Calculating Maximum Resistance & Inductance for Theater Light Dimmer

[reising1]

Homework Statement

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 lightbulb. The electrical supply is 120 V (rms) at 60.0 Hz; the lightbulb is rated as 120 V, 1300 W. (a) What Lmax is required if the rate of energy dissipation in the lightbulb is to be varied by a factor of 4 from its upper limit of 1300 W? Assume that the resistance of the lightbulb is independent of its temperature. (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?

Homework Equations

I know the equations for RLC circuits, and I know P = (i^2)(R)

The Attempt at a Solution

I'm really just stuck. I don't really understand the question. Are we increasing it by a factor of 4 or decreasing it? Can someone get me started on the right track?

 

[reising1]

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. Does this seem correct?

Now what about part b. Not sure about that one.