Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 36

36 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 $L_{max}$) connected in series with a lightbulb $B$, as shown in Fig. 31-25. The electrical supply is $120 \text{ V (rms)}$ at $60.0 \text{ Hz}$; the lightbulb is rated at $120 \text{ V}, 1200 \text{ W}$. (a) What $L_{max}$ 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 $1200 \text{ W}$? Assume that the resistance of the lightbulb is independent of its temperature. (b) Could one use a variable resistor (adjustable between zero and $R_{max}$) instead of an inductor? (c) If so, what $R_{max}$ is required? (d) Why isn't this done?