The purpose of this work was to study how patient size affects the exponent of the power law relating dose to x-ray tube potential in clinical x-ray imaging using phantoms. Computed tomography (CT) dose phantoms of 16 cm and 32 cm in diameter were used to model children and adults respectively. A Fujifilm digital radiographic imaging system and a GE Discovery HD 750 CT scanner were employed to image both phantoms. For the Fujifilm radiographic imaging system, doses were measured at various locations of entrance, centre, exit as well as side locations of the phantoms using a PTW DIADOS diagnostic dosimeter. Standard procedure was employed for CT dose measurements for the GE CT scanner. X-ray exposures were varied by employing various tube voltages kVp and tube current-time product or mAs. This study found that the exponent in dose power law in phantoms increases as phantom size increases. Doses measured at body centres have lower uncertainties than those at x-ray exit surfaces. The power law exponent in phantoms was found to be a linear function of the depth from the entrance surface consistent with theoretical prediction and data from the literature. These results led to both kVp and body size dependent governing equations for the variations of imaging parameters in CT and radiographic imaging. These equations provide better estimates in guiding selection of optimal scan parameters in clinical x-ray imaging.