Question

A Light-Dimmer Circuit The intensity of a lightbulb with a resistance of 150 Ω 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 Hz and an rms voltage of 120 V.

Part A:

What is the average power dissipated in the lightbulb when L=0?

Express your answer using two significant figures.

Part B:

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?

Express your answer using two significant figures.

Answer 1

R=ibor ) t = Gollz =) We a 1205 Hz 20 V IMS 2 A) Power dissipated when (Lao) => (Vrms ) = 120X120 R 150 - 96 W B) Now L=Lman is connected in series Power dissipated [2= 2 man}= 1 x 96=24W 4 & iPodissipateds I'XR 150 I? 5) I 24 0.4A 150

Now ! I. V where z= impedence of Circuit = VR2+(Xe 1² =) 25 2 2 ~22 TH ally I 2 =) (150)²7 (120 KXLman) = (120) 2 (0.492 =) 22500t 14400 N² Iman 90000 =) Iman 90000-2500 1440002 0.4749 H 0.47H