If C and L denote capacitance and inductance | vedclass

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(B) The resonant frequency of an $LC$ circuit is given by the formula $f = \frac{1}{2\pi \sqrt{LC}}$.Rearranging this formula to solve for $LC$,we get

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${M^0}{L^0}{T^2}$

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(B) The resonant frequency of an $LC$ circuit is given by the formula $f = \frac{1}{2\pi \sqrt{LC}}$.Rearranging this formula to solve for $LC$,we get $\sqrt{LC} = \frac{1}{2\pi f}$,which implies $LC = \frac{1}{4\pi^2 f^2}$.Since $4\pi^2$ is a dimensionless constant,the dimensions of $LC$ are the same as the dimensions of $\frac{1}{f^2}$.The dimension of frequency $f$ is $[T^{-1}]$.Therefore,the dimensions of $LC$ are $[T^{-1}]^{-2} = [T^2]$.In terms of fundamental dimensions,this is written as $[M^0 L^0 T^2]$.

If $C$ and $L$ denote capacitance and inductance respectively,then the dimensions of $LC$ are

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