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

(c ) In the given circuit the resistor's `R_(2)` and `R_(3)` are connected in parallel hence potential difference `(V)` across them is same. In order that they undergo same energy loss,
Here `H = (V^(2))/(R ) t`
Hence `R_(2)` must be equal to `R_(3)`.
i.e., `R_(2) = R_(3)`
`H = (V^(2))/(R ) . t, R_(2) = R_(3)` `:. i^(2) R_(1) t = i_(1)^(2) R_(2) t`
Using `i_(1) = (R_(3))/(R_(2) + R_(3)) i = (R_(3))/(R_(3) + R_(3)) i = (1)/(2) i`
Thus `i^(2) = R_(1) t = (i^(2))/(4) R_(2) t` or , `R_(1) = (R_(2))/(4)`