Question

Dimensions of $\frac{L}{RCV}$ are

• A. $[A^{-1}]$
• B. $[A^{-2}]$
• C. $[A]$
• D. $[{{A}^{2}}]$

Answer 1

Answer: (A)

$[A^{-1}]$

Answer 2

$\frac{L}{R}$ has the dimensions of time. Because $\frac{L}{R}$ is the time constant of $L-R$ circuit.
$\therefore \left[\frac{L}{R}\right]=[ T ]$
Charge $=$ Capacitance $\times$ Potential difference
$Q=C V$
and ${[Q]=[A T]}$
$\therefore \left[\frac{L}{R C V}\right]=\left[\frac{L}{Q}\right]$
$=\left[\frac{T}{A T}\right]$
$\left[\frac{L}{R C V}\right]=\left[A^{-1}\right]$

Therefore, the correct option is (A): $[A^{-1}]$