A `100 W` bulb `B_1`, and two` 60 W` bulbs `B_2 `and `B_3` are connected to a `250 V` source as shown in the figure. Now `W_1,W_2` and `W_3` are the output powers of the bulbs `B_1, B_2` and `B_3` respectively. Then

Options

A. `W_1 gt W_2=W_3`
B. `W_1 gt W_2gtW_3`
C. `W_1 lt W_2=W_3`
D. `W_1 lt W_2ltW_3`

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`