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www.GOALias.blogspot.comAlternating CurrentFIGURE 7.6 (a) A Phasor diagram for the circuit in Fig. 7.5.(b) Graph of v and i versus ωt.We see that the current reaches its maximum value later than the⎡Tπ/2⎤voltage by one-fourth of a period ⎢=⎣4ω ⎥. You have seen that an⎦inductor has reactance that limits current similar to resistance in adc circuit. Does it also consume power like a resistance? Let us try tofind out.The instantaneous power supplied to the inductor is⎛ π⎞pL = iv = im ⎜ t − vmt⎝⎟2⎠sin ω × sin ( ω )( ω ) sin( ω )=−i v cos t tmmimvm=− sin ( 2ωt)2So, the average power over a complete cycle isimvmPL = − sin 22( ω t)imvm=− sin ( 2ω t ) = 0,2since the average of sin (2ωt) over a complete cycle is zero.Thus, the average power supplied to an inductor over one completecycle is zero.Figure 7.7 explains it in detail.Example 7.2 A pure inductor of 25.0 mH is connected to a source of220 V. Find the inductive reactance and rms current in the circuit ifthe frequency of the source is 50 Hz.Solution The inductive reactance,XL= .– 32π ν L=2× 314× 50× 25×10 W= 7.85ΩThe rms current in the circuit isV 220 VI = = = 28AX 7.85 ΩLEXAMPLE 7.2239