In the circuit given below, a 100W bulb `B_1` and two 60W bulbs `B_2` and `B_3`, are connected to a 250 V direct current source. If `W_(1), W_(2)` and `W_3` are the powers of the three bulbs then, which of the following statements is corect ?

Options

A. `W_(1) gt W_(2) gt W_(3)`
B. `W_(1) gt W_(2) gt W_(3)`
C. `W_(1) lt W_(2) = W_(3)`
D. `W_(1) lt W_(2) ltW_(3)`

Answer

D

Explanation

`P = v^(2)/R` so,`R = v^(2)/P`
`therefore R_(1) =v^(2)/100` and `R_(2) = R_(3) = v^(2)/60`
Now, `W_(1) = (250)^(2)/(R_(1) + R_(2))^(2).R_(1)`
`W_(2) = (250)^(2)/(R_(1) +R_(2))^(2).R_(2)` and `W_(3) = (250)^(2)/R_(3)`
`W_(1) : W_(2) : W_(3) = 15 : 25 : 64`
or `W_(1) lt W_(2) lt W_(3)`