s+3 This option This optionarrow_forward
- %A. l l 0 H.W-Z-transfor... H.W: Obtain Z-transform for the Followings 1) x(t) = Coswt 2) x(s) %3D (s+a)2 1 3) x(s) = s(s+1) 4)x(t)=1(t+4T) 5)x(t)=t (t-2T) 6)x(t)=sin(t-3T)arrow_forwardInstructions: • Write the GIVEN with their respective symbols and units. Do not skip the SOLUTIONS, do it step-by-step with their respective symbols and units Problem: Using the convolution integral find the inverse transform of 1/s(s + 2). Answer: |[1 – e-2"]arrow_forward2(s+9) The Inverse Laplace Transform of is: s2+2s+50 Select one: O a. 3.03e-tcos (7t – 48.7)u(t) O b. 3.03e-tsin (7t + 48.7°)u(t) Oc. 6.06e-tcos (7t + 56.3°)u(t) O d. 3.03e-tcos (7t + 48.7°)u(t) O e. 3.03e-tsin (7t – 48.7°)u(t)arrow_forward
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