Question

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

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

Answer 1

The correct option is A $1/RC$

The dimensions of the resistance is $R=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$

The dimensions of the capacitance is $C=\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$

The dimensions of the inductance is $L=\left[M{L}^2{T}^{-2}{A}^{-2}\right]$

So, the dimensions of:

$\frac{1}{RC}=\frac{1}{\left[M{L}^2{T}^{-3}{A}^{-2}\right]\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]}=\left[T^{-1}\right]$

$\frac{R}{L}=\frac{\left[M{L}^2{T}^{-3}{A}^{-2}\right]}{\left[M{L}^2{T}^{-2}{A}^{-2}\right]}=\left[T^{-1}\right]$

$\frac{1}{\sqrt{LC}}=\frac{1}{\left(\right[M{L}^2{T}^{-2}{A}^{-2}\left]\right[M^{-1}{L}^{-2}{T}^4{A}^2]{)}^{1/2}}=\left[T^{-1}\right]$