A typical \"light dimmer\" used to dim the stage lights in a theater consists of

Question

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 the figure. The electrical supply is 120 V (rms) at 60.0 Hz; the lightbulb is rated as 120 V, 1000 W. (a) What L_max 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. (b) What would he the maximum resistance of a variable resistor (adjustable between zero and R_max) which can be used in place of an inductor?

Explanation / Answer

(Current ThruLight Bulb @ 120 V)= (Imax) =
= (Power Dissipated @ 120 V)/(120 V)
= (1000 W)/(120 V)
= 8.3Amps

(Resistance Of LightBulb) = R =
= (Voltage)/(Current)
= (120 V)/(8.3A)
= 14.4 Ohms

(Current To Dissipate (1000/4 =250) Watts Power In Resistor) = I =
= sqrt( P/R )(<----P=(I^2)*R)

= sqrt( (250 W)/(14.4 Ohms))
= 17.3 Amps

=( Total circuitlmpedancet to Dissipat (1000/4=250) Watt power in resistor)=Z
= V/I
= (120 V)/(17.3 Amps)

=6.93 Ohms

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