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प्रश्न
The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is (in part) responsible for Ohm’s law whereas the second fact leads to variation of ρ with temperature. Elaborate why?
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उत्तर
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.]
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संबंधित प्रश्न
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(B) Free-electron density in a metal depends on temperature.
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Derive an expression for resistivity of a conductor in terms of the number density of charge carriers in the conductor and relaxation time.
Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence, obtain an expression for it.
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Based on this, answer the following:
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- A copper wire of length 'l' is connected to a source. If the copper wire is replaced by another copper wire of the same area of cross-section but of length '4l', how will the drift velocity change? Explain your answer.
