What aspect of the lamp in the circuit is proportional to the current passing through it?

The brightness of the lamp is directly proportional to the current passing through it. When current flows through a lamp, such as an incandescent bulb, it heats up the filament, which in turn produces light. The greater the current, the more energy is supplied to the lamp, resulting in a brighter output. This relationship is a fundamental principle of electrical circuits, where an increase in current leads to an increase in power consumption, and therefore, more brightness from the lamp.

The other aspects, while they may be influenced by current to some degree, are not as directly proportional. For instance, while voltage across the lamp does relate to current according to Ohm's Law, it is not the only factor affecting brightness; it requires the lamp's resistance. The temperature of the lamp may rise with increased current but is not a direct measure of brightness. Similarly, the color of light emitted can vary based on factors such as the type of lamp used rather than solely the current amount flowing through it. Thus, brightness is the most straightforward and relevant measure of how much current is impacting the lamp's output.