(dw)=q(dv) v=ir by ohms law dv=r*(di) q=it (dw)=rti(di) integrating, w=rt*i^2/2 w/t=P(power)=i^2*r/2 but actually its i^2*r only wheres the mistake please point out

In actual, the i is the peak current, Imax , which sqrt(2)times the rms quantity, just take care of rms quantity and peak value.

No dought you are doing integration to find power and your ans is half. Actually if you study integration in math, it will area between wrt to which you are doing integration. And it will provide avg value. But actually peak value is double