A constant voltage `V = 25 V` is maintained between points `A` and `B` of the circuit (Fig). Find the magnitude and direaction of the current flowing through the segment `CD` if the resistances are equal to `R_(1) = 1.0 Omega, R_(2) = 2.0 Omega, R_(3) = 3.0 Omega` adn `R_(4) = 4.0 Omega`.

Explanation

Current is as shown in From Kirchholff's Secound law ,brgt `i_(1) R_(1) = i_(2) R_(3)`,
`i_(1) R_(1) + (i_(1) + i_(3)) R_(2) = V`,
`i_(2) R_(3) + (i_(3) + i_(2)) R_(4) = V`
Eliminating `i_(2)`
`i_(2) (R_(1) + R_(2))- i_(3) R_(2) = V`
`i_(1) (R_(1))/(R_(3)) (R_(3) + R_(4)) + i_(3) R_(4) = V`
Hence `i_(3) [R_(4) (R_(1) + R_(2)) + (R_(1) R_(2))/(R_(3)) (R_(3) + R_(4))]`
`= V [(R_(1) + R_(2)) - (R_(1))/(R_(3)) (R_(3) + R_(4))]`
or, `i_(3) = (R_(3) (R_(1) + R_(2)) - R_(1) (R_(3) + R_(4)))/(R_(3) R_(4) (R_(1) + R_(2)) + R_(1) R_(2) (R_(3) + R_(4)))`
Onsituustion we get `i_(3) = 1.0 A` from `C` to `D`