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

Answer

C

Explanation

(c ) If `R_(2) = R_(3)` and `R_(2) = 4R_(1)`, then
Now, `P_(R_(1)) = ((V//3)^(2))/(R_(1)) = (V^(2))/(9 R_(1))`
`P_(R_(2)) = ((2 V//3)^(2))/(4 R_(1)) = (V^(2))/(9R_(1))` and `P_(R_(3)) = ((2 V//3)^(2))/(4 R_(1)) = (V^(2))/(9 R_(1))`