Electrical Circuits _ transient response Q2. The switch in the circuit shown below has been closed for a long time and is opened att=0. Analyze the circuit in the time-domain to find the transient response and v(t) fort > 0.t=00.25H15 A(V. *0.04 F10Q

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Answered: Q2. The switch in the circuit shown…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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The switch in the circuit has been closed for along time before it is opened at t=0. Assume that the circuit parametersare such that the response is underdamped.1. Derive the expression for vo(t) as a function of Vg, α, ωd, C, and Rfor t≥0.2. Derive the expression for the value of t when the magnitude of vois maximum
Consider the circuit on the left. DC voltage u1(t ≥ 0) = U is applied at time t = 0. Both meshes must include the input voltage. At time t = 0, the capacitors are free of energy. The following applies: τ = R*C. Derive the 2nd order differential equation for the capacitor voltage u2(t).
Assume that the circuit in the image has been connected for a very long time. (a) As time approaches infinity, what wtll happen to the capacitor and inductor? (b) From your answer in (a), draw the equivalent circuit (label appropriately).(c) From your circuit in (b), determine the "steady-state" or "final" values of Vc, lc, IL and VL
The mathematical models of some continuous time systems are given above. x(t) is the input signal of the system, and y(t) is the output signal of the system. Which of the following systems is linear and which is nonlinear? For linear systems, write "linear" in the space next to the option. For non-linear systems, write "non-linear" in the space next to the option.
Make the equation s(s+1)(s+2)+K=0 in the form of 1+KF(s) and explain the drawing of root-locus curves. (Note: Indicate the splitting points, centers and angles of the asymptotes)
For the circuit below with the switch closed and then opening at t=0, and R1= 9Ω, R2= 4Ω, L = 9H, C=3F, vg = 7V, calculate the initial conditions. For t > 0, develop the differential equation for the solution using mesh analysis.
For the RLC circuit shown in the image below, assume the circuit has long reached a steady state, and then the switch closes at t = 0. 1- In the circuit, R = 13 Ω and Is = 7.4 H. Determine the current, i, when t = 0.91 s. 2- If R = 19 Ω and Is = 4.4 H. Determine the voltage, v, when t = 0.28 s. (3 places after the decimal point)
The response of a system, h(t) is given as in Figure 1 below where the amplitudeof this signal is 7. Then,this system is excited by an input of x(t) = (u(t) × (u(-t)+u(t))) /1. 1)Illustrate the input signal, x(t). 2)Calculate the convolution output of the system y(t) = x(t) ∗ h(t). Nextdetermine y(t) when t is 1 sec 2)Prove the solution in Q2 is comparable when solving in frequency domain(Laplace). Next, sketch the signal for convolution output.
a) Calculate the range of values K will take so that the steady-state error ess <= 0.04 when the input of the system is u(t) = t. b) Damping ratio 1 > ξ ≥ 1/2√6 Calculate the range of values K will take so that c) Calculate the damping ratio ξ and the undamped natural frequency wn for K = 0.5.
For the system with forward path gain G(s)=s+5s2+3s+2G(s)=s+5s2+3s+2 and feedback gain H(s)=1s+3H(s)=1s+3, input R(s)=8sR(s)=8s will be applied. Find the steady-state error (ess) that will occur in the system and enter it into the space given below
A)Perform the N=5 point circular convolution of x and h using DFT. B)Perform the N=5 point circular convolution of x and h in time-domain.
The voltage source in the circuit is changed to a unit impulse; that is, vg=δ(t). 1. a) How much energy does the impulsive voltage source store in the capacitor? 2. b) How much energy does it store in the inductor? 3. c) Use the transfer function to find vo(t). 4. d) Show that the response found in (c) is identical to the response generated by first charging the capacitor to 1000 V and then releasing the charge to the circuit, as shown .

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Q2. The switch in the circuit shown below has been closed for a long time and is opened at t=0. Analyze the circuit in the time-domain to find the transient response and v(t) for t2 0. t=0 0.25H 15 A() Ve *0.04 F 10 2