Which of the following does not have the dimensions of time ?

Options

A. `[L/R]`
B. `[RC]`
C. `[sqrt(LC)]`
D. `[1/(sqrtLC)]`

Answer

D

Explanation

`c = L[(dI)/(dt)]`
`therefore [L] = ([e][dt])/([dI]) = ([w//q][dt])/([dI]) = ([w][dt])/([q][dt]) ([w])/([dI]^2)`
`= ([ML^2 T^(-2)])/([A]^2) = [ML^2 T^(-2) A^(-2)]`
`[C] = ([q])/([v])`
`([q^2])/([w^2])`
`= ([A^2 T^2])/([ML^2 T^(-2)])`
`= [M^(-1)L^(-2)T^4 A^2]`
`[sqrt(LC)] = ([ML^2 T^(-2)A^(-2)] xx [M^(-1) L^(-2) T^4 A^2])^(1//2)`
`[T^2]^(1//2) = [T]`
`therefore [(1)/(sqrt(LC))] = [T]^(-1)`