Question

KHW 4 P 4.65 Part A Consider the circuit shown in (Figure 1) in which the switch has been open for a long time prior to t: 0 and we are given R-50 ? Compute the undamped resonant frequency of the circuit Express your answers using three significant figures Wy= 1.00x10' evious Ans Correct Part B Compute the damping coefficient of the circuit after the sv Express your answers using three significant figures ?: 1.00x10' revious Ans Correct PartC Figure 1 of 1 Compute the damping ratio of the circuit after the switch Express your answers using three significant figures 1.00 revious Ans ut Correct iLlC) L= 10,«H C-1000 pF

iL(0+)=1A.

a.) Assume that the capacitor is initially charged by a 25-V dc source not shown in the figure, so we have v(0+) = 25 V. Determine the value of v(0+) in V/s. (it is not 25, if you get 25, its wrong)

Express your answer using three significant figures.

b.) Find the particular solution for v(t).

c) Find the general solution for v(t), including the numerical values of all parameters.

Answer 1

I_R = 25/50 = 0.5A i_c(0^+) = -25/50 i_c(0^+) = -0.5A i_c(t) = cdu/dt rightdoublearrow du_0/dt = i_c(t) du_0(0^+)/dt = i_c(0^+)/c = -0.5/1000p = -500H(500 times 10^6) with KCL ashore shown, - 1 + u_0/R + 1/410 mu integral theta variant_0 dt + 1000 d theta variant_0/dt = 0 differential with respect to time, 1000pd^2 theta variant_0/dt^2 + 1/50 d theta variant_0 + 1/50 d theta variant_0/dt + theta variant_0/10mu = 0 particular solution rightdoublearrow on Right side of differential equation There is no actuating signal therefore theta variant_0p(t) = 0v Complementary part rightdoublearrow 1000p D^2 + 1/50 D + 1/10mu = 0 D = -10 times 10^6, -10 times 10^6 (-10mu) therefore theta variant_0 c (t) = (C_1 + C_2) c - 10 Ht therefore theta variant_0(t) = theta variant_0p(t) + theta variant_0 c (t) = (C_1 + C_2 t) c - 10 Mt (1) \r\n using initial condition, V_0(0^+) = 25v rightdoublearrow C-1 + 0 = 25 rightdoublearrow C_1 = 25 rightdoublearrow d thethavariant_0/dt =