A copper wire of radius $$1 \mathrm{~mm}$$ contains $$10^{22}$$ free electrons per cubic metre. The drift velocity for free electrons when $$10 \mathrm{~A}$$ current flows through the wire will be (Given, charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$ ) :

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: