Question

dimensional formula of 1/√LC​

Answer 1

Dimensions of Inductance(L) = ML²T⁻²A⁻²

Dimensions of Capacitance(C) = M⁻¹L⁻²T⁴A²

L x C = ML²T⁻²A⁻² x M⁻¹L⁻²T⁴A²

=T²

$\frac{1}{ \sqrt{lc} } = {t}^{ - 1}$

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Answer 2

dimension of 1/√LC is [T-¹]

method 1 : if you have read alternating current , then it is just a piece of cake for you.

because formula, f = 1/2π√LC

where f is frequency and we know dimension of frequency is [T-¹]

from dimensional analysis,

dimension of f = dimension of 1/√LC

hence, dimension of 1/√LC = [T-¹]

method 2 : L is inductance, dimension of L = ML²T-²A-²

C is capacitance , dimension of C = [M-¹L-²T⁴A²]

now, dimension of LC = [ML²T-²A-²M-¹L-²T⁴A²] = [T²]

now, dimension of √LC = [T]

dimension of 1/√LC = [T-¹]

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