Two electic bulbs rated `P_(1)` watt `V` volts and `P_(2)` watt `V` volts are connected in parallel and `V` volts are applied to it. The total power will be

Options

A. `P_(1)+P_(2)` watt
B. `sqrt(P_(1)P_(2))` watt
C. `(P_(1)P_(2))/(P_(1)+P_(2))` watt
D. `(P_(1)+P_(2))/(P_(1)P_(2))` watt

Answer

A

Explanation

`P_(1)=(V^(2))/(R_(1)):P_(2)=(V^(2))/(R_(2))`
after connecting in parallel
`R_("eff") =(R_(1)R_(2))/(R_(1)+R_(2))`
`therefore P_("total") =(V^(2))/(R_("eff"))=(V^(2)(R_(1)+R_(2)))/((R_(1)R_(2)))`
`(V^(2)R_(1))/(R_(1)R_(2)) +(V^(2)R_(2))/(R_(2)R_(2)) =(V^(2))/(R_(2))+(V^(2))/(R_(2))+(V^(2))/(R_(1))`
`therefore P_("total")=P_(1)+P_(2)`