Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Chapter 14.6, Problem 13P
(a)
To determine
The initial and final value of the given function
(b)
To determine
The initial and final value of the given function
(c)
To determine
The initial and final value of the given function
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At t = 0, the switch is opened after being closed for a very long time. Use the Laplace method. Use the series equivalent circuit for the inductor and the parallel equivalent circuit for the capacitor.
a) Find iL(0).
b) Find vC(0).
c) Find VC(s) using partial fractions.
d) Find an expression for vC(t) for t > 0.
Find the inverse Laplace transform of the following:
1. X(s) = [s + 2 + 4e^(−3s)]/[(s + 3)(s + 1)]
2. Y(s) = (s + 5)/[(s + 1)(s + 3)]
3. Z(s) = (s^2 + 6s + 7)/(s^2 + 3s + 2), Re(s) > −2
4. W(s) = (s^3 + 2s^2 + 6)/(s^2 + 3s) , Re(s) > 0
5. V (s) = (s^2 + 2s + 5)/[(s + 3)(s + 5)^2), Re(s) > −3
Where ROC is not specified, you may consider all of the s-plane to be ROC.
An LRC-series circuit has the following parameters L = 0.5 h, R =10 omega and C = 0.01 f. The voltage impressed on the circuit is constant E0 = 400V. The charge on the capacitor at time t = 0 is 5C. The current at time t = 0 is zero.
Use the Laplace transform to find q(t), where q(t) is the charge on the capacitor.
Chapter 14 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Ch. 14.1 - Identify all the complex frequencies present in...Ch. 14.1 - Use real constants A, B, C, , and so forth, to...Ch. 14.2 - Let f (t) = 6e2t [u(t + 3) u(t 2)]. Find the (a)...Ch. 14.3 - Prob. 4PCh. 14.3 - Prob. 5PCh. 14.4 - Prob. 6PCh. 14.4 - Prob. 7PCh. 14.4 - Prob. 8PCh. 14.4 - Prob. 9PCh. 14.5 - Prob. 10P
Ch. 14.5 - Prob. 11PCh. 14.5 - Prob. 12PCh. 14.6 - Prob. 13PCh. 14.7 - Prob. 14PCh. 14.7 - Prob. 15PCh. 14.8 - Find the mesh currents i1 and i2 in the circuit of...Ch. 14.8 - Prob. 17PCh. 14.8 - Prob. 18PCh. 14.9 - Using the method of source transformation, reduce...Ch. 14.9 - Prob. 20PCh. 14.10 - The parallel combination of 0.25 mH and 5 is in...Ch. 14.11 - Prob. 22PCh. 14.11 - Prob. 23PCh. 14.11 - Prob. 24PCh. 14.11 - Prob. 25PCh. 14.12 - Prob. 26PCh. 14 - Determine the conjugate of each of the following:...Ch. 14 - Compute the complex conjugate of each of the...Ch. 14 - Several real voltages are written down on a piece...Ch. 14 - State the complex frequency or frequencies...Ch. 14 - For each of the following functions, determine the...Ch. 14 - Use real constants A, B, , , etc. to construct the...Ch. 14 - The following voltage sources AeBt cos(Ct + ) are...Ch. 14 - Prob. 8ECh. 14 - Compute the real part of each of the following...Ch. 14 - Your new assistant has measured the signal coming...Ch. 14 - Prob. 11ECh. 14 - Prob. 12ECh. 14 - Prob. 13ECh. 14 - Prob. 14ECh. 14 - Prob. 15ECh. 14 - Prob. 16ECh. 14 - Determine F(s) if f (t) is equal to (a) 3u(t 2);...Ch. 14 - Prob. 18ECh. 14 - Prob. 19ECh. 14 - Prob. 20ECh. 14 - Prob. 21ECh. 14 - Evaluate the following: (a)[(2t)]2 at t = 1;...Ch. 14 - Evaluate the following expressions at t = 0: (a)...Ch. 14 - Prob. 24ECh. 14 - Prob. 25ECh. 14 - Prob. 26ECh. 14 - Prob. 27ECh. 14 - Prob. 28ECh. 14 - Prob. 29ECh. 14 - Prob. 30ECh. 14 - Prob. 31ECh. 14 - Prob. 32ECh. 14 - Prob. 33ECh. 14 - Obtain the time-domain expression which...Ch. 14 - Prob. 35ECh. 14 - Prob. 36ECh. 14 - Prob. 37ECh. 14 - Prob. 38ECh. 14 - Prob. 39ECh. 14 - Prob. 40ECh. 14 - Prob. 41ECh. 14 - Obtain, through purely legitimate means, an...Ch. 14 - Prob. 43ECh. 14 - Employ the initial-value theorem to determine the...Ch. 14 - Prob. 45ECh. 14 - Prob. 46ECh. 14 - Prob. 47ECh. 14 - Prob. 48ECh. 14 - Prob. 49ECh. 14 - Prob. 52ECh. 14 - Determine v(t) for t 0 for the circuit shown