Thermal Runaway in Electrical Discharges (Electrical Engineering)

In high-voltage transmission substation equipment, the leakage current intensity $I$ (in milliamperes) across a deteriorating ceramic insulator gap is modeled as a function of the applied breakdown electrical stress $V$ (in kilovolts) by the rational expression:

If localized voltage surges approach the critical breakdown dielectric rating of $V_c = 12\text{ kV}$ from an overvoltage condition ($V \to 12^+$), substation protection engineers need to map the polarity and magnitude trajectory of the energy discharge.

1. Classify the behavior of $I(V)$ as $V \to 12^+$ using directional sign analysis.
2. Evaluate the limit analytically:
   $$\lim_{V \to 12^{+}} \frac{-2.5}{V - 12}$$
3. Explain how the resulting vertical asymptote informs arc-flash circuit breaker trigger ratings.