Question

The dimensions of $\frac{L}{RCV}$ ($L=$ inductance, $R=$ resistance, $C=$ capacitance, $V=$ potential difference) are

• A. [$A$]
• B. $\left[A^{-1}\right]$
• C. [$AT$]
• D. dimensionless

Answer 1

Answer: (B)

$\left[A^{-1}\right]$

We know that:

$\left[V\right]=\left[iR\right]=\left[L\frac{di}{dt}\right]$

$\left[i\right]\left[R\right]=\frac{\left[L\right]\left[i\right]}{\left[t\right]}$

Thus, $\left[\frac{L}{R}\right]=\left[t\right]=T$
$\left[L\right]=\frac{\left[V\right]\left[t\right]}{\left[i\right]}$

Also, $i=C\frac{dV}{dt}$, or $\left[CV\right]=\left[i\right]\left[t\right]=AT$
Thus, $\left[\frac{L}{RCV}\right]=\frac{T}{AT}=A^{-1}$