Question

The dimensions of $R$ in the equation $Q=Q_{0}\left(1-e^{-tR/C}\right)$ are

• A. $\left[ML^{2}T^{-3}A^{-2}\right]$
• B. $\left[ML^{2}T^{-2}A^{-3}\right]$
• C. $\left[M^{2}L^{2}T^{-3}A^{-2}\right]$
• D. $\left[ML^{2}T^{-1}A^{-2}\right]$

Answer 1

Answer: (A)

$Q=Q_{0}\left(1-e^{t/RC}\right)$. As $t/RC$ is dimensionless.
$\therefore RC=t$ or $R=\frac{t}{C}=\frac{t}{QV}=\frac{V.t}{Q}$
$R=\frac{\left[ML^{2}T^{-2}\right]}{\left[AT\right]} \frac{\left[T\right]}{\left[AT\right]}$
$=\left[ML^{2}T^{-3}A^{-2}\right]$