A 0.1 henry inductor, a 4x10^(-3)farad capacitor, a O ohm resistor,and a voltage source having a valueof 180 cos 40t volts (for t > 0 or t =0) are connected in series. Let | = 0and Q = 0 at t = 0 for the circuit.1. Which of the followingdifferential equationsrepresent the circuit? (Let Q =charge and t = time)None of the other choicesQ' + 250 Q = 180 cos 40tQ' +2500 Q = 1800 cos 40tQ' + 25 Q = 18 cos 40t

In this question we will find differential equation for series RLC circuit...

Answered: A 0.1 henry inductor, a 4x10^(-3) farad…

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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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?
The voltage pulse applied to the 100 mH inductor shown is 0 for t<0 and is given by the expressionv(t)=20te−10t V for t>0. Also assume i=0 for t≤0.. Find the inductor current as a function of time.
As displayed in attachment figure and LC circuit can be modeled by the following system of differential equations as attachment. Where L = inductance (H), t = time (s), i = current (A), and C = capacitance (F). Assuming that a solution is of the form = Ij sin (wt), determine the eigenvalues and eigenvectors for this system using Faddeev-Leverrier Method and Power Method with L = 1 H and C = 0.25 C. Draw the network, illustrating how the currents oscillate in their primary nodes. Assume initial value for power method.
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.
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.
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
The voltage pulse applied to the 100 mH inductor shown is 0 for t<0. and is given by the expression v(t)=20te−10t V for t>0. Also assume i=0 for t≤0. Sketch the voltage as a function of time.
Derive the expression for heart ratein beats per minute given the values of R and C and assuming that thecapacitor discharges when its voltage reaches 75% of the source voltageVs. The expression, given in the Practical Perspective, is repeated herefor convenience:H=60−RC ln 0.25 [beats per minute].
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.
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
The circuit shown below is an underdamped system, and the current through the inductor has the form iL(t)=e^at ( ) (K1sinwt + K2coswt ) for t≥0 a. Determine the numerical values, including signs, of a and w b. If the initial conditions are iL(0) = 1A and Vc (0) =12V , determine the numerical values, including signs, of K1 and K2 c. Using the numbers determined above, write out the complete expression for iL(t)
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