LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS
CHAP. 31
(b)
Fig. 3-16
From Fig. 3-16(b) the loop equation can be written as
or Hence,
Taking the inverse Laplace transform of I(s), we obtain
Note that i(O+) = 2 = i(0-); that is, there is no discontinuity in the inductor current before and after the switch is opened. Thus, we have
3.42. Consider the circuit shown in Fig. 3-17(a). The two switches are closed simultaneously at t = 0. The voltages on capacitors C, and C, before the switches are closed are 1 and 2 V, respectively.
(a) Find the currents i , ( t ) and i,(t). ( b ) Find the voltages across the capacitors at (a)
t = 0'
From the given initial conditions, we have uCl(O-) = 1 V
and
L!=~(O-)= 2 V
Thus, using Fig. 3-10, we construct a transform circuit as shown in Fig. 3-17(b). From