Question

The dimensional formula of the quantity $\frac{L}{RCV}$ is
(Here $L$ is inductance of inductor, $R$ is resistance, $C$ is capacitance, $V$ is potential difference )

• A. $M^0{L}^0{T}^1{A}^1$
• B. $M^0{L}^0{T}^{-1}{A}^{-1}$
• C. $M^0{L}^0{T}^0{A}^1$
• D. $M^0{L}^0{T}^0{A}^{-1}$

Answer 1

The correct option is D $M^0{L}^0{T}^0{A}^{-1}$

We know that
$\left[V\right]=\left[iR\right]=\left[L\frac{di}{dt}\right]$
$\left[V\right]=\left[i\right]\left[R\right]=\frac{\left[L\right]\left[i\right]}{\left[t\right]}$
$\Rightarrow \left[\frac{L}{R}\right]=\left[t\right]=\left[T\right]$

Also,
$i=C\frac{dV}{dt}$
$\left[CV\right]=\left[i\right]\left[t\right]=AT$

$\Rightarrow \left[\frac{L}{RCV}\right]=\frac{T}{AT}=A^{-1}$