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 emf and current in inductive circuit are given by E=E0sin⁡ωt and i=i0sin⁡ωt−π2 respectively.   So, Pinst =Ei=E0sin⁡ωt×i0sin⁡ωt−π2 =E0i0sin⁡ωtsin⁡ωtcos⁡π2−cos⁡ωtsin⁡π2=E0i0sin⁡ωtcos⁡ωt=12E0i0sin⁡2ωt (sin⁡2ωt=2sin⁡ωcos⁡ωt)Hence, angular frequency of instantaneous power is 2 ω