Two wires $$A$$ and $$B$$ of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at $$40 \mathrm{~cm}$$ from left end. Diameters of the wire $$A$$ and $$B$$ are in that ratio $$3: 1$$. The ratio of specific resistance of $$A$$ to the of $$B$$ is

A potentiometer wire is $$4 \mathrm{~m}$$ long and potential difference of $$3 \mathrm{~V}$$ is maintained between the ends. The emf of the cell, which balances against a length of $$100 \mathrm{~cm}$$ of the potentiometer wire is

A potentiometer wire has length $L$ For given cell of emf $E$, the balancing length is $\frac{L}{3}$ from the positive end of the wire. If the length of potentiometer wire is increased by $50 \%$, then for the same cell, the balance point is obtained at length

In the network shown cell E has internal resistance $r$ and the galvanometer shows zero deflection. If the cell is replaced by a new cell of emf $2 E$ and internal resistance $3 r$ keeping everything else identical, then