The equivalent capacitance of the arrangement shown in figure is:

To produce an instantaneous displacement current of $$2 \mathrm{~mA}$$ in the space between the parallel plates of a capacitor of capacitance $$4 ~\mu \mathrm{F}$$, the rate of change of applied variable potential difference $$\left(\frac{\mathrm{dV}}{\mathrm{dt}}\right)$$ must be :-

The equivalent capacitance of the system shown in the following circuit is:

The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to