Which of the following have same dimension ?

Options

A. `LC`
B. `(R)/(L)`
C. `(L)/(R)`
D. `(C)/(L)`

Explanation

`LC=(1)/(W^(2)) [ :. (1)/(sqrt(LC))=w]`
`:.[LC]=(1)/([W^(2)])=(1)/((M^(0)L^(0)T^(-1))^(2))=M^(0)L^(0)T^(-2)`
(B) Unit of `(R)/(L)=("ohm")/("ohm" xx "sec") =(1)/(sec)`
`:.[(R)/(L)]=(1)/([sec])=M^(0)L^(0)L^(-1)`
`(C)[(L)/(R)]=(1)/([(R)/(L)])=M^(0)L^(0)T^(-1)`
(D) units `(C)/(L)=("Faraday")/("Henry")=(("Columb")/("Volt"))/(ohm xx sec)=(1t)/(V xx Rt)`
`=(I)/(IRxxR)=(1)/(R^(2))`
`:.[(C)/(L)]=[R]^(-2)`
`=(M^(1)L^(2)A^(-2))^(-2)`
`=M^(-2)L^(-4)T^(6)A^(4)`