Question

the length of a wire of resistance 1 ohm and area of cross section made half what will be the new resistance

Answer 1

Hi

Since the length of the wire is doubled, its area of cross-section is halved so as to keep the volume of the wire constant.

Now the resistance of the wire is proportional to length of the wire, since the length of the wire is doubled its resistance also doubles due to doubling of the length. But resistance is also inversely proportional to the area of cross-section, and as area of cross-section is halved due to doubling of length, the resistance is once more doubled due to the halfing of the area of cross-section. So overall the resistance of the wire becomes four times the original resistance.