A `100W` bulb and a 25W bulb are desigened for the same voltage. They have filaments of the same length and material. The ratio of the diameter of `100W` bulb to that of the `25W` bulb is

Options

A. `4:1`
B. `2:1`
C. `sqrt(2):1`
D. `1:2`

Answer

B

Explanation

`R_(1) = (V^2)/(P_1) = (V^2)/(100) =R`
`R_(2) = (V^2)/(P_2) = (V^2)/(25) = 4R`
`R = (rhol)/(A) = (rhol)/(pir^2)=(rhol)/(pid^(2)//4), d: diameter`
`R prop 1//d^(2)`
`(R_1)/(R_2) = ((d_2)/(d_1))^(2) implies R/(4R) = ((d_2)/(d_1))^(2) implies (d_2)/(d_1) = 1/2`
`d_(1)/d_(2) = 2//1`.