Calculate the currents in the following circuit.

Explanation

Applying Kirchoff.s `1^(st)` Law at junction B
`I_(1)-I_(2)-I_(3)=0`
`I_(3)=I_(1)-I_(2)" "…(1)`
Applying Kirchoff.s `II^(nd)` Law at junction in ABEFA
`100I_(3)+100I_(1)=15`
`100(I_(3)+I_(1))=15`
`100I_(1)-100I_(2)+100I_(1)=15`
`200I_(1)-100I_(2)=15" "...(2)`
Applying Kirchoff.s `II^(nd)` Law at junction in BCDED
`-100I_(2)+100I_(3)=9`
`-100I_(2)+100(I_(1)-I_(2))=9`
`100I_(1)-200I_(2)=9" "...(3)`
Solving equating (2) and (3)
`{:(equ.(2)xx2,400I_(1)-cancel(200I_(2))=30),(,100I_(1)-cancel(200I_(2))=9),(,ul((-) " "(+) " "=(-))),(," "ul(300I_(1)=21)):}`
`I_(1)=0.07A`
Substitute `I_(1)` values in equ (2)
`200(0.07)-100I_(2)=15`
`14-100I_(2)=15`
`-100I_(2)=15-14`
`I_(2)=(-1)/(100)`
`I_(2)=-0.01A`
Substitute `I_(1)` and `I_(2)` value in equ (1), we get
`I_(3)=I_(1)-I_(2)=0.07-(-0.01)`
`I_(3)=0.08A`