Two resistance `R_(1)` and `R_(2)` when connected in series and parallel with `120 V` line, power consumed will be `25 W` and `100 W` respectively. . Then the ratio of power consumed by `R_(1)` to that consmed by `R_(2)` will be

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `1:4`

Answer

A

Explanation

(a) `P = (V^(2))/(R ) = (P_(P))/(P_(S)) = (R_(S))/(R_(P)) = ((R_(1) + R_(2)))/(R_(1) R_(2) // (R_(1) + R_(2))) = ((R_(1) + R_(2))^(2))/(R_(1) R_(2))`
`implies (100)/(25) = ((R_(1) + R_(2))^(2))/(R_(1) R_(2)) implies (R_(1))/(R_(2)) = (1)/(1)`