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

Answer

C

Explanation

Since, Voltage across `R_2` and `R_3` are same
Hence, `R_(2) = R_(3)`

`i^(2)R_(1) = i_(1)^(2)R_(2)`
`rArr i^(2)R_(1) =(R_(3)/(R_(2) + R_(3))i)^(2) R_(2)`
`rArr R_(1) = R_(2)/4`