When does the temperature on a wet-bulb thermometer equal the dry-bulb temperature?

The scenario in which the temperature on a wet-bulb thermometer equals the dry-bulb temperature occurs when the air is saturated with moisture. When the air reaches this saturation point, the moisture in the air means that any heat energy from the air has been fully utilized in the evaporation process, resulting in the wet-bulb temperature matching the dry-bulb temperature.

In this condition, the wet-bulb thermometer reads the same temperature as the dry-bulb thermometer because the wet-bulb thermometer gets influenced by the moisture in the air, effectively measuring the lowest temperature that can be achieved by the evaporation of water into the air. When the air is fully saturated, it cannot take on more moisture, and the temperatures equalize.

Furthermore, although there may be other scenarios regarding temperatures and moisture, they do not apply well to this context where equalization occurs only at saturation.