A typical \"light dimmer\" used to dim the stage lights in a theater consists of

Question

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 Lmax) connected in series with a light bulb B as shown in the figure below. The electric supply provides an emf E (rms) at a frequency f; the light bulb is rated for power P at this emf. (Use any variable or symbol stated above as necessary.)

(a) What Lmax is required if the rate of energy dissipated in the light bulb is to be varied by a factor of 4 from its upper limit? Assume that the resistance of the light bulb is independent of its temperature.

Lmax = _________

(b) What would be the maximum resistance of a variable resistor (adjustable between zero and Rmax) which can be used in place of an inductor?

Rmax = ___________

Explanation / Answer

I also know that P = V^2 / R Taking the ratio of Pmax to Pmin we get Pmax/Pmin = (Imax / Imin)^2 = ( (E/Zmax) / (E/Zmin) )^2 = 4 So (sqrt( (R^2) + ((w*Lmax)^2) ) / R)^2 = 4 which implies that Lmax = R / w (when we solve for Lmax in the above equation) Thus, pluggin in for P = V^2 / R we get ( (2V^2 / P) / w) = Lmax Solving, I get Lmax = .059. Now what about part b. Not sure about that one.

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