Question

 Consider the circuit depicted in Fig. 2. The switch SW1 has been closed for a long time before it is opened at time t = 0. The switch SW2 has been open for a long time before it is closed att = 0.1 (sec).

 i) Find the initial current I(0) flowing in the inductor and the initial voltage V(0) across the capacitor.

 ii) Find the voltage V(t) across the capacitor and the current I(t) through the inductor for 0 ≤ t ≤ 0.1 (sec). Identify the nature of the obtained solutions.

 iii) Find the voltage V(0.1) across the capacitor and the current (0.1) through the inductor.

 iv) Find the voltage V(t) and the current I(t) fort ≥ 0.1 (sec). What is the nature of the current and the voltage responses?

 v) Plot V(t) and I(t) for all time t ≥ 0.

Answer 1

please zoom in the pics for better viewing experience

MATLAB CODE TO FIND INVERSE LAPLACE TRANSFORM:

syms s x

v=(96-(2.2404*s)-0.921*s^2)/(s*(24+(0.96*s)+(0.6*s^2)));

ilaplace(v)

I=(96+(10.748*s)+(2.8931*s^2)+(0.3288*s^3))/((48*s)+(18.72*s^2)+(2.592*s^3)+(0.12*s^4));

ilaplace(I)