An AC voltage v= V0 sin wt is applied across pure inductor Obtain expression for current flowing in circuit - Physics - Alternating Current

Question

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

Pintu B. · Accepted Answer

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 voltage⇒LdIdt=V0Sinωt⇒∫dI=V0L∫Sinωt dt⇒I=V0L-cosωtω⇒I=-V0ωLcosωt⇒I=-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

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.

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.