Three resistors having resistances `r_(1), r_(2)` and `r_(3)` are connected as shown in the given circuit. The ratio `i_(3)/i_(1)` of currents in terms of resistances used in the circuit is-

Options

A. `r_(2)/(r_(2) + r_(3))`
B. `r_(1)/(r_(1) + r_(2))`
C. `r_(2)/(r_(1) + r_(2))`
D. `r_(1)/(r_(2) + r_(3))`

Answer

A

Explanation

V= ir
`i=V/r rArr I prop 1/r` [V is same for `r_(2)` & `r_(3)`]
`i_(2)/i_(3) = r_(3)/r_(2)`
`i_(3) = r_(2)/(r_(2)+ r_(3)) i_(1)`

`i_(3)/i_(1) = r_(2)/(r_(2) + r_(3))`