The output current i(t) at t<0 is equal to zero Amperes. Determine the following: a. an expression for v/(t) using the sum of ramp functions b. transfer function G,(s) = Vc(s)/V.(s) c. transfer function G₂(s)= I(s)/V.(s) d. the output current i(t) using Laplace at the time interval 0 < t < 5 v;(t) 5 5 10 t V₁ 1ΚΩ 100mF VC i(t) 1ΚΩ

The output current i(t) at t<0 is equal to zero Amperes. Determine the following: a. an expression for v/(t) using the sum of ramp functions b. transfer function G,(s) = Vc(s)/V.(s) c. transfer function G₂(s)= I(s)/V.(s) d. the output current i(t) using Laplace at the time interval 0 < t < 5 v;(t) 5 5 10 t V₁ 1ΚΩ 100mF VC i(t) 1ΚΩ

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...

See similar textbooks

Similar questions

Given the following ordinary differential equation describing the dynamics of a system y'''+17y''+80y'+100y=3(u''+5u'+4u) Here, y(t) is the output and u(t) is the input. Laplace table is given below. Find the transfer function G(s) [=Y(s)/U(s)] by applying Laplace transform (all initial valus are zero) Find the poles and zeros of the system. Is the system stable or unstable? Which pole(s) is/are slow and which ones is/are fast? Find Y(s) if input is unit step function. Find initial and final values of the system by applying the theorems.
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. Find the circuit’s input, or driving-point, impedance, Zi, in the s-domain.
If G(s) = 1 / (s + 2), find the response c(t) if the input r(t) = u(t), a unit step, assuming zero initial condition.
Formulate and solve the 2nd order homogeneous differential equation for node voltage v(t). Given that the constant source current, resistor, capacitor and inductor are 10A, 12ohm, 6F and 64H, respectively. Use Laplace Transform to solve the differential having an initial condition, v’(0) = 1, v(0)=0.
The dynamics of a system which has an input and output of the differential equation, d^2y(t)/dt + 3dy(t)/dt + 2y(t) = r(t), where the initial conditions are given as y(0) = 0, dy(t)/dt =0, r(t) =1, t>=0. Use Laplace transform to solve for the time response of the system, (ie solve for y(t), t>=0)
2) In the circuit shown in Fig. 1, the capacitor is initially charged to V0 volts and the switch isclosed at t = 0. Obtain the current, i(t), for t> 0 using the Laplace transform.
Problem 2. Which gives the Laplace transforms of the given time-domain function? -2.5 ln [(s+1)(s+4)] -2.5 ln [(s-1)/(s-4)] -2.5 ln [(s+1)/(s+4)] -2.5 ln [(s+4)/(s+1)]
In the following circuit, R=1 [ohm], C=1[F], and all initial values are 0. 1. Using Laplace Transform, find the ratio H(s)=Vo(s)/Vi(s).2. Find the roots of the characteristic equation.3. Find the conditions for K which will make the circuit over-damped and under-damped, respectively.4. When K=2, vi(t)=sqrt(10)cost, find vo(t) after a long time has passed.
The differential equations below represent systems where x is the input and y is the output. Determine a) the transfer function of the given systems, b) whether the following systems are stable, or unstable, and c) the number of roots with positive real part
a) Find the differential equation that will represent the dynamic behaviour of the circuits given in Figures (a) and (b) , and Find the Laplace transfer function using the identified input V1 and the output V2 of the circuits given in Figures (a) and (b), then Given that V1 is a step of 3 volts, determine V2 as a function of time of the circuits shown in Figures (a) and (b).
For a DA converter, the LRC circuit chosen has inductance L= 10 H , resistance R= 10 ohms and inductance C= 0.2 F . The input digital signal is a power surge (impulse) of magnitude 100 V lasting an instant at t = a . Use your notes to model the second order differential equation in terms of the charge q suited to this application. Simplify the equation with the coefficient of q'' as 1. Use the Laplace transform and calculate the (general) output voltage vo if vo = 1/C q . Your solution will be in terms of a . Use the initial conditions q(0)=0 and q'(0)=0 . Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution:1. The simplified differential equation in terms of the charge q you will be solving2. The simplified Laplace transform of this equation where you have made L{q} subject of the equation3. The partial fractions process if required4. The completing the square process if required5. Express the solution q as a piecewise…