Discussion Forum



1)

 In terms of potential difference V, electric current i, Permittivity  $\epsilon_{0}$ , permeability  $\mu_{0}$ and speed of light c, the dimensionally correct equations is /are


A) $\mu_{0}I^{2}=\epsilon_{0}V^{2}$

B) $\epsilon_{0}I=\mu_{0}I$

C) $I=\epsilon_{0}cV$

D) $\mu_{0}cI=\epsilon_{0}V$

Answer:

Option A,C

Explanation:

 (A)  Energy of inductor

                    $\frac{1}{2}LI^{2}=\frac{1}{2}\frac{\mu_{0}N^{2}A}{l}I^{2}e$

 Energy of capacitor

                  $\frac{1}{2}CV^{2}=\frac{1}{2}\epsilon_{0}\frac{A}{d}V^{2}\mu_{0}\frac{A}{l}I^{2}$            and

$\epsilon_{0}\frac{A}{d}V^{2}$     have same dimensions.

  So, $\mu_{0}I^{2}$   and    $\epsilon_{0}V^{2}$    have same dimensions.

  (C)     $Q=CV\Rightarrow\frac{Q}{t}=\frac{CV}{t}$

                                  $I=\epsilon_{0}\frac{A}{l}\frac{V}{t}$

   $\frac{A}{lt}$   have unit of speed

   so,                      $I=\epsilon_{0}cV$