Consider the building block called 'Network N' shown in the figure.
Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$.

Two such blocks are connected in cascade, as shown in the figure.

The transfer function $${{{V_3}\left( s \right)} \over {{V_1}\left( s \right)}}$$ of the cascaded network is

For the Y-network shown in the figure, the value of R₁ (in Ω) in the equivalent ∆ -network is ________.

In the circuit shown in the figure, the value of node voltage V₂ is

In the circuit shown in the figure, the angular frequency $$\omega$$ (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b' is purely resistive, is _______.