A 100 W bulb `B_1`, and two 60 W bulb `B_2` and `B_3`, are connected to a 250 V source, as shown in 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_1gtW_2 = W_3`
B. `W_1gtW_2gtW_3`
C. `W_1ltW_2 = W_3`
D. `W_1ltW_2ltW_3`

Answer

D

Explanation

(d) KEY CONCEPT : `R = V^2/P`
`:. R_1 = V^2/100 , R_2 = V^2/60 = R_3,`

`W_1 = (V_(1)^2)/(R_1) = (v^2R_1)/(R_1 + R_2)^2 , W_2 = (V_(2)^2)/R^2 = (V^2R_2)/(R_1 + R_2)^2` .
and `W_3 = V^2/R_3`
`W_3 : W_2: W_1 = (250)^2/R_3 : ((250)^2R_2)/(R_1+R_2)^2 R_2 : (250)^2 / (R_1 + R_2)^2 R_1`
or `W_3 : W_2 : W_1. `
`=(250)^2/V^2 xx 60 : (250)^2/([1/100 + 1/60]^2 V^4) xx v^2/60 : ((250)^2V^2)/([1/100 + 1/60]^2 V^4 xx 100)`
or `W_3 : W_2 : W_1,`
`= 60 : (100 xx 100 xx 60 xx 60)/(160 xx 160 xx 60) : (100 xx 100 xx 60 xx 60)/(160 xx 160 xx 100)`
`=64:25:15` .