According to the sources, the resonant frequency ($\nu_0$) of a series LCR circuit is given by the formula $\nu_0 = \frac{1}{2\pi\sqrt{LC}}$ . Given $L = 10$ H and $C = 10$ \mu F ($10 \times 10^{-6}$ F), the calculation is: $\nu_0 = \frac{1}{2\pi\sqrt{10 \times 10 \times 10^{-6}}} = \frac{1}{2\pi\sqrt{10^{-4}}} = \frac{1}{2\pi \times 10^{-2}} = \frac{100}{2\pi} = \frac{50}{\pi}$ Hz. For the AC source frequency ($\nu$), we use the general voltage equation $V = V_m \sin(\omega t)$. Comparing this with $V = 200 \sin(100t)$, we find the angular frequency $\omega = 100$ rad/s. Since $\omega = 2\pi\nu$, the source frequency is $\nu = \frac{100}{2\pi} = \frac{50}{\pi}$ Hz. Therefore, $\nu_0 = \nu = \frac{50}{\pi}$ Hz.