If L,C,and R denote the inductance,capacitanc | vedclass

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(B) We know that the resonant frequency of an $LC$ circuit is given by $f = \frac{1}{2\pi \sqrt{LC}}$.Therefore,the dimensions of $LC$ are $[LC] = [T^

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$[M^{0}L^{0}T^{3}I^{0}]$

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(B) We know that the resonant frequency of an $LC$ circuit is given by $f = \frac{1}{2\pi \sqrt{LC}}$.Therefore,the dimensions of $LC$ are $[LC] = [T^{2}]$.Also,the time constant of an $LR$ circuit is $	au = \frac{L}{R}$,so the dimensions of $\frac{L}{R}$ are $[T]$.This implies that the dimensions of $\frac{R}{L}$ are $[T^{-1}]$.Now,we need to find the dimensions of $C^{2}LR$.We can rewrite the expression as $C^{2}LR = (LC) \cdot (RC)$.Since $RC$ is the time constant of an $RC$ circuit,its dimensions are $[T]$.Thus,$[C^{2}LR] = [LC] \cdot [RC] = [T^{2}] \cdot [T] = [T^{3}]$.Alternatively,$[C^{2}LR] = [LC] \cdot [LC] \cdot [R/L] = [T^{2}] \cdot [T^{2}] \cdot [T^{-1}] = [T^{3}]$.Therefore,the dimensional formula is $[M^{0}L^{0}T^{3}I^{0}]$.

If $L$,$C$,and $R$ denote the inductance,capacitance,and resistance respectively,the dimensional formula for $C^{2}LR$ is

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