in...Ch. 14 - Prob. 54ECh. 14 - Prob. 55ECh. 14 - For the circuit of Fig. 14.54, (a) draw both...Ch. 14 - Prob. 58ECh. 14 - Prob. 59ECh. 14 - Prob. 60ECh. 14 - For the circuit shown in Fig. 14.58, let is1 =...Ch. 14 - Prob. 63ECh. 14 - Prob. 64ECh. 14 - For the circuit shown in Fig. 14.62, determine the...Ch. 14 - Prob. 67ECh. 14 - Prob. 68ECh. 14 - Determine the poles and zeros of the following...Ch. 14 - Use appropriate means to ascertain the poles and...Ch. 14 - Prob. 71ECh. 14 - For the network represented schematically in Fig....Ch. 14 - Prob. 73ECh. 14 - Prob. 74ECh. 14 - Prob. 75ECh. 14 - Prob. 76ECh. 14 - Prob. 77ECh. 14 - Prob. 78ECh. 14 - Prob. 79ECh. 14 - Prob. 80ECh. 14 - Prob. 81ECh. 14 - Prob. 82ECh. 14 - Design a circuit which produces the transfer...Ch. 14 - Prob. 84ECh. 14 - Prob. 85ECh. 14 - An easy way to get somebodys attention is to use a...Ch. 14 - Prob. 87E
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- 2) In the circuit shown in Fig. 1, the capacitor is initially charged to V0 volts and the switch isclosed at t = 0. Obtain the current, i(t), for t> 0 using the Laplace transform.arrow_forwardThe switch has been closed for a very long time. At t = 0, the switch is opened. Using the Laplace method and the series equivalent circuit for the inductor and the parallel equivalent circuit for the capacitor, find:a. iL(0)b. vC(0)arrow_forwardThe switch has been closed for a very long time. At t = 0, the switch is opened. (Note: Use the Laplace method in your solutions. Use the series equivalent circuit for the inductor and the parallel equivalent circuit for the capacitor.) Find iL(0), vC(0), vC(s) using partial fractions, and find an expression for vC(t) for t > 0.arrow_forward
- 1. What is the Transfer Function of this Differential Equation? 2. Find the solution to the dierential equation in the time domain assuming y (t) = Aest (you are not allowed to use Laplace transforms). Use the initial conditions y (0) = 1/6 , y'(0) = 5, with f (t) = u(t).arrow_forwardIn the following circuit, R=1 [ohm], C=1[F], and all initial values are 0. 1. Using Laplace Transform, find the ratio H(s)=Vo(s)/Vi(s).2. Find the roots of the characteristic equation.3. Find the conditions for K which will make the circuit over-damped and under-damped, respectively.4. When K=2, vi(t)=sqrt(10)cost, find vo(t) after a long time has passed.arrow_forwardA causal linear time-invariant continuous-time system has impulse response h(t) = e-t +sin(t) , t >= 0 Compute the output response for all t>=0 when the input is the unit-step function u(t).arrow_forward
- The circuit is at a steady state before the switch closes at time=0. Determine the inductor current, i(t), for t>0. ( Do not use Laplace Transform)arrow_forwardIn the circuit below, switch S has been closed for a long time, and opens at t=0 . Usethe Laplace transform method to compute Vc(t) for t ˃0.arrow_forwardUsing Laplace, what is the output current i(t) at 0<t<15 given that i(t) at t<0 is 0A?arrow_forward
- Sketch the poles and zeros on the s-domain plot( complex plane) for the following function: H(s)= [(s+6)(s-2)]/[(s-3)(s+5)((s-3)^2 +9) For each pole and zero, examine its location in the s-plane and comment on its contribution to the systems behavior. Please answer in typing format please ASAParrow_forwardApply 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).arrow_forwardSuppose for the circuit shown, Idc=24 mA, R=625 Ω, L=25 mH, and C=25 nF. There is no energy stored in the circuit when the switch opens at t=0. 1. Find V(s), the Laplace transform of v(t). 2. Find v(t) by finding the inverse transform of the partial fraction expansion of V(s).arrow_forward
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