Question

If $q=q_{0}(1-e^{\frac{-\tau}{RC}}]$ Here, $q =$ electric charge, $R =$ electric resistance, $C =$ electric capacitance. The dimensional formula for ${\tau}$ are

• A. $\left[A^{-1}MLT^{-2}\right]$
• B. $\left[AM^{0}L^{0}T^{-1}\right]$
• C. $\left[M^{0}L^{0}T\right]$
• D. $\left[M^{0}L^{0}T^{-2}\right]$

Answer 1

Answer: (C)

$\left[RC\right]$ is time constant $=\left[M^{0}L^{0}T\right]$
Exponents have no dimensions
$\therefore \frac{\tau}{RC}=\left[M^{0}L^{0}T\right]$
$\Rightarrow \tau=\left[M^{0}L^{0}T\right]$