Given is the parallel connected RLC network as depicted in the figure below.RCI(t)The controllable current source I(1) is the system input. The current iz(1) flowingthrough an inductive load is the system output. The constant system parametersare the resistance R, the capacitance C, and the inductance L.a) Using the Kirchhoff's current and voltage laws, derive and write down thelinear differential equation which describes the input-output behavior of theRLC network.b) Using the transfer blocks and signals flow, draw the block diagram whichcorresponds to the differential equation from the task a); denote all signalsand transfer elements. In addition, use the block diagram's algebra andreduction, so as to obtain the single transfer element with the input I(t) andoutput iz(t). Now, imagine there is a parasitic current leakage in the mergingnode of the network elements R, C, and L. How can this be incorporated as adisturbance? Extend, correspondingly, the detailed block diagram.

Given parallel RLC circuit as shown below: a) Using Kirchoff's current and voltage laws, we need to…

Answered: Given is the parallel connected RLC…

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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Similar questions

A series RLC circuit consist of 5 Ω resistor, 50 mH inductor and 1 mF capacitor. If it is supplied with a voltage of v = 100sin200t volt, find the values of impedance and power. Also, write the expression of instantaneous current in the circuit.
The resistance, inductance, and capacitance in a parallel RLC circuit are 1900 ohms, 240 mH, and 15 nF,respectively. a) Calculate the roots of the characteristic equation that describe the voltage response ofthe circuit. b) Will the response be over-, under-, or critically damped? c) What value of R will yield adamped frequency of 12 krad/s ? d) What are the roots of the characteristic equation for the value of Rfound in (c)? e) What value of R will result in a critically damped response?
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?
An inductance of 1 H, a resistance of 8 Ω and capacitance of 0.04 F are connected in series with a variable voltage E = 50 sin 3t. Find the current and charge in the system, given the initial conditions q = 0 and l = 0 when t = 0, using method of solution of higher order linear ordinary differential equation.
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.
4.b 1- Draw the SFG diagram 2- When8u(t)is applied as input, enter the steady-state value of the system into the solution field given below
Consider the RLC circuit shown where the initial current flowing through the circuit at time t = 0 is I_0 = 5 and the initial charge on the capacitor at time t = 0 is Q_0 = 2. The components have values of R = 100 ohms, L = 5 H, and C = 1/450,500 F. Write the differential equation for Q(t), the charge across the capacitor, assuming the voltage source V(t) = 0
In the given circuit, consider M = 1 H. Determine the energy stored in the coupled inductors at t = 2 s. The energy stored in the coupled inductors is J
Calculate vc, il and the energies stored in the capacitor and inductor in the circuit attached under steady state DC conditions.
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?
A constant voltage vst = 10V is applied to the RC circuit shown. The voltage v(t) across the capacitor satisfies the first-order differential equation:0.2 dv(t)/dt + v(t) = 10a) Find the transient solution. What is the time constant of the response?b) Find the steady state solution.c) If the initial voltage across the capacitor is v(0) = 5V, determine the total solution v(t).
Consider an LRC series circuit with a resistance of 2.5 ohms, capacitance of 0.1 farad, aninductance of 0.1 henry and electromotive force, volts. Given thatAssume there is no initial charge and no initial current on thecapacitor.The equation of the charge q(t), on the capacitor at any time t q(t)=C1e−5t+C2e−20t+0.05cost+0.2sint . (Do not solve the coefficients). a) State the equation of the current, i(t). b) State the transient and the steady-state current. c) What is the current after a long time.

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