Question

If $L,R,C$ and $V$ respectively represent inductance, resistance, capacitance and potential difference, then the dimensions of $\frac{L}{RCV}$ are the same as those of:

• A. $Charge$
• B. $\frac{1}{Charge}$
• C. $Current$
• D. $\frac{1}{Current}$

Answer 1

The correct option is D $\frac{1}{Current}$

$L=M{L}^2{I}^{-2}{T}^{-2}$
$R=M{L}^2{I}^{-2}{T}^{-3}$
$C=M^{-1}{L}^{-2}{I}^2{T}^4$
$V=M{L}^2{I}^{-1}{T}^{-3}$
$\frac{L}{RCV}=\frac{M{L}^2{I}^{-2}{T}^{-2}}{\left(M{L}^2{I}^{-2}{T}^{-3}\right)\left(M^{-1}{L}^{-2}{I}^2{T}^4\right)\left(M{L}^2{I}^{-1}{T}^{-3}\right)}$
$\frac{L}{RCV}=M^0{L}^0{T}^0{I}^{-1}=\frac{1}{current}$
Hence, option D is currect.