Question

Let $L,R,C$ and $V$ represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{L}{RCV}$ in $SI\text{units}$ will be:

• A. $\left[LTA\right]$
• B. $\left[L{A}^{-2}\right]$
• C. $\left[L{T}^2\right]$
• D. $\left[A^{-1}\right]$

Answer 1

The correct option is D $\left[A^{-1}\right]$

We know that, the time constant in $L-R\text{circuit}$ is given by,

$\tau =\frac{L}{R}$

$\Rightarrow \left[\frac{L}{R}\right]=\left[T\right]$

$\text{Also, charge}Q=CV$

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

Hence, option $\left(B\right)$ is correct.