Three wires are connected at a branch point. One wire carries a positive current of 18 A into the branch point, and a second wire carries a positive current of 7 A away from the branch point. Find the current carried by the third wire into the branch point.

The current in third branch is 11 A.

Explanation:

incoming current in one branch = 18 A

outgoing current in the other branch = 7 A

let the current in the third branch is i.

According to the Kirchoff's fist law in electricity

incoming current = out going current

18 = 7 + i

i = 11 A

The current in third branch is 11 A.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west