Verified Solution • 2025–26 Session moderate

QJEEM16Pha0e7: JEE Main 2016 Physics - Class 11 JEEM16Pha0e7 Solution: In the following ‘I’ refers to current and other symbols have…

In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :

Multiple Choice Options

  • A ML −- 3 T −- 3 I2
  • B M −- 1 L3 T3 I
  • C M −- 1 L −- 3 T3 I2
  • D M −- 1 L −- 3 T3 I

Step-by-Step Verified Solution

We know. resistivity ( ρ\rho ) = RAL{{RA} \over L}

and conductivity = 1ρ{1 \over \rho } = 1RA{1 \over {RA}}

As   R = VI{V \over {\rm I}}

∴\therefore    conductivity = LIVA{{L{\rm I}} \over {VA}}

Also  V = ωq{\omega \over q} = ωit{\omega \over {it}} = [ML2T−2][I][T]{{\left[ {M{L^2}{T^{ - 2}}} \right]} \over {\left[ {\rm I} \right]\left[ T \right]}} = [ML2T−3I−1]\left[ {M{L^2}{T^{ - 3}}{{\rm I}^{ - 1}}} \right]

∴\therefore    Conductivity = [L][I][ML2T−3I−1][L2]{{\left[ {\rm{L}} \right]\left[ {\rm I} \right]} \over {\left[ {M{L^2}{T^{ - 3}}{{\rm{I}}^{ - 1}}} \right]\left[ {{L^2}} \right]}}

=    [M−1L−3T3I2]\left[ {{M^{ - 1}}{L^{ - 3}}{T^3}{{\rm I}^2}} \right]

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