Final answer:
The primary controlling factor of x-ray penetration is the kilovoltage (kVp), as it determines the energy of the x-ray photons, which in turn influences their ability to penetrate materials.
Step-by-step explanation:
The primary controlling factor of penetration of x-rays is kilovoltage (kVp). The penetration of x-rays through a material largely depends on the energy of the x-ray photons. The higher the kilovoltage, the more energy the x-ray photons possess, and consequently, the greater their ability to penetrate materials. For example, an x-ray tube may be operated at a lower kilovoltage like 50.0 kV for chest x-rays, which requires less penetration, and at a higher kilovoltage such as 100 kV for examining a broken leg in a cast, which requires more penetration due to the increased density of the cast material. Factors like milliamperage (mA), exposure time, and source-to-image distance (SID) also play a role in the quality of the x-ray image; however, when it comes to penetration, kilovoltage (kVp) is the key parameter.