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)/( R_2) =(V^(2) // P_1)/( V^(2) // P_(2))= (P_2)/( P_1)`
`(rho l // pi (d_(1)// 2)^(2) )/( rho l// pi (d_(2) // 2)^(2) ) =(d_(2)^(2))/( d_(1)^(2))= (100 W)/( 25 W) rArr (d_2)/( d_1) = (10)/(5) = (2)/(1)`