An alternating e.m.f. of angular frequency ω is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

The instantaneous values of e.m.f. and current in inductive circuit are given by E=E0sinωt and i=i0sinωt−π2 respectively.So, Pinst =Ei=E0 sin ωt × i0 sinωt−π2=E0i0 sin ωtsin ωt cosπ2−cos ωt sinπ2=E0i0 sin ωt cos ωt=12 E0 i0 sin 2 ωt(sin 2 ωt = 2 sin ωt cos ωt)Hence, angular frequency of instantaneous power is2ω.