Question

In terms of potential difference $V$, electric current $I$, permittivity ${\epsilon }_0$, permeability ${\mu }_0$ and speed of light $c$, the dimensionally correct equation(s) is/are

• A. ${\mu }_0{I}^2={\epsilon }_0{V}^2$
• B. ${\mu }_{0}cI={\epsilon }_{0}V$
• C. ${\mu }_{0}I={\epsilon }_{0}V$
• D. $I={\epsilon }_{0}cV$

Answer 1

Answer: (A), (D)

Form relations,

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

From relation 2,

Option A:

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

Hence, A is correct.

Option C:

$I=\frac{V}{R}$

$I=V\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$

Multiplying numerator and denominator by ${ϵ}_0$

$I=V{ϵ}_{0}C$

Hence, A is correct.
C is also correct.