Final answer:
The filament and focusing cup are located at the cathode end of an X-ray tube. The cathode is where electrons are emitted and directed towards the anode, where they produce X-rays upon impact.
Step-by-step explanation:
The end of an X-ray tube that contains the filament and the focusing cup is the cathode. In a cathode ray tube (CRT), which is the predecessor to modern X-ray equipment, the cathode is the source of electrons. These electrons are emitted from the filament when it is heated -- a process known as thermionic emission. The focusing cup is used to direct the electrons towards the anode. When this stream of high-energy electrons strikes the anode, X-rays are produced through interactions with the material of the anode, typically made of copper or tungsten due to their high atomic numbers and high melting points.
In the context of circuit elements, a diode is a semiconducting device that allows current flow only if the diode is forward biased, which means the anode is positive with respect to the cathode. Resistors, on the other hand, are components that dissipate power as heat, and capacitors store electrical energy in an electric field.