In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E₁ and E₂ as well. For key K₁ (closed), the jockey is adjusted to touch the wire at point J₁ so that there is no deflection in the galvanometer. Now the first battery (E₁) is replaced by second battery (E₂) for working by making K₁ open and K₂ closed. The galvanometer gives then null deflection at J₂. The value of $${{{E_1}} \over {{E_2}}}$$ is $${a \over b}$$, where a = _________.

A cylindrical wire of radius 0.5 mm and conductivity 5 $$\times$$ 10⁷ S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x³$$\pi$$ mA. The value of x is _________.

Four resistances 40 $$\Omega $$, 60 $$\Omega $$, 90 $$\Omega $$ and 110 $$\Omega $$ make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible.The potential difference across BD in V is _______.

In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is $$l$$ = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing distance $$l'$$ (in cm) will now be________.