An inventor designed a light fixture with a dimmer knob that uses a series RCL circuit containing a 50-μF capacitor, inductor, and 100-W light bulb. When the knob is set to MAX, the resonant frequency is 60 Hz, allowing the bulb to operate at 100 W. Turning the knob gradually pulls cardboard (? = 3.3) out of the capacitor, decreasing its capacitance and changing the resonant frequency to dim the bulb. When set to MIN, the bulb should operate at 40 W. However, it is unclear if the fixture will work as designed.

1. An inventor has a rough design for a light fixture with a dimmer
knob. The fixture contains a
50-µF capacitor, an inductor, and a 100-W light bulb (the
resistor), forming a series RCL
circuit. The idea is that when the dial is set to MAX, the
resonant frequency of the circuit is
60 Hz, the frequency of the standard household ac service in the
US. Thus, the circuit is at
resonance, and the light bulb operates at 100 W.
Turning the dimmer knob down from MAX gradually pulls a
thin cardboard sheet (? = 3.3) out
from between the capacitor's plates, decreasing its capacitance
and thereby changing the
circuit's resonant frequency. This lowers the power output of
the bulb, dimming it. When the
knob is turned to MIN, the cardboard sheet is completely out of
the capacitor, and the bulb is
meant to be operating at just 40 W. (The OFF setting opens the
circuit, but that's unrelated to
the question.)
Question: will the fixture work as designed? If not, should a
material with a higher or lower
dielectric constant should be used in constructing the capacitor?