When electric bulbs of same power, but different marked voltage are connected in series across the power line, their brightness will be :

Options

A. directly proportional to their marked voltages directly proportional to the squares of their marked voltages
B. inversely proportional to the squares of their marked voltages
C. directly proportional to the squares of their marked voltages
D. inversely proportional to the squares of their marked voltages.

Explanation

For a bulb, power `(P)=(V^(2))/(R)`
`therefore P=(V_(1)^(2))/(R_(1))=(V_(2)^(2))/(R_(2))`
`therefore R_(1)=(V_(1)^(2))/(P)` and `R_(2)=(V_(2)^(2))/(P)`
The seres current through each is same. Heat `prop I^(2) Rt`.
or `(H_(1))/(H_(2))=(R_(1))/(R_(2))` or `(H_(1))/(H_(2))=(V_(1)^(2))/(V_(2)^(2))`
or `H propV^(2)`
or Brightness `porp("voltage")^(2)`.