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confirm with dimensional analysis: w (omega) = 1/sqrt (LC) I need first three lines

confirm with dimensional analysis:

w (omega) = 1/sqrt (LC)

I need first three lines

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Answer #1

The unit of L is Henry which is the equivalent of one kilogram meter squared per Coulomb squared

So the dimension of L is

where m is mass, l is length and Q is charge

The unit of C is Farad which has a dimension of

where T is the time

Therefore the dimension of LC is

Hence dimension of

is

and the unit of is rad/s which has a dimension

Therefore by dimensional analysis, we can confirm that

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