In the circuit shown in Fig. switch $$S{w_1}$$ is initially CLOSED and $$S{w_2}$$ is OPEN. The inductor $$L$$ carries a current of $$10$$ $$A$$ and the capacitor is charged to $$10$$ $$V$$ with polarities as indicated. $$S{w_2}$$ in initially CLOSED at $$t = {0^ - }$$ and $$S{w_1}$$ is OPENED at $$t=0.$$ The current through $$C$$ and the voltage across $$L$$ at $$t = {0^ + }$$ is

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2$$ $$\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {{\rm I}^2}{}_{NL}$$. The power dissipated in the non-linear resistance is

The resonant frequency for the given circuit will be

The matrix $$A$$ given below is the node incidence matrix of a network. The columns correspond to braches of the network while the rows correspond to nodes. Let
$$V = {\left[ {{v_1}\,\,{v_2}....{v_6}} \right]^T}$$ denote the vector of branches voltages while
$${\rm I} = {\left[ {{i_1}\,{i_2}....{i_6}} \right]^T}$$ that of branch currents. The vector $$E = {\left[ {{e_1}\,{e_2}\,\,{e_3}\,{e_4}} \right]^T}$$ denotes the vector of node voltages relative to a common ground. $$$A = \left[ {\matrix{ 1 & 1 & 1 & 0 & 0 & 0 \cr 0 & { - 1} & 0 & { - 1} & 1 & 0 \cr { - 1} & 0 & 0 & 0 & { - 1} & { - 1} \cr 0 & 0 & { - 1} & 1 & 0 & 1 \cr } } \right]$$$

Which of the following statements is true?