shown below. (10 points). rmine the differential equation relating vi) and vot) for the RLC circuit...
(2) a) An RLC circuit has the following differential equation (DE) for t > 0. d’v(t)/dt + 10 dv(t)/dt + 16 v(t) = 0) Determine the value of the damping ratio 5, the type of damping, and the form of the natural response for t > 0. Include all values where possible. (7 pts.) b) An RLC circuit has the following differential equation (DE) for t> 0. d’i(t)/dt? +4 di(t)/dt + 9 i(t) = 0 Determine the value of the...
Section 3: Laplace transform for RLC circuit analysis (10 marks) A second-order RLC circuit with a dependent source is shown in Fig. 3. 22 + VO - 132 1F + 15e-2 u(t) V ) 9[1-u(t)] V Y 0.50 » Fig. 3 A second-order RLC circuit with a dependent source Take the Laplace transform of the circuit and hence find the response io(t) for t > 0. Specify whether it is an underdamped, critically damped or overdamped case. Sketch the response.
Solve the Next second order system Draw the electric circuit and assign the RLC values with the differential equation data. Solve with the natural and forzed answer. u(t)-''(t) + 7' (t) + 12i(t) i(0) = 2 (t)- 5 v(t)1.5e u(t)-''(t) + 7' (t) + 12i(t) i(0) = 2 (t)- 5 v(t)1.5e
2. Given 10 pF 50 V( o(t) 1k10 Figure 1 (a) (10 points) The switch in the circuit below has been closed for a long time and it opens at t -0. Find vo(t) for t>0. (b) (5 points) Use MATLAB to plot vo(t) for t>0.
1. RLC Circuits Revisited. The first example of a RLC circuit illustrates the use of circuit elements in the s domain to represent initial conditions and a forced response. Next an example of sinusoidal excitation will follow where the transient response and steady state response are combined into one response waveform.. Transient RLC Circuit with Initial Conditions. Consider the RLC circuit below in Figure 7.14 which has two DC sources (Vco and V) applied before and after a switch is...
problem 7 Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
Solve all the problems shown below Problem 1 In a source free RLC series circuit If R=1092 ,L=5H ,and C= 2 mF 1) Find a.,0, and the characteristics roots $,$2. 2) Find the response i(t) knowing that v(0)=5V and i(0)=1A Problem 2 In a source free RLC parallel circuit If R=52 ,L= 1H ,and C= 10 m 1) Find a ,0, and the characteristics roots S1,S2. 2) Find the response V(t) knowing that v(O)=10V and i(0)=5A Problem 3 In a...
3) In the circuit shown assume constant battery model, Plot Vo versus Vi, for -5V<Vi<5V. At what value of Vi the diode will be ON? 1 k Ri 0.5 k
0 in the series RLC circuit shown in Figure 2 switches 51 and 52 both open at t -0. Solve the differential equation for loop current I (t) when the res has a value of 1 Ohm. Be sure to show all work and specify values for alpha, WO, W d, S1, S2, (o), V(o), etc. if they are required for the solution (e.g. s1 and s2 are only needed for an overdamped solution. (300 pts a: - Wo =...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE) for the capacitor voltage. Find the zero-state unit step responses of v(t) and i(t) if vs-u(t) V using each of the following three methods of solving the ODE: a. b. i. ii. Solve the ODE by integrating for the solution; Solve the ODE by assuming homogeneous and particular solutions; Solve the ODE by using the general form solution for a 1st order ODE. iii....