Question

Charge on the capacitor is given by $Q=I\alpha e^{\frac{-tI}{\Delta v{\epsilon }_0\beta }},$ where $\alpha$ and $\beta$ are constants. $t$ = time, $I$ =current, $\Delta V$= potential difference. Then dimensions of $\frac{\beta }{\alpha }$ is same as the dimensions of

• A. $\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
• B. ${\mu }_0{\epsilon }_0$
• C. $\sqrt{{\epsilon }_0{\mu }_0}$
• D. $\frac{1}{{\mu }_0{\epsilon }_0}$

Answer 1

Answer: (A)

$\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Since exponent is dimensionless,

$Beta$ has dimensions of length (m)

Since Charge $Q=It$

On comparing $\alpha$ has dimensions of time.

Therefore, Units of $\frac{\beta }{\alpha }=m/s$

Since option A is the expression for velocity of light, it will have units $m/s$.

Hence, Option A is correct.