Question

The dimensions of $R$ in the equation $Q=Q_0\left(1-e^{-tR/C}\right)$ are

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

Answer 1

Answer: (A)

$Q=Q_0\left(1-e^{t/RC}\right)$. As $t/RC$ is dimensionless.
$\therefore RC=t$ or $R=\frac{t}{C}=\frac{t}{QV}=\frac{V.t}{Q}$
$R=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[AT\right]}\frac{\left[T\right]}{\left[AT\right]}$
$=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$