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

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1Ω , respectively, the operating angular frequency (in rad/s) is ________.

A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is

A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______ .