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(Solved): PROBLEM 02: Second Order Parallel RLC Circuits In Fig. P2 below the switch has been closed for a ver ...
PROBLEM 02: Second Order Parallel RLC Circuits
In Fig. P2 below the switch has been closed for a very long time, there is
no current (i_(o)(0^(-))=0) flowing through the capacitor, and the inductor's
voltage has been stable at v_(o)(0^(-))=0. We open the switch at time t=0 in
order to connect the source current i_(f)(t)=I_(dc)u(t)=12u(t). The formulation
for the inductor's voltage v_(o)(t) is given by the following expression:
(d^(2))/(dt^(2))v_(o)(t)+(1)/(RC)(d)/(dt)v_(o)(t)+(1)/(LC)v_(o)(t)=((1)/(C))I_(dc)\delta (t)=((1)/(C))12\delta (t)
R=(5)/(100)=50m\Omega ;L=(1)/(64)=15.625mH;C=1F
2a.- 15 points: Using Laplace, and for zero initial conditions, obtain a
general output formulation, v_(o)(t), for the inductor's voltage (Fig. P2).
2a.- 10 points: For zero initial conditions, obtain a general output
formulation, i_(o)(t), for the capacitor's current (Fig. P2).
Fig. P2: Second Order Parallel RLC Circuit