In an LC circuit, the resonant angular frequency $\omega$ is given by $\omega = \frac{1}{\sqrt{LC}}$. The dimension of angular frequency $\omega$ is $[T^{-1}]$ (since $\omega = 2\pi/T$, where $T$ is period). From the formula, we have $\frac{1}{\sqrt{[LC]}} = [T^{-1}]$. This implies $\sqrt{[LC]} = [T]$. Squaring both sides gives $[LC] = [T^2]$. Alternatively, one can find the dimensions of L and C separately: Inductance $L$: From Faraday's law, $V = L \frac{dI}{dt}$, so $[L] = \frac{[V]}{[I][T^{-1}]}$. Since $V = W/Q = W/(IT)$, $[V] = \frac{[ML^2T^{-2}]}{[AT]} = [ML^2T^{-3}A^{-1}]$. Therefore, $[L] = \frac{[ML^2T^{-3}A^{-1}]}{[A][T^{-1}]} = [ML^2T^{-2}A^{-2}]$. Capacitance $C$: From $Q = CV$, so $C = Q/V$. Since $Q = IT$, $[C] = \frac{[AT]}{[ML^2T^{-3}A^{-1}]} = [M^{-1}L^{-2}T^4A^2]$. Multiplying $[L]$ and $[C]$: $[LC] = [ML^2T^{-2}A^{-2}] \times [M^{-1}L^{-2}T^4A^2] = [M^{1-1}L^{2-2}T^{-2+4}A^{-2+2}] = [M^0L^0T^2A^0] = [T^2]$.