For mixed connection shown in figure derive equation of equivalent resistance.

Explanation

`rArr` As shown in figure `R_(2) and R_(3)` are connected in parallel with B and C and with this `R_(1)` is connected between A and B.

where R. = equivalent resistance of `R_(2) and R_(3)` connected in parallel.
`therefore (1)/(R.) = (1)/(R_(2)) + (1)/(R_(3)) `
`R. = (R_(2) R_(3))/(R_(2) + R_(3)) " "` ... (1)
`rArr` Equivalent resistance of all three resistors,
`R_(eq) = R_(1) + R.`
`= R_(1) + (R_(2) R_(3))/(R_(1) + R_(3)) " " ` ... (2)
`rArr` Let voltage between A and C be v, then current through `R_(1)`,
`I = (V)/(R_(eq)) = (V)/(R_(I) + (R_(2) R_(3))/(R_(2) + R_(3))) `
`therefore I = (V(R_(2) + R_(3)))/(R_(1) R_(2) + R_(1) R_(3) + R_(2)R_(3))`