Two bulbs consume same energy when operated at `200 V and 300 V` , respectively . When these bulbs are connected in series across a dc source of `500 V`, then

Options

A. Ratio of potential difference across then is `3//2`
B. Ratio of potential difference across then is `4//9`
C. Ratio of power connected across then is `4//9`
D. Ratio of power connected across then is `2//3`

Answer

b,c

Explanation

Here `V_(1) = 200 V,V_(2) = 300V`
As `P = (V^(2))/(R)` so `R = (V^(2))/(P)`
For same power `'P',R prop V^(2)` ?
So `(R_(1))/(R_(2)) = ((V_(1))/(V_(2)))^(2) = ((200)/(300))^(2) = (4)/(9)`
For series current is same `P = I^(2)R`, so `P prop R` and `V = IR` so `V prop R`
`(V_(1))/(V_(2)) = (R_(1))/(R_(2)) = (4)/(9) and (P_(1))/(P_(2))=(R_(1))/(R_(2)) = (4)/(9)`