Question

$L,C,R$ represent physical quantities inductance, capacitance and resistance respectively. The combinations which have the dimensions of frequency are

• A. $1/RC$
• B. $R/L$
• C. $1/\sqrt{LC}$
• D. $C/L$

Answer 1

Answer: (C)

$1/\sqrt{LC}$

As, $\left[R\right]=\left[M{L}^2{T}^{-3}{A}^{-2}\right],\left[L\right]=\left[M{L}^2{T}^{-2}{A}^{-2}\right]and\left[C\right]=\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$
So, $\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{\left(M{L}^2{T}^{-2}{A}^{-2}\right)\times \left(M^{-1}{L}^{-2}{T}^4{A}^2\right)}}$$=\frac{1}{\sqrt{T^2}}=T^{-1}$