Multiple Choice

In terms of potential difference V; electric current I, permittivity $$\varepsilon_0$$, permeability $$\mu_0$$ and speed of light c, the dimensionally correct equation(s) is(are).

A$$\mu_0I^2=\varepsilon_0V^2$$
Correct Answer
B$$\varepsilon_0I=\mu_0V$$
C$$I=\varepsilon_0cV$$
Correct Answer
D$$\mu_0cl=\varepsilon_0V$$

Solution

Dimensional formula of potential difference $$=ML^2T^{-3}A^{-1}$$
Current $$=A$$
$$C=LT^{-1}\\N_0=MLT^{-2}A^{-2}\\\varepsilon _0=M^{-1}L^{-3}T^4A^2$$
By evaluation equation we get
$$N_0I^2=\varepsilon_0V^2\rightarrow(1)\\I=\varepsilon _0cV$$

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