why we do not apply the triangle law of vector addition while adding electric current ?
Answers
Explanation:
Electric Current - A Scalar Quantity
The simple answer is No, Electric Current does not follow the Triangular Law.
Vector quantities are those which have a magnitude as well as direction. They also have some properties. Vectors follow the Triangular Law of Vector Addition.
Triangular Law
In the triangular law, we have two vectors pointing in any arbitrary direction. Let's call these vectors as and . [Vectors are denoted with an arrow over the letter]
Vectors can be dragged and relocated anywhere, as long as their length and sense of direction is maintained.
The direction where the vector points is its head. The other end of the vector is the tail.
Place such that its tail coincides with the head of . Now, the resultant (i.e. the sum) of vectors and , say , can be obtained by joining the tail of and head of
This is a geometrical interpretation. We can form a triangle this way to find the sum of any two vectors pointing in any arbitrary directions. The vector represents the magnitude and direction of the vector that you get on adding and
Why Electric Current is not a Vector
Electric Current has a magnitude (represented in amperes) and also a direction.
Conventionally, the direction of electric current is the direction of flow of positive charges. Or, in other words, it is the directions against the flow of negative charges (electrons).
However, this is a restricted directionality. It is restricted to flow in a wire, only along the wire.
Suppose we have a piece of wire going east, which then turns and goes towards north. In both parts of the wire, the current is the same. Say, it is 2 A. Both current directions are the same and there is no meaning to the term "adding the currents", because you are referring to the same current flowing in the same wire.
What is the sum of currents in the two pieces of wires? We have 2 A current eastward, and then the same wire carrying 2 A current northward.
There is no sum. Because it's the same current.
Even if there were two different pieces of wires, say one piece carrying 2 A current eastward and one piece carrying 3 A current northward, there would be no sense of "summation". They are different entities. Try to think how would you add them. Does it make sense? No, right?
This is not the case of vectors. The summation of two vector quantities oriented this way would be a vector pointing North-East. However, in case of electric current, the current is just moving northward now. No summation like the Triangular Law.
The Triangular Law doesn't hold good for Electric Current.
Actual vectors have free directionality. Based on their direction, their summation can give different results.
In 2D space, they can have any of the direction around the circle.
For electric current, the directionality is only that along the wire (opposite to flow of electrons).
In Summary, since the electric current doesn't follow the Triangular Law, it is not a vector. It is just a scalar quantity.
[Another such quantity is Time. Time always seems to move towards the future. We call this the Arrow of Time. There have been intense discussions on the direction of this arrow of time. Time remains a scalar as of now.]