The magic of units
Physics Narrative for 14-16
Using units carefully can help you reason fruitfully
Calculate the power in an electrical pathway in watts. Remind yourself that one watt is just one joule of energy shifted each second (discussed in detail in the SPT: Energy topic).
Remember also, covered in detail in the SPT: Electric circuits topic, that: one ampere = one coulombone second and one volt = one jouleone coulomb.
Now perhaps you can see why the electrical power has to be calculated by multiplying potential difference and current: just check on the units.
Checking for consistency in units is always a good guide to talking sense about a physical situation: the measures coded by the units are not arbitrary, nor obvious, and took a good deal of hard work to settle on in the early days of investigation of electric circuits.
Because you can only equate or add similar things, the units must be identical, or be able to be shown to be so.