JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions JEE PYQ - Mathematical Tools Units and Dimensions

  • question_answer
    The electrical resistance R of a conductor of length \[l\] and area of cross section a is given by\[R=\frac{\rho l}{a}\]where\['\rho '\]is the electrical resistivity. What is the dimensional formula for electrical conductivity \['\sigma '\] which is reciprocal of resistivity?            [JEE ONLINE 26-05-2012]

    A) \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]

    B) \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{2}}]\]

    C) \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{-2}}]\]

    D) \[[{{M}^{-2}}{{L}^{3}}{{T}^{2}}{{A}^{-1}}]\]

    Correct Answer: A

    Solution :

    [a] Dimensional formula for electrical resistivity,\[\rho =[M{{L}^{3}}{{T}^{-3}}{{A}^{-2}}]\]
    Dimensional formula for electrical conductivity, \[\sigma =\frac{1}{\rho }\] is \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]


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