Final answer:
When the filament current is sufficient for thermionic emission, a small increase in filament current results in a large increase in x-ray tube current due to the larger number of electrons being ejected and accelerated towards the anode to produce x-rays.
Step-by-step explanation:
When the filament current is high enough for thermionic emission, a small increase in filament current results in a large increase in x-ray tube current. The electrons ejected from the hot filament in an x-ray tube are accelerated towards the anode by the filament voltage. Upon striking the anode, these electrons convert their kinetic energy into various forms, including x-rays. The process whereby electrons are ejected by thermal agitation from the hot filament is crucial for the generation of x-rays.
An increase in filament current amplifies the intensity of the thermionic emission, thus increasing the number of electrons ejected. This increase in the number of electrons results in an increased tube current because more electrons are available to be accelerated and produce x-rays upon striking the anode.