Final answer:
The electrical energy method involving a high-temperature luminous discharge crossing a gap is called arcing, which happens when an intense electric current creates a continuous plasma discharge. Thus, the correct answer is option a.
Step-by-step explanation:
When a high-temperature luminous discharge crosses a gap, the method of electrical energy that occurs is known as arcing. Arcing refers to a continuous electrical discharge between two electrodes that forms a bright, high-temperature plasma. This phenomenon is commonly observed in arc lamps, electric welding, and lightning.
The method of electrical energy described in the question, where a high-temperature luminous discharge crosses a gap, is known as arcing. This phenomenon occurs when electric current flows through a gas, such as air, and becomes so intense that it produces a continuous plasma discharge between two points. The intense heat and light generated are due to the electrical energy being converted into thermal energy, often at dangerously high levels that can lead to melting or ignition of surrounding materials, as stated in the explanation relating to undesired heating effects of electric power. High voltages, in particular, can create a significant hazard due to the higher initial power production in an arc.