A source is supplying a load through a $2$-phase, $3$-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $v_{an}=220 \sin (100 \pi t) V$ and $i_{a}=10 \sin (100 \pi t) A$, respectively. Similarly for phase-b, the instantaneous voltage and current are $v_{bn}=220 \cos (100 \pi t) V$ and $i_{b}=10 \cos (100 \pi t) A$, respectively.
The total instantaneous power flowing from the source to the load is
- $2200$W
- $2200 \sin^{2} (100 \pi t) W$
- $4400$W
- $2200 \sin (100 \pi t) \cos (100 \pi t) W$