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Current Electricity — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsCurrent Electricity5 Marks
Question
  1. Define the term drift velocity.
  2. On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?
  3. Why alloys like constantan and manganin are used for making standard resistors?
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Answer

  1. Average velocity acquired by the electrons in the conductor in the presence of external electric field.
Alternate Answer
$[\text{V}_{d} =\frac{-eE\tau}{\text{m}}$ where $\tau$is the relaxation time.$]$
  1. $\text{V}_{d} =\frac{-eE\tau}{\text{m}}$ 
We have $\text{E} = - \frac{\text{V}}{\ell'}$
where $V$ is potential difference across the length $\ell$
of the conductor
$\text{V}_{d} = \frac{\text{eV}\tau}{\text{m}\ell}$ Current flowing $I = neAv_d​​​​​​​$
I = neA$\text{V}_{d}\frac{\text{eV}\tau}{\text{ml}} = \frac{ne^{2}\text{AV}\tau}{\text{ml}}$
$\frac{\text{I}}{\text{V}} = \frac{\text{ne}^{2}A\tau}{ml} = \frac{1}{\text{R}} . . . . . (i)$
Also,  $\text{R} = \rho\frac{\ell}{\text{A}} . . . . (ii) $
Comparing $(i)$ and $(ii)$
$\rho = \frac{m}{ne^{2}\tau}$
Resistivity of the material of a conductor depends on the relaxation time, i.e., temperature and the number density of electrons.
  1. Because constantan and manganin show very weak dependence of resistivity on temperature.

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