When two resistances `R_1 and R_2` are connected in series , they consume 12 W powers . When they are connected in parallel , they consume 50 W powers . What is the ratio of the powers of `R_1 and R_2` ?

Options

A. `1//4`
B. 4
C. `3//2`
D. 3

Answer

C

Explanation

`(P_(1)P_(2))/(P_(1)+P_(2)) = 12 rArr P_(1)P_(2) = 12 xx 50, therefore P_(1) + P_(2) = 50`
`rArr (P_(1)-P_(2))^(2) + 4P_(1)P_(2) = (P_(1) + P_(2))^(2)`
`P_(1) = 30W, P_(2) = 20 W`
`P_(1)/P_(2) = 30/20 = 3/2`