Question

If $L,R,C$ denote inductance, resistance, and capacitance, respectively. Then dimension of$\frac{L}{R^{2}C}$ are

• A. $\left[M^0{L}^{0}T\right]$
• B. $\left[M^0{L}^0{T}^0\right]$
• C. $\left[A^{-1}{M}^0{L}^0{T}^{-1}\right]$
• D. $\left[ML{T}^{-1}\right]$

Answer 1

The correct option is B $\left[M^0{L}^0{T}^0\right]$

As we know,
The dimension of time constant of $L-R$ circuit $=\left[M^0{L}^{0}T\right]$
The dimension of time constant of $R-C$ circuit $=\left[M^0{L}^{0}T\right]$
Given, $\frac{L}{R^{2}C}$
$\frac{L}{R^{2}C}=\left(\frac{L}{R}\right)\times \frac{1}{RC}$

$\frac{\left[M^0{L}^{0}T\right]}{\left[M^0{L}^{0}T\right]}=\left[M^0{L}^0{T}^0\right]$