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When electric bulbs of same power, but d...

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

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.

Text Solution

Verified by Experts

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)`.
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