Question

relaxation time is nearly independent of applied electric field where has it changed significantly with temperature t first factors responsible for Ohm's law where has second factories to the variation of rho with temperature elaborate why

Answer 1

Here is the solution of one of the question. For other solutions, kindly post different query in different thread.
1-
The bulb with power rating 100 W will glow brighter because in parallel connection voltage applied in both the cases will be same and power will be higher for lower resistance bulb.Power, P=V2R where P is power, V is voltage and R is resistance.The bulb with higher power rating has less resistance than the bulb with lower rating.

Answer 2

Relaxation time is bound to depend on velocities of electrons and ions. Applied electric field affects the velocities of electrons by speeds at the order of 1mm/s, an insignificant effect. Change in T, on the other hand, affects velocities at the order of 102 m/s. This can affect τ significantly.  

[ρ = ρ(E,T ) in which E dependence is ignorable for ordinary applied voltages.]