Question

Even though electric current has direction why it is not a vector

Answer 1

A Vector quantity is that quantity, which has magnitude and direction, both ; and which also follow the rules of Vector Addition.

Electric Current has magnitude and direction, both. But it does not follow the rules of Vector Addition. When we add two or more Electric Current quantities , we use rule of scalar addition. In the other words we use algebraic method.

Thus, Electric Current is not a Vector.

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Answer 2

There are two quantities that we often loosely refer to as current. The first is the current density J, which is the sum over all charge carriers of the product of the charge and velocity divided by the volume.
J = n<qv>
I’m using Bold type to indicate vectors, and <> to denote an average. n is the number of charge carriers per volume, q is the charge per charge carrier, and v is the velocity of the charge carrier. Since the velocity is a vector quantity, J is definitely a vector.The second quantity is the current I, which is the flux of charge per time through a surface. (flux = flow through) To fully define the flux I have to specify the direction normal to the surface,as for any surface there are two directions that are perpendicular(i.e.normal) to the surface. Formally, the current is then
I = |J| A cos (theta)where theta is the angle between J and the direction normal to the surface and A is the area of the surface. The | | here indicate the magnitude of the vector inside.(I’ve assumed the current is uniform across the surface here to keep things simple.Since I only depends on scalar quantities, current is a scalar , and technically it has no direction. Informally, though, we often refer to the “direction of the current” when we really mean the direction of the current density.