Physics - Unit & Dimension Question with Solution | TestHub

Using$C=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$&$R=\sqrt{\frac{{\mu }_0}{{ϵ}_0}}$we can check corrections
(i)${\mu }_0{I}^2={ϵ}_0{V}^2$
$\frac{{\mu }_0}{{ϵ}_0}=\frac{V^2}{I^2}=R^2$
$\therefore R^2=R^2$Correct
(ii)${ϵ}_{0}I={\mu }_{0}V$
$\frac{{ϵ}_0}{{\mu }_0}=\frac{V}{I}$
$\frac{1}{R^2}=R$Not correct
(iii)$I={ϵ}_{0}cV$
$\frac{1}{V}={ϵ}_{0}c=\frac{{ϵ}_0}{\sqrt{{\mu }_0{ϵ}_0}}$
$\frac{1}{R}=\sqrt{\frac{{ϵ}_0}{{\mu }_0}}=\frac{1}{R}$Correct
(iv)${\mu }_{0}CI={ϵ}_{0}V$
$\frac{{\mu }_{0}C}{{ϵ}_0}=\frac{V}{I}$
$\frac{{\mu }_0}{{ϵ}_0}\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}=R$
$\therefore \frac{1}{{ϵ}_0}\sqrt{\frac{{\mu }_0}{{ϵ}_0}}=R\Rightarrow \frac{R}{{ϵ}_0}=R\mathrm{ }$Incorrect