The goal is to find the frequency at which resonance occurs in a series LCR circuit. To achieve resonance, the inductive reactance ($X_L$) should equal the capacitive reactance ($X_C$).

Given are:

• Inductance, $$L = 10 ~\mathrm{mH} = 10 \times 10^{-3} ~\mathrm{H}$$
• Capacitance, $$C = 1 ~\mu\mathrm{F} = 1 \times 10^{-6} ~\mathrm{F}$$
• Resistance, $R = 100 ~\Omega$ (which does not directly impact the resonance frequency)

Resonance occurs when the angular frequency ($\omega$) meets the condition $$\omega L = \frac{1}{\omega C}$$, leading to the formula for calculating the resonance frequency ($f$) as $$f = \frac{\omega}{2\pi} = \frac{1}{2\pi\sqrt{LC}}$$.

Substituting the given values:

$$f = \frac{1}{2\pi\sqrt{10 \times 10^{-3} \cdot 1 \times 10^{-6}}} = 1.59 \mathrm{kHz}$$

Thus, the frequency at which resonance occurs in this LCR circuit is 1.59 kHz.