If `L,C` and `R` denote the inductance, capacitance and resistance respectively, the dimensional formula for `C^(2)LR` is

Options

A. `[ML^(-2)T^(-1)I^(0)]`
B. `[M^(0)L^(0)T^(3)I^(0)]`
C. `[M^(-1)L^(-2)T^(6)I^(2)]`
D. `[M^(0)L^(0)T^(0)I^(0)]`

Answer

B

Explanation

Given dimensional formula
`[C^(2)LR]=[C^(2)L^(2)(R)/(L)]=[(LC)^(2)((R)/(L))]`
and we know that frequency of L-C circuits, `f=(1)/(2pi)(1)/(sqrt(LC))`
Here, the dimension of L-C is equal to `[T^(2)]`
`[(L)/(R)]` given the time contant of L R circuit, so that the dimension of `L/R` is equal to [T].
Hence the required dimenions,
`[(LC)^(2)((R)/(L))]=[T^(2)][T^(-1)]=[T^(3)]=[M^(0)L^(0)T^(3)I^(0)]`