An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of $${4 \over 3}$$ and $${2 \over 3}$$, then the ratio of the current passing through the wires will be

Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \circ C$$ to $$40{}^ \circ C$$ is

In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one end of the wire when resistance $$X$$ is balanced against another resistance $$Y.$$ If $$X < Y$$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $$4$$ $$X$$ against $$Y$$

In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the resonant frequency to remain unchaged, the inductance should be changed from $$L$$ to