First slide
Power in a.c. circuit

 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=E0sinωt and i=i0sinωtπ2 respectively.   So, Pinst =Ei=E0sinωt×i0sinωtπ2 =E0i0sinωtsinωtcosπ2cosωtsinπ2=E0i0sinωtcosωt=12E0i0sin2ωt (sin2ωt=2sinωcosωt)
Hence, angular frequency of instantaneous power is 2 ω

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