In a series LCR circuit, resonance occurs when the inductive reactance equals the capacitive reactance ($X_L = X_C$). The resonant angular frequency is defined as $\omega_0 = 1/\sqrt{LC}$ . The resonant frequency in Hertz is calculated using the formula $\nu_0 = \frac{1}{2\pi\sqrt{LC}}$ . Given $L = 10 \text{ mH} = 10^{-2} \text{ H}$ and $C = 1 \text{ \mu F} = 10^{-6} \text{ F}$, we have: $\nu_0 = \frac{1}{2\pi\sqrt{10^{-2} \times 10^{-6}}} = \frac{1}{2\pi\sqrt{10^{-8}}} = \frac{1}{2\pi \times 10^{-4}} = \frac{10000}{2\pi} \approx \frac{10000}{6.283} \approx 1591.5 \text{ Hz}$, which is approximately 1.59 kHz.