Increasing the base current of an NPN transistor leads to a proportional increase in collector current, particularly in linear mode, where the collector current is approximately β times the base current. In switch mode, while the collector diode begins to conduct, an increase in base current results in a slight decrease in Vce rather than a significant change in collector current. Understanding these behaviors requires knowledge of transistor operation modes and current gain concepts. For a deeper understanding, semiconductor textbooks provide comprehensive explanations from a physics perspective. Overall, the relationship between base and collector currents is crucial for effective transistor function in various applications.