Question

If $q=q_0(1-e^{\frac{t}{RC}})$, here,
$q=$ electric charge, $R=$ electric resistance,
$C=$ electric capacitance. The dimensional formula for is

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

Answer 1

The correct option is D $[M^0{L}^0{T}^{]}$

Formula containing trigonometric,
exponential functions cannot be derived with the help of dimensional analysis. They are dimensionless.
$\frac{t}{RC}=\left[M^0{L}^0{T}^0\right)]$

Here,

$\left[RC\right]$ is time constant $=\left[M^0{L}^{0}T\right)]$

According to given equation,
$q=q_0(1-e^{\frac{t}{RC}})$

$\frac{t}{RC}=\left[M^0{L}^0{T}^0\right]\Rightarrow \left[M^0{L}^{0}T\right]$