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Electricity

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13 Mar 2008 19:14:54 IST
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Resistivity and temperature
None

resistivity  = m/(ne^2 )
Now the resistivity of a conductor increases with increasing temperature while for an insulator resistivity decreases with increasing temperature. Wondor how could one explain these behaviours with the help of the equation?


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Gaurav |spideyunlimited| Ragtah's Avatar

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13 Mar 2008 19:26:36 IST
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this eqn is only for resistivity of a conductor..
as temp increases, collision frequency increases and relaxation time (time diff between 2 collisions) decreases, so resistivity increases.                             


for conductors -
p = po ( 1 + @.dt )

for insulators -
p = po.e^-Ea/RT
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13 Mar 2008 19:35:49 IST
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SIR,AS TEMP. INCREASES,THE AMPLITUDE AND FREQUENCY OF ATOMS IN THE CONDUCTOR INCRESES.SO MORE COLLSSIONS WILL TAKE PLACE IN A SHORT TIME,SO RELAXATION TIME DECREASES AS    IS THE AVG.TIME B/W 2 SUCCESIVE COLLISIONS.RESISTIVITY IS INVERSELY PROPORTIONAL TO RELAXATION TIME,THEREFORE RESISTIVITY INCREASES.
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Hot goIITian

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13 Mar 2008 19:35:52 IST
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in case of insulator p = po.e^-Ea/RT equation accounts only for the variation of number density of free electrons with temperature.
why it doesnot show any factors from the variation of relaxation time with temperature.

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13 Mar 2008 19:40:17 IST
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hi brainbank
i do agree with that part absolutely. but what about the insulators.
thank you very much for your response
Gaurav |spideyunlimited| Ragtah's Avatar

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13 Mar 2008 19:41:20 IST
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number density doesn't matter since in insulators the electrons are not able to cross forbidden gap and cross over to conducting band from valence band.
Gaurav |spideyunlimited| Ragtah's Avatar

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13 Mar 2008 19:41:53 IST
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But as the temp increases, they are able to do so as they gain the energy required for jumping to conducting band
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13 Mar 2008 19:43:54 IST
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SIR,IN INSULATORS THERE ARE NO FREE ELECTRONS AND ENERGY GAP IN INSULATORS IS GREATER THAN 2ELECTRONVOLT.SO IT DOESNOT CONDUCT at room temp..IN INSULATORS NUMBER DENSITY OF ELECTRONS IS A CONSTSANT .BUTAS WE SUPPLY HIGH ENERY >2eV,THE KINETIC ENERGY BY VIRTUE OF THERMAL ENERGY OF ELECTRONS DOMINATES AND IT BECOMES FREE.SO NUMBER DENSITY OF FREE ELECTRONS INCREASES WITH TEMPERATURE.BUT INCREASES ONLY WHEN THE ENERGY SUPPLIED IS >2eV ie energy gap
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Hot goIITian

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13 Mar 2008 20:01:45 IST
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But I think p = po.e^-Ea/RT this equation comes from the variation of number density with increasing temperature. The increase in the number density of free electron in conduction band jumping across the forbidden gap follows an exponontial decrease with the forbidden gap energy.
well that was my idea wherer this equation originate from.
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13 Mar 2008 20:10:39 IST
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SIR Ea is activation energy.ie energy supplied to activata molecules
but Ea is constant for an insulator
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13 Mar 2008 20:12:04 IST
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SIR Ea is activation energy.ie energy supplied to activae molecules in an insulator
but Ea is constant for an insulator

Hot goIITian

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13 Mar 2008 20:25:57 IST
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I think it is in fact the energy gap between the conduction and valance band and it will be a constant for a material ofcourse. When we say activating the molecules does it mean that the current carriers in an insulator are ions. Even in insulators i think the current carriers are free electrons. Since the energy gap is large you will find only very few free electrons in the conduction band which manage to jump from valance band with the help of thermal energy. But as the temperature icreasaes defunitely more and more electrons may jump in to conduction band. May be i am wrong. But that was the idea that i had all the time.



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