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the relaxation time t is nearly independent of applied E whereas it changes significantly with temprature T. first fact is responsible for ohm’s law whereas second fact leads to variation of p with temprature. elaborat e why?

 the relaxation time t is nearly independent of applied E whereas it changes significantly with temprature  T. first fact is responsible for ohm’s law whereas second fact leads to variation of p with temprature. elaborat e why?
 

Grade:12

3 Answers

Arun
25750 Points
6 years ago
Dear student

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 1 mm/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.]

Regards

Arun (askIITians forum expert)

Ashutosh
12 Points
6 years ago
Here T,m are relaxation time and mass of electronAs we know.....i=neAv v is drift velocityv=((-eE)/m)*TSince,E=-V/lOn putting these valuesi=(ne^2ATV)/(ml)As P=RA/lHere,P is resistivitySince,R=ml/(ne^2AlT)Therefore, P=m/(ne^2T)Thus,change in temperature implies change in T which implies change in resistivity (P)
Ashutosh
12 Points
6 years ago
Here T,m are relaxation time and mass of electron As we know..... i=neAv v is drift velocity v=((-eE)/m)*T. Since,E=-V/l. On putting these values. i=(ne^2ATV)/(ml). As P=RA/l. Here,P is resistivity Since,R=ml/(ne^2AlT) Therefore, P=m/(ne^2T) Thus,change in temperature implies change in T which implies change in resistivity (P)

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