Choice AC over DC allowed high-voltage power transmission from the power generating plant to customer.
Instaneous power p(t) absorbed by an element is the product of instaneous voltage v(t) accross the element and instaneous current i(t) through it. it is the rate at which an element absorbs energy.
for AC excitation this will equal v(t).i(t)=V
Average power, in watts is the average of the instaneous power over one period.