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Two electric bulbs rated P(1) and P(2) w...

Two electric bulbs rated `P_(1)` and `P_(2)` watt at V volt are connected in series across V volt mains then thier total power consumption P is

A

`(P_(1)+P_(2))`

B

`sqrt(P_(1)P_(2))`

C

`P_(1)P_(2)//(P_(1)+P_(2))`

D

`(P_(1)+P_(2))//P_(1)P_(2)`

Text Solution

Verified by Experts

Resistance of `I^(st)=` bulb `R_(1)=(V^(2))/(P_(1))`
Resistance of `II^(nd)` bulb `R_(2)=(V^(2))/(P_(2))`
When both bulb are connected in series
`R_(eq)=V^(2)[(1)/(P_(1))+(1)/(P_(2))]=(V^(2)(P_(1)+P_(2)))/(P_(1)P_(2))`
Hence power consumed `P=(V^(2))/(R )=(V^(2))/(V^(2)((P_(1)+P_(2))/(P_(1)P_(2))))=(P_(1)P_(2))/(P_(1)+P_(2))`
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