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 emf of a cell having internal resistance $$1 \Omega$$ is balanced against a length of $$330 \mathrm{~cm}$$ on a potentiometer wire. When an external resistance of $$2 \Omega$$ is connected across the cell, the balancing length will be :

The magnitude and direction of the current in the following circuit is :-

If the galvanometer $$G$$ does not show any deflection in the circuit shown, the value of $$R$$ is given by: