A complete circuit is essential for a continuous flow of current because it ensures charge conservation and adheres to the principle of relativity. Without a complete circuit, electrons would not have a defined path, leading to a violation of charge conservation as they would seemingly disappear and reappear in different locations. Connecting a light bulb to both terminals of a battery allows electrons to flow towards the positive terminal, creating a stable configuration that enables the bulb to light up. The flow of electrons is driven by their attraction to the positive terminal, which is crucial for maintaining current. Thus, a complete circuit is necessary for the effective operation of electrical devices.