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JEE Main and JEE Advanced Syllabus of Current Electricity

Electric current in simple words refers to the rate at which the electric charge flows in an electric field or an electric circuit.

Basic concept of current:
Electric current can also be defined as the rate of flow of charge through a particular area of cross section of a conductor. The current always flows in a direction which is from a region of higher potential to a region of lower potential. The direction of flow of electrons is opposite to direction of current because they carry negative charge and will move from a region of higher potential. Electric current is a scalar quantity. If we consider the case of water pipes, the water current flowing through the pipe can be assumed to be the electric current.
The unit of measurement of electric current is ampere (amp). If we consider the case of electric charges, then the rate at which electric charges pass through a conductor is also defined to be electric current. These charged particles may have any charge either positive or negative. Generally, some kind of force or a push is required by a charge to flow and this force is provided by either voltage or potential difference. The word ‘current’ is indeed an abbreviation for electric current. When we discuss this topic, the context of the situation is such that it automatically implies the adjective ‘electrical’.
Current in gases and liquids includes flow of positive ions in one direction and of negative ions in the direction opposite to the first direction. If there exists a current of negative charge which is moving in opposite direction, then even that is included in the total current as it is assumed to be equal to positive charge of the same magnitude moving in the usual direction.
Electric current also leads to the formation of magnetic fields similar to the case of electromagnetics. Any kind of heat loss or loss of energy that occurs in a conductor by electric current is proportional to the square of the current.

Current density, as it follows from the word itself refers to the density of the current. Mathematically, current density is the ratio of the electric current that flows in a conductor at a particular point to the cross-sectional area of the conductor. Hence, it denotes the amount of current flowing across a particular area. It is denoted by the symbol ‘J’ and its unit of measurement is amperes per square metre.

The mathematical formula for the calculation of current density is given by
J = I/A, where
‘I’ is the current in amperes that flows through the conductor.
‘A’ is the cross sectional area in m2.
Current density is a vector quantity and has the same direction as that of current. If we consider ‘I’ to denote the total electric current then the relationship between ‘I’ to the current density can be represented as
I = ∫ J. dS, where the integral runs over the area where current is flowing
This shows that the total current (I) equals the summation of current density over the area where charge is flowing.
Illustration: A copper wire of area 5 mm2 has a current of 5 mA of current flowing through it. Calculate the current density?
 Given: Total Current I = 5 mA,
           Total Area A = 5 mm2
 The Current density is given by J = IA
                                                 = 5×10−3A5×10−3m
                                                 = 1 A/m2.

Drift Velocity: It is a known fact that charged particles don’t travel in straight lines in a conductor due to the obvious reason that they often collide with other particles present in the material. Therefore, the average speed at which the particle travels along the conductor is called the drift velocity. Inn other terms, the drift velocity may be defined as the average or the mean velocity attained by a particle as a result of electric field. It can also be called as the axial drift velocity since the particles are assumed to be moving in the plane.

Drift velocity formula: The mathematical formula for calculation of drift velocity in a material exhibiting constant cross-sectional area is given by:
v = I/ nAq