L, C and R represent physical quantities inductance, capacitance and resistance respectively. What is the combination representing dimension of frequency ?

Options

A. LC
B. `(LC)^((-1)/2)`
C. `(L/C)^((-1)/2)`
D. `C/L`

Answer

B

Explanation

(A)Unit of LC= ohm x second x `"second"/"ohm"`
`=["second"^2]`
`=M^0L^0T^2`
(B)`(LC)^(-1/2)`
As explained in (A) `[(LC)^(-1/2)]=[M^0L^0T^2]^(-1/2)`
`=M^0L^0T^(-1)`
Which is dimension of frequency .
(C) `(L/C)^(-1/2)`
Unit of `(L/C)^(-1/2)=["Ohm x Second"/("Second"/"Ohm")]^(-1/2)=[(Ohm)^2]^(-1/2)`
`=[Ohm^(-1)]`
`=M^(-1) L^(-2) T^3 A^2`
(D) Unit of `C/L = ("second"/"ohm")/"ohm x second"="second"^2/"ohm"^2`
`=[("second"/"ohm")^2]`
`=(M^0L^0T^2)/(M^2L^4T^(-6)A^(-4))`
`=M^(-2) L^(-4) T^4 A^4`