Question

Derivation of S.I. unit of resistivity:​

Answer 1

Derivation of S.I. unit of resistivity:

• We know the formula to calculate the resistivity of a material. Now, let's derive its S.I. unit. First, we shall recall the S.I. unit of resistance, area and length.

$\begin{gathered} \begin{array}{|c|c|} \sf Resistance & \Omega \\ \sf Area & \sf {m}^{2} \\ \sf Length & \sf m\end{array}\end{gathered}$

• Now, insert the S.I. units in the formula in their respective places.

$:\implies{\sf{Resistivity=\Omega\times \dfrac{m^2}{m}}}$

$\:\:\:\::\implies{\sf{\rho=\Omega\times \dfrac{\cancel{m}\:^2}{\cancel{m}}}}$

$\:\:\:\:\:\:\::\implies{\sf{\rho=\Omega\times m}}$

$\:\:\:\:\:\:\:\:\:\:\::\implies\underline{\sf{\red{\rho=\Omega\:metre}}}$

• Hence, the S.I. unit of Resistivity is "Ohm metre".

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