Due to change in main voltage, the temperature of an electric bulb rises from 3000K to 4000K. What is the percentage rise in electric power consumed?

Answer

216

Explanation

Electric power consumed in first case ,
`P_(1)=sigmaT_(1)^(4) =sigma(3000)^(4)`
Electric power consumed in second case ,
`P_(2)=sigmaT_(2)^(4)=sigma(4000)^(4)`
` :. (P_(2))/(P_(1)) = ((4000)^(4))/((3000)^(4))=256/81 `
`(P_(2)-P_(1))/(P_(1))=(P_(2))/(P_(1))-1=256/81 -1 = 175/81 `
` :. ` Percentage rise in power
`=((P_(2)-P_(1))/(P_(1)))xx100=175/81 xx100=216` .