A Light-Dimmer Circuit The intensity of a lightbulb with a resistance of 110 is

Question

A Light-Dimmer Circuit The intensity of a lightbulb with a resistance of 110 is controlled by connecting it in series with an inductor whose inductance can be varied from L=0 to L=Lmax. This "light dimmer" circuit is connected to an ac generator with a frequency of 60.0 Hzand an rms voltage of 110 V . The inductor is now adjusted so that L=Lmax. In this case, the average power dissipated in the lightbulb is one-fourth the value found in part A. What is the value of Lmax? (the answer to part A was 110 W)

Explanation / Answer

given data is resistance R=110 ,frequency n=60HZ,rms voltage V=110V,powerP=110W

average powerPav=1/4 ofP=1/4*(110)=110/4W

average power Pav=V2rms/Z here Z=root(R2+w2L2)

Pav=V2rms/root(R2+w2L2)

110/4=1102/root((1102+(2*3.14*60L)2)

L2=550*33/(144*3,142)

L=3.575henry

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