Chapter 31, Problem 056 A typical \"light dimmer\" used to dim the stage lights

Question

Chapter 31, Problem 056 A typical "light dimmer" used to dim the stage lights in a theater consists of a variable inductor L (whose inductance is adjustable between zero and Lmx) connected in series with a lightbulb B as shown in the figure The electrical supply is 120 V (rms) at 60.0 Hz; the lightbulb is rated as 120 V, 810 W. (a) What Lmax is required if the rate of energy dissipation in the lightbulb is to be varied by a factor of 7 from its upper limit of 810 W Assume that the resistance of the lightbulb is independent of its temperature. (b) What would be the maximurm resistance of a variable resistor (adjustable between zero and Rmax) which can be used in place of an inductor? To enerHY supply (a) Number (b) Number Click if you would like to Show Work for this question: Units Units Open Show Work

Explanation / Answer

given

f = 60 Hz

P = 810 W

V = 120 V

(a)

the power consumed by the light bulb is

P = I2*R /2

Pmax/Pmin = (Imax /Imin)2 = 7

(Imax/Imin)2 = (Zmax /Zmin)2

[sqrt( R2 +(w*Lmax)2 ) /R]2 =7

( R2 +(w*Lmax)2 ) /R2 = 7

(w*Lmax /R)2 = 6

Lmax = 2.44*R/w

Lmax = 2.44*(V2/P) / 2*pi*f

Lmax = 2.44*(120)2 / 810*2*3.14*60

Lmax = 11.51*10-2 H

(b)

[(Rmax + Rbulb) / Rbulb ]2 = 7

Rmax = ( sqrt(7) -1 )*Rbulb

Rmax = ( sqrt(7) - 1 )*(120)2 / 810

Rmax = 29.25 ohm

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