Q. If $C$ is the capacitance and $V$ is the potential, the dimensional formula for $CV^{2}$ is
A) $\left\lbrack {ML}^{2}T^{- 1} \right\rbrack$
B) $\left\lbrack {ML}^{- 2}T^{- 3} \right\rbrack$
C) $\left\lbrack {ML}^{2}\ T^{- 2} \right\rbrack$
D) $\left\lbrack {ML}^{- 2}T^{- 2} \right\rbrack$
Explanation
$\lbrack C\rbrack = \left\lbrack M^{- 1}L^{- 2}T^{4}A^{2} \right\rbrack$ $\lbrack V\rbrack = \left\lbrack ML^{2}T^{- 3}A^{- 1} \right\rbrack$ $\therefore\left\lbrack CV^{2} \right\rbrack = \left\lbrack M^{- 1}L^{- 2}T^{4}A^{2} \right\rbrack\left\lbrack ML^{2}T^{- 3}A^{- 1} \right\rbrack^{2}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack ML^{2}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.