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I cannot seem to solve this problem:
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 the lightbulb B as shown in Figure 31-36. The electrical supply is 240 V (rms) at 50.0 Hz; the lightbulb is rated as "240 V, 1000 W."
What Lmax is required if the rate of energy dissipation in the lightbulb is to be varied by a factor of 5 from its upper limit of 1000 W? Assume that the resistance of the lightbulb is independent of its temperature.
It seems like this is an RL circuit with ac current, but my book seems to speak nothing of them. I figure if you want the light bulb to draw a minimum of 200W that the rms current through it must be ~1.863A. That is I found the resistance of the bulb to be 57.6 ohms with the given (240V, 1000W) and for there to be a 200W output 200W = Irms^2 * 57.6 ohms => Irms = ~1.863A.
But I have no idea how to incorporate the inductor.
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 the lightbulb B as shown in Figure 31-36. The electrical supply is 240 V (rms) at 50.0 Hz; the lightbulb is rated as "240 V, 1000 W."
What Lmax is required if the rate of energy dissipation in the lightbulb is to be varied by a factor of 5 from its upper limit of 1000 W? Assume that the resistance of the lightbulb is independent of its temperature.
It seems like this is an RL circuit with ac current, but my book seems to speak nothing of them. I figure if you want the light bulb to draw a minimum of 200W that the rms current through it must be ~1.863A. That is I found the resistance of the bulb to be 57.6 ohms with the given (240V, 1000W) and for there to be a 200W output 200W = Irms^2 * 57.6 ohms => Irms = ~1.863A.
But I have no idea how to incorporate the inductor.