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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

The correct Answer is:
D
Resistance of` I^(st)` bulb = `R_(1)=(V^(2)/(P_(1)`
Resistance of `11^(nt)` bulb =` R_(2) = (V^(2))/(P^(2))`
When both bulbs 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, powerconsumed`P=(V^(2))/(R)=(V^(2))/(V^(2))(P_(1)+P_(2))/(P_(1)P_(2))=(P_(1)P_(2))/(p_(1)+p_(2))`
Hence, (C) is correct
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