If `R_(1)` and `R_(2)` are respectively the filament resistances of a 200 watt bulb and 100 watt bulb designed to operate on the same voltage, then

Options

A. `R_(1)` is two times `R_(2)`
B. `R_2` is two times `R_1`
C. `R_(2)` is four times `R_(1)`
D. `R_(1)` is four times `R_(2)`

Answer

B

Explanation

Since, `P = V^(2)/R`, as V = constant
`P prop 1/R, therefore P_(1)/P_(2) = R_(2)/R_(1) rArr R_(2)/R_(1) = 200/100`
`rArr R_(2) = 2R_(1)`