Question

Four wires meet at a junction. in two of the wires currents i1 = 1.67 a and i2 = 2.37 a enter the junction. in one of the wires current i3 = 6.85 a leaves the junction. find the current in the fourth wire and indicate its direction.

Answer 1

Total current that enters the junction is equal to total current that leaves the junction.
$I_{in} = I_{out}$
We are given:
$I_{in1} =1.67A \\ I_{in2} =2.37A \\ I_{out} =6.85A \\ \\ I_{in}=1.67A+2.37A=4.04A$ 

We can see that current that enters the junction is smaller than current leaving the junction. So we need to deliver more current.
I = 6.85A - 4.04A = 2.81A

The current in fourt wire is 2.81A and it enters the junction.