A Light-Dimmer Circuit The intensity of a lightbulb with a resistance of 110 ? i
ID: 1402645 • Letter: A
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 50.0 Hz and an rms voltage of 120 V .
Item 3 Part A What is the average power dissipated in the lightbulb when L Express your answer using two significant figures 0? 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" to an ac generator with a frequency of 50.0 Hz and an rms voltage of 120 V circuit is connected Submit My Answers Give Up Part B The inductor is now adjusted so that L- Lmax. In this case, the averag 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 Submit My Answers Give UpExplanation / Answer
A) Average power dissipated, Pavg = Vrms^2/R
= 120^2/110
= 131 W <<<<<<-------------------------Answer
B) Let Irms is the rms current in the ckt.
Pavg = Irms*Vrms
131/4 = Irms*120
==> Irms = 131/(4*120)
= 0.2729 A
we know, Irms = Vrms/z
z = Vrms/Irms
sqrt(R^2 + XL^2) = Vrms/Irms
sqrt(R^2 + XL^2) = 120/0.2729
R^2 + XL^2 = 439.7^2
110^2 + XL^2 = 439.7^2
XL = sqrt(439.7^2 - 110^2)
= 425.7 ohms
2*pi*f*Lmax = 425.7
f = 425.7/(2*pi*f)
= 425.7/(2*pi*50)
= 1.36 H <<<<<<-------------------------Answer
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