1.

In terms of potential difference `C`, electric current`I` , permittivity `epsilon_(0)`, permeability `mu_(0)` and speed of light `c`, the dimensionally correct equation `(s)` is `(are)`A. (a) `mu_(0)I^(2) = epsilon_(0)V^(2)`B. (b) `mu_(0)I = mu_(0)V`C. ( c ) `I = epsilon_(0)cV`D. (d) `mu_(0)cI = epsilon_(0)V`

Answer» Correct Answer - A::C
(a, c) We know that
`C = (1)/(sqrtmu_(0)epsilon_(0)) and = R sqrt((mu_(0))/(epsilon_(0))`
Now, `mu_(0)I^(2) = epsilon_(0)V^(2)`
:. `(mu_(0))/(epsilon_(0)) = (V^(2))/(I^(2)) = R^(2)` rArr Option `A` is correct
Now,`epsilon)(0)I = mu_(0)V`
:. `(mu_(0))/(epsilon_(0)) = (I)/(V) = (I)/(R)` rArr option `B` is incorrect
Now, `I = epsilin_(0)CV`
:. `(1)/(epsilon_(0)C) = (V)/(I) = R`
:. `(1)/(epsilon_(0)(1)/(sqrtmu_(0)epsilon_(0)) = R`
:. `sqrt((mu_(0))/(epsilon_(0))) = R` rArr Option `C` is correct
Now, `mu_(0)cI = epsilon_(0)V`
:. `(mu_(0))/(epsilon_(0)) = (V)/(I_(c)) = (R)/(C) = sqrt((mu_(0))/(epsilon_(0))) xx ((1)/(1))/sqrt(mu_(0)epsilon_(0)) = mu_(0)`
rArr Option `(d)` is incorrect


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