For ensuring dissipation of same energy in all three resistors `(R_(1), R_(2), R_(3))` connected as shown in figure, their values must be related s

Options

A. `R_(1) = R_(2) = R_(3)`
B. `R_(2) = R_(3)` and `R_(1) = 4R_(1)`
C. `R_(2) = R_(3)` and `R_(1) = R_(2)//4`
D. `R_(1) = R_(2)+R_(3)`

Answer

C

Explanation

`i_(1)=((R_3)/(R_(2)+R_(3)))i, i_(2) = ((R_2)/(R_(2)+R_(3)))i`
`P_(1) = P_(2)=P_(3)`
`i^(2)R_(2)=i_(2)^(2)R_(3)`
`i_(2)R_(1) = i_(1)^(2)R_(2) = i_(2)^(2)R_(3)`
`i^2R_1 = ((R_3)/(R_(2)+R_(3)))^(2) i^(2)R_(2) = ((R_3)/(R_(2)+R_(3)))^(2) R_(3)`
`R_(1) = ((R_3)/(R_(2)+R_(3)))^(2) R_(2) = ((R_3)/(R_(2)+R_(3)))^(2) R_(3)`
` ((R_3)/(R_(2)+R_(3)))^(2) R_(2) + ((R_3)/(R_(2)+R_(3)))^(2) R_(3) implies R_(3)^(2) R_(2) = R_(2)^(2)R_(3)` Mbrlt `R_(3)=R_(2)`
`R_(1) = ((R_3)/(R_(2)+R_(3)))^(2) R_(2) = ((R_3)/(R_(2)+R_(3)))^(2) R_(2) = (R_2)/(4)`.