Many lamps have a switch that lets you choose three levels ofbrightness. The bul

Question

Many lamps have a switch that lets you choose three levels ofbrightness. The bulbs in this type of lamp have not one but twofilaments inside, which are wired in parallel and have their ownswitches. One of the filaments is designed to give off more lightthan the other when connected to the average 120 V emfprovided by a wall outlet. In the dimmest position, only the leastbright filament is on. In the next position, only the brighterfilament is on. In the brightest position, both filaments are on.Suppose one of the filaments consumes 51.0 watts andthe other consumes 70.0 watts. What is their equivalent resistancein the brightest position (when both are turned on)?

Explanation / Answer

Let the resistance of each filaments are x,y respectively
for 1st mode:   x*51=1202   => x=282 for 2nd mode: y*70=1202    => y=206 => equivalent resistance for 3rd mode: (brightest)=xy*/(x+y)= 119 => equivalent resistance for 3rd mode: (brightest)=xy*/(x+y)= 119

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