Two lamps of 200 W and 100 w are connected in series in 200 V mains . Assuming the resistance of the two lamps to remain unchanged , calculate the power consumed by each of them .

Explanation

`P=(V^(2))/(R)"or , " (V^(2))/(P)`
So , resistance of the first lamp , `R_(1)=(200xx200)/(200)=200Omega`
and resistance of the second lamp , `R_(2)=(200xx200)/(100)=200Omega`
Now , I few coonect the two lamps in series with 200 V mains , current flowing through of them ,
`I=(V)/(R_(1)+R_(2))=(200)/(200+400)=(1)/(3)A`
`therefore ` power of the first lamp , `P_(1)=I^(2)R_(1)=(1)/(3)xx(1)/(3)xx200=22.2W`
power of the second lamp , `P_(2)=I^(2)R_(1)=(2)/(3)xx(1)/(3)xx400=44.4W`