A single-loop RLC electrical circuit can be modeled as a second-order system in terms of current.Show that the differential equation for such a circuit subjected to a forcing function potential isgiven by Lt + R + = E(t). Determine the natural frequency of and damping ratio fordt²dtthis system. For a forcing potential, E(t) = 1 + sin 2000t volts, determine the system steadyresponse when L = 2 H, C = 1μF, and R = 10,000 . Plot the steady output signal and input signalversus time. I (0) = İ (0) = 0.

Given, The forcing potential, Et=1+sin200t V The value of the inductor, L=2 H The value of the…

Answered: A single-loop RLC electrical circuit…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Consider the circuit given below, where V = 120 V, R = 2.4 kΩ, and L = 60 mH. What is the time constant of the circuit with S1 closed? What is the time constant of the circuit with S1 closed? What is the eventual steady-state current with S1 closed? What is the value of the circuit current at the first instant (t = 0 s) S1 is closed? What is the value of the circuit current exactly one time constant after S1 is closed? How long after S1 is closed will it take before the circuit current reaches its steady-state value?
How can an underdamped second-order system be identified? What form does its complementary solution take? Repeat for a critically damped system and for an overdamped system.
It is known that the switch shown, T, is initially open and then it closed in theinstant t = 0. If it is assumed that the circuit has reached the stable state before the action of said switch:1.1. Determine the value of the capacitance of capacitor C so that the given circuit is critically damped.1.2. For the damping conditions of the previous part, find the expression for the current, i (t), forall t> 0.
1. What effect does increasingg the system gain have upon a SECOND ORDER STEADY-STATE ERROR? a) It has no effect on the system steady state error b) Its effect depends on the system characteristic equation c) It will decrease the steady state error d) It will increase the steady state error e) It depends on the tupe of system 2. Does a stable first order system have overshoot? 3. If the damping ration of a s.o.s is greater than 1, are types are the poles and where are they located on the plane? please answer all 3 carefully
DIFFERENTIAL EQUATION An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an inductance of 1/2 henry has an applied voltage E(t) = 16 cos 2t. Assuming no initial current and no initial charge on the capacitor, find an expression for the current flowing through the circuit at any time t. a. Model the problem in terms of a differential equation.b. Solve the differential equation. Present the general solution.c. Determine the particular solution by applying initial conditions given.
The resistance, inductance, and capacitance in a parallel RLC circuitare 1 kΩ, 12.5 H, and 2 μF, respectively.1. Calculate the roots of the characteristic equation that describe thevoltage response of the circuit.2. Will the response be over-, under-, or critically damped?3. What value of R will yield a damped frequency of 120 rad/s?4. What are the roots of the characteristic equation for the value of Rfound in (c)?5. What value of R will result in a critically damped response?
Since E = e(t) is a given function, find the differential equation provided by the current i.Find i in steady state when E = constant = 10 V.Find i in the steady state when B = 25 sin 150t.and When E = constant = 10V, i in transient find.
An electric circuit, consisting of a capacitor, resistor, andan electromotive force can be modeled by the differentialequationR dq/dt +1/C q = E(t),where R and C are constants (resistance and capacitance) andq = q(t) is the amount of charge on the capacitor at timet. For simplicity in the following analysis, let R = C = 1,forming the differential equation dq/dt + q = E(t). In Exercises 17–20, an electromotive force is given in piecewise form,a favorite among engineers. Assume that the initial charge onthe capacitor is zero [q(0) = 0].(i) Use a numerical solver to draw a graph of the charge onthe capacitor during the time interval [0, 4].(ii) Find an explicit solution and use the formula to determinethe charge on the capacitor at the end of the four-secondtime period. E(t)=5 if 0<t<2 E(t)=0 if t>=2
In the circuit below, it is given that R=3Ω, C=7 F, V1=8 volts, and vC(t) at t=0 is 13 volts. What is the capacitor current iC(t), in amperes, at time t=16 seconds?
The equation in Excel should be of the form: , where A and b are constants. In this case, x is the independent variable representing time, and y is your current measurements. A represents the initial value of the current from , and b represents the reciprocal of the time constant, RC. This means that b = 1/RC. Since RC = (100,000 Ω)(100x10-6 F) = 10 s, therefore the reciprocal should be: b = 0.1. It is this value that want to use to verify the theoretical equation in the Background. Please answer questions in image.
In the circuit below, it is given that R = 2 Ω, C = 2 F, V1 = 7 volts, and vC(t) at t=0 is 10 volts. What is the capacitor current iC(t), in amperes, at time t = 16 seconds?
Application of Differential Equation A circuit has in series of electromotive force given by E(t) = 100 sin 60t V, a resistor of 2 Ω, an inductor of 0.1 H, and a capacitor of 1/260 farads. If the initial current and the initial charge on the capacitor are both zero coulombs, find the charge on the capacitor at any time t > 0.

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