Question

The dimensional formula for resistivity is

• A. $ [M{{L}^{3}}{{T}^{-3}}{{A}^{-2}}] $
• B. [ $ {{M}^{-1}}{{L}^{2}}{{T}^{-3}}{{A}^{-2}} $ ]
• C. [ $ {{M}^{3}}{{L}^{-2}}{{T}^{-1}} $ ]
• D. [ $ M{{L}^{3}}{{T}^{-4}}{{A}^{-3}} $ ]

Answer 1

Answer: (A)

As we know that resistance, $ R=\rho \frac{l}{A} $ where, $ \rho = $ resistivity $ l= $ length of conductor wire and A = area of cross- section of conductor wire. or $ \rho =\frac{RA}{l} $ $ \Rightarrow $ Dimensions, $ \rho =\frac{[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}][{{L}^{2}}]}{[L]} $ $ =[M\,{{L}^{3}}{{T}^{-3}}{{A}^{-2}}] $