The intensity of a lightbulb with a resistance of 130 \\Omega is controlled by c

Question

The intensity of a lightbulb with a resistance of 130 Omega is controlled by connecting it in series with an inductor whose inductance can be varied from L = 0 to L = L_{{ m{max}}}. This "light dimmer" circuit is connected to an ac generator with a frequency of 50.0 Hz and an rms voltage of 120 V. The inductor is now adjusted so that L = L_{{ m{max}}}. In this case, the average power dissipated in the lightbulb is one-fourth the value found in part A. What is the value of L_{{ m{max}}}? (I found L=0 to be 1110W, nut I'm stuck on Part B.

Explanation / Answer

Pdiss = 120^2 / 130 = 110.8 W i = 111 / 120 = 0.925 A Z = 2 * 120 / (0.925) = 260 ohms w Lmax = sqrt (260^2 - 130^2) = 225.2 ohm L max = 225.2/(2 pi 50) = 0.717 Hy

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