For the lattice circuit shown in Fig., $${Z_a} = j\,2\,\Omega \,\,and\,\,{Z_b} = \,\,2\Omega $$. The values of the open circuit impedance parameters
$$Z\,\left[ {\matrix{ {{Z_{11}}} & {{Z_{12}}} \cr {{Z_{21}}} & {{Z_{22}}} \cr } } \right]\,$$ are

The transfer function $$H\left( s \right) = {{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}}$$ of an R-L-C circuit is given by
$$H\left( s \right) = {{{{10}^6}} \over {{s^2} + 20s + {{10}^6}}}$$

The Quality factor (Q-factore) of this circuit is

For the circuit shown in figure, the time constant $$RC = 1$$ $$ms$$. The input voltage is $${v_i}\left( t \right) = \sqrt 2 \,\sin \,{10^3}t$$. The output voltage $${v_0}\left( t \right)$$ is equal to

The circuit shown in figure, with $$R = 1/3\Omega $$, $$L = 1/4H$$, $$C = 3F$$ has input voltage $$v\left( t \right) = \sin \,2t$$. The resulting current $$i(t)$$ is