The current in a series LCR circuit is maximum at the resonant frequency, where the inductive reactance ($X_L$) equals the capacitive reactance ($X_C$). The condition for resonance is given by $\omega L = \frac{1}{\omega C}$ . Solving for inductance $L$: $L = \frac{1}{\omega^2 C}$ Given $\omega = 1000 \text{ s}^{-1} = 10^3 \text{ rad/s}$ and $C = 10 \, \mu\text{F} = 10 \times 10^{-6} \text{ F} = 10^{-5} \text{ F}$. $L = \frac{1}{(10^3)^2 \times 10^{-5}} = \frac{1}{10^6 \times 10^{-5}} = \frac{1}{10} \text{ H} = 0.1 \text{ H}$. Converting to millihenries: $0.1 \text{ H} = 100 \text{ mH}$.