Sol. and

At distance r from left end of the conductor, its horizontal dimension is equal to

=

and vertical dimension is equal to

=

Hence, the cross-sectional area,

A =

If an elemental length dr is considered, then its resistance will be equal to

dR = =

But such elemental lengths are in series with each other, therefore, total resistance of the conductor is:

R = = log e 2

Hence, the option is wrong.

The rate of generation of heat per unit length is equal to i 2 ρ /A. Hence, the rate of generation of heat per unit length is maximum where A is minimum.

For the given conductor, the cross-sectional area A is maximum at its middle section and that is equal to (1.5x) (1.5x) = 2.25xy. Therefore, the rate of generation of heat is minimum there. Hence, the option is wrong.

Since, i = neAv d , therefore, drift velocity v d = .

Since, the cross-sectional area A is maximum at middle section, hence, drift velocity v d is minimum at that section. Hence, the option is correct.

Electric field intensity in a current carrying conductor is given by : E = i ρ /A.

Since, the conductor is made of a uniform material, therefore, ρ is constant throughout the material and since, cross-sectional area A is same at two ends, therefore, electric field intensity is same at two ends of the conductor. Hence, the option is also correct.