Many lamps have a switch that lets you choose three levels of brightness. The bu

Question

Many lamps have a switch that lets you choose three levels of brightness. The bulbs in this type of lamp have not one but two filaments inside, which are wired in parallel and have their own switches. One of the filaments is designed to give off more light than the other when connected to the average 120 V emf provided by a wall outlet. In the dimmest position, only the least bright filament is on. In the next position, only the brighter filament is on. In the brightest position, both filaments are on. Suppose one of the filaments consumes 69.0 watts and the other consumes 70.0 watts. What is their equivalent resistance in the brightest position (when both are turned on)?

Explanation / Answer

average emf E = 120 V power of one filament P = 69 W power of other filament P ' = 70 W resistance of the 1 st filament R = E^ 2/ P = 208.69 ohm resistance of the 2 nd filament R ' = E ^ 2/ P ' = 205.71 ohm their equivalent resistance in the brightest position = (RR' ) / ( R + R ' )                                                                              = 103.59 ohm

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