The switch in Fig. has been in position $$1$$ for a long time and is then moved to position $$2$$ at $$t\, = \,0$$.

(a) Determine $${V_C}\left( {{0^ + }} \right)$$ and $${I_{_L}}\left( {{0^ + }} \right)$$
(b) Determine $${{d{V_C}\left( t \right)} \over {dt}}\,\,$$ at $$t\, = \,{0^ + }$$
(c) Determine $${{V_C}\left( t \right)}$$ for $$t > 0$$

For network shown in Fig. $$R\, = \,1\,k\Omega $$
$${L_1} = 2\,H,\,{L_2} = 5\,H,\,{L_3}\, = \,1H,{L_4} = 4H\,\,\,$$ and $$C - 0.2\,\,\mu F.$$. The mutual inductances are $${M_{12}} = 3\,H$$ and $${M_{34}} = 2\,H$$.

Determine
(a) the equivalent inductance for the combination of $${L_3}$$ and $${L_4}$$,
(b) the equivalent inductance across the points A and B in the network,
(c) the resonant frequency of the network.

Consider the network in Fig.

(a) Find its short-circuit admittance parameters.
(b) Find the open-ciruit impedance $${Z_{22}}$$.

The dependent current source shown in Figure