A source of constant potential difference is connected across a conductor having irregular cross section as shown.

Options

A. Electric field intensity at `P` is greater than that at `Q`.
B. Rate of electrons crossing per unit area of cross-section at `P` is less than that at `Q`.
C. The rate of generation of heat per unit length at `P` is greater than at `Q`.
D. Mean kinetic energy of free electrons at `P` is greater than that at `Q`.

Explanation

When a source is connected, a current starts to flow through the conductor. Let it be `I`. Then current density at a section is equal to `I//A` where `A=` cross-sectional area.
Since cross-sectional area at `P` is maximum, therefore current density at `P` is minimum. Hence `(B)` is correct.
Since electric field is `(J')/(sigma)(=(I)/(Asigma)=(Irho)/(A))`, therefore at `P` electric field is minimum while that at `Q` is maximum.
Rate of generation of heat per unit length at a section will be equal to `(I^(2)rho)/A)`. It is minimum at `P` and maximum at `Q`.
The mean kinetic energy of free electrons `=(1)/(2)mv_(d)^(2)` which is minimum at `P` and maximum at `Q`.