Question

The \[{m^2}{V^{ - 1}}{s^{ - 1}}\] is the SI unit of which of the following?
A. Drift Velocity
B. Mobility
C. Resistivity
D. Potential gradient

Answer 1

Hint: In order to solve this question we will understand the definition of SI unit which states that SI unit is Standard Internal Unit defined for each of physical observed parameters which in turn define different physical phenomena. Internationally only $7$ basic parameters standard unit is defined and their definition is changing with increase in technology. These $7$ parameter can define all other parameters. $7$ Parameters are time (sec), length (m), Amount of substance (mole), Electric Current (ampere), Temperature (kelvin), Luminous Intensity (candela) and Mass (kilogram).

Complete step by step answer:
Let us explore each option,
A. Drift Velocity is defined as average velocity attained by any charged particle in presence of opposite electric field. It is given by ${v_d} = \dfrac{i}{{neA}}$ and its SI unit is $m{s^{ - 1}}$.

B. Mobility is defined as Drift Velocity per unit Electric field. It physically means how much charge is able to move freely. It is defined as $\mu = \dfrac{{{v_d}}}{E}$ and its SI unit is ${m^2}{V^{ - 1}}{s^{ - 1}}$.

C. Resistivity is defined as a measure of resistance of a material of specified dimensions or it is defined as specific electrical resistance. It is defined as $\rho = \dfrac{{RA}}{l}$ and its SI unit is $kg{m^3}{s^{ - 3}}{A^{ - 2}}$.

D. Potential gradient is defined as change in potential per unit length in a perpendicular direction to surface. It is defined as $\nabla V = \left( {\dfrac{{\delta V}}{{\delta x}}} \right)$ and its SI unit is $V{m^{ - 1}}$.

Hence, the correct option is B.

Note:It should be remembered that, the parameters defined here depend on basic $7$ fundamental SI units that means all other parameters which can be property of any physical phenomena other than basic fundamental SI units could be derived and expressed in the same. Both mobility and drift velocity are important considerations during study of semiconductor physics.