Two electric appliances of power rating `W_(1) and W_(2)` at 220 V are connected in series with a source of alternating voltage `e=220sqrt(2)sin omegat`. The resultant power consumed is

Options

A. `W_(1)+W_(2)`
B. `W_(1)-W_(2)`
C. `(1)/(W_(1))+(1)/(W_(2))`
D. `(W_(1)W_(2))/(W_(1)+W_(2))`

Answer

D

Explanation

`R_(1)=(V^(2))/(W_(1)) and R_(2)=(V^(2))/(W_(2)) and R_(S)=(V^(2))/(W_(S))`
Now, `R_(S)=R_(1)+R_(2)`
`therefore (V^(2))/(W_(S))=(V^(2))/(W_(1))+(V^(2))/(W_(2))" "thereforeW_(S)=(W_(1)W_(2))/(W_(1)+W_(2))`