In terms of potential difference V, electric current I, permittiv… - Vidyadip

MCQ

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)

$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$

A
$(B,D)$
B
$(B,C)$
✓
$(A,C)$
D
$(A,D)$

✓

Answer

Correct option: C.

$(A,C)$

c
$BI \ell c \equiv VI \Rightarrow \mu_0 I ^2 c \equiv VI \Rightarrow \mu_0 Ic = V$

$\Rightarrow \mu_0^2 I ^2 c ^2= V ^2$

$\Rightarrow \mu_0 I ^2=\varepsilon_0 V ^2 \Rightarrow \varepsilon_0 cV = I$

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