An AC voltage v= V0 sin wt is applied across pure inductor. Obtain expression for current flowing in circuit. Hence write expression for instantaneous power supplied by voltage source to inductor. Show that average power supplied over a complete cycle is zero.

Dear Student ,
Here in this case alternating voltage V = V0Sinωt is applied across a pure inductor of inductance L  .
The magnitude of induced e.m.f is given by,e=LdIdtFor the circuit , magnitude of induced emf=applied voltageLdIdt=V0SinωtdI=V0LSinωt dtI=V0L-cosωtωI=-V0ωLcosωtI=-V0XLsinωt-π2Where ,XL= ωL=inducting reactance,I=I0sinωt-π2where , I0=peak value of acNow power supplied by the source is ,P=VI =V0I0Sinωt sinωt-π2Now look the average power suppied over a complete cycle is , 02πPavg=02πV0I0Sinθ sinθ-π2dθ where θ=ωtNow look over a complete cycle 02πSinθ sinθ-π2dθ=0Therefore ,02πPavg=02πV0I0Sinθ sinθ-π2dθ =0
Hope it helps you .
Regards
 

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