P$3.$ A typical dimmer switch used to dim the lights in a room consists of a variable inductor L $($whose inductance is adjustable between zero and Lmax$)$ connected in series with the lightbulb. Consider a case with a $250$W $($maximum$)$ light bulb $($treat this bulb as purely resistive$).($a$)$ What Lmax is required if the power output of the lightbulb is to be varied by a factor of $5$ from its maximum of $250$ W$?$ Assume that the resistance of this $250-$W bulb is measured to be $0\mathrm{.}38$ when the bulb is not operating, and that the resistance increases linearly with power dissipated. $($b$)$ Could one use a variable resistor $($adjustable between zero and Rmax$)$ instead of an inductor? If so$,$ what Rmax is required? Why isn$$t this done?