Physics - Unit & Dimension Question with Solution | TestHub

$C=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$ and $R=\sqrt{\frac{{\mu }_0}{{ϵ}_0}}$,

(A) ${\mu }_0{I}^2={ϵ}_0{V}^2$

$$\frac{{\mu }_0}{{ϵ}_0}=\frac{V^2}{I^2}=R^2$$

Therefore, $R^2=R^2$, which is correct.

(B) ${ϵ}_{0}I={\mu }_{0}V$

$$\frac{{ϵ}_0}{{\mu }_0}=\frac{V}{I}$$

$$\frac{1}{R^2}=R$$

This is not correct.

(C) $I={ϵ}_{0}cV$

$$\frac{I}{V}={ϵ}_{0}c=\frac{{ϵ}_0}{\sqrt{{\mu }_0{ϵ}_0}}$$

$$\frac{1}{R}=\sqrt{\frac{{ϵ}_0}{{\mu }_0}}=\frac{1}{R}$$

This is correct.

(D) ${\mu }_{0}CI={ϵ}_{0}V$

$$\frac{{\mu }_{0}C}{{ϵ}_0}=\frac{V}{I}$$

$$\frac{{\mu }_0}{{ϵ}_0}\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}=R$$

Therefore, $\frac{1}{{ϵ}_0}\sqrt{\frac{{\mu }_0}{{ϵ}_0}}=R\Rightarrow \frac{R}{{ϵ}_0}=R$, which is incorrect.