need help with d e and f 1. For the following circuit, switch is closed at t=0.a. Write a differential equation in i(t).b. Find a and wo.c. Find the characteristic equation and the roots of the characteristic equation.d. Find the final value of current i(t) through the inductor.e. Find current i(t) through the inductor for t> 0 and sketch i(t).f. Find voltage v(t) for t≥ 0 and sketch v(t).PSSolutionSwitch SVs20VR1ΣΚΩwwwR22k2v(t)V=4V I50 nFi(t)40mHlo=5mA

Answered: Image /qna-images/answer/e16ed251-2713-4f6b-9acc-824410381f2d.jpg

Answered: 1. For the following circuit, switch is…

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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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. At t = 0, the charge on the capacitor and the current in the circuit are 0. Find the charge and the current in the circuit at t > 0 using method of solution of higher order linear ordinary differential equation.
What is the differential equation governing the growth of current in the circuit as a function of time after t=0? Express in terms of dI(t)/dt, I(t), Vb, R, and L Solve the differential equation obtained in Part A for the current I(t) as a function of time after the switch is closed at t=0. Express in terms of Vb, R, and L. Use the notation exp(x) for ex
Consider the circuit below with V = 20 V, R1 = 100 ohms, R2 = 60 ohms, and L1 = 900 mH. Assume the initial energy stored in the inductor is zero. a. Find the differential equation for the current through the inductor for t greater than zero. (Hint: Find the Thevenin equivalent with respect to the inductor.) b. Find the current through the inductor i(t) based on the solution to the differential equation. c. Find the voltage across the inductor v(t) using the current you found in b. d. Using Laplace transforms, find the voltage across the inductor.
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.
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.
Consider the circuit below with V = 40 V, R1 = 12 ohms, R2 = 18 ohms, R3 = 30 ohms, and C1 = 60 mF. The switch in the circuit has been closed for a long time before it is opened at t = 0. 1:Find the initial voltage across the capacitor. 2:For the natural response of the circuit after t > 0, find the time constant for the circuit. 3:Find the expression for the magnitude of the voltage across the capacitor. 4:Find the expression for the magnitude of the current through R3.
Please see attachment and please show handwritten work! A system is described by the differential equation: Determine the values of the natural frequency, damping ratio and the dampednatural frequency for this system. This system is: _____Undamped _____Underdamped _____Critically Damped _____Overdamped *** Please see attachment, and please show handwritten work! Thank you!
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.
In the circuit shown below, the switch has been open a long time and the circuit is initially in steady-state. At t=0, the switch is closed. R1=0.2Ω, and R2=0.4Ω. The batteries have EMFs E1=1V and E2=3V. The capacitor has capacitance 10 μF. Hint: What is the voltage on the capacitor just before the switch is closed? Note that there is a voltage drop over the open switch. a) What is the voltage over the capacitor before the switch is closed? b) Draw the Thevenin equivalent circuit as seen by the capacitor. c) What is the time constant for charging the capacitor? d) What is the voltage on the capacitor as a function of time?
Find the roots of the characteristic equation that governs the transientbehavior of the voltage if R=200Ω, L=50 mH, andC=0.2 μF. 2. Will the response be overdamped, underdamped, or critically damped?3. Repeat (a) and (b) for R=312.5 Ω.4. What value of R causes the response to be critically damped?
For the circuit below with the switch closed and then opening at t=0, and R1= 3Ω, R2= 7Ω, C = 0.2H, ig = 8A, vs = 2v, calculate the initial condition. Develop the differential equation for the solution for t > 0. Calculate the current ia(t) for all times.
Set up a system of first-order differential equations for theindicated currents I1 and I2 in the electrical circuit ofFig. 4.1.14, which shows an inductor, two resistors, anda generator which supplies an alternating voltage drop ofE(t) = 100 sin 60t V in the direction of the current I1. except with the generator replacedwith a battery supplying an emf of 100 V and with the inductor replaced with a 1-millifarad (mF) capacitor

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