A typical “light dimmer” used to dim the stage lights in a theatre consists of a variable inductor L connected in series with the light bulb B as shown in the figure. The power supply is 120 V (rms) at 60.0 Hz; the light bulb is marked “120 V, 1000 W.” (a) We have to find the maximum inductance L required if the power in the light bulb is to be varied by a factor of five. We may assume that the resistance of the light bulb is independent of its temperature. (b) We have to answer whether a variable resistor instead of an inductor could have been used. If so, what maximum resistance is required? Why isn’t this done?

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(a)

We will find the resistance of the light bulb from its ratings “120 V, 1000 W”.

In a purely resistive load

When the inductor is connected in series with the light bulb, the power dissipation is given by the equation

where

In order that power in the light bulb could be varied by a factor of five, the maximum value of the required inductance will be given by the equation

Solving this equation, we find

(b)

If the power in the light bulb is to be dimmed by using a variable resistor instead of an inductor, the equation that will fix the maximum value of the additional resistance r that will be required is

Yes, a variable resistor instead of a variable inductor can be used as a “light-dimmer”, but then more power will be drawn from the mains, which would get dissipated as heat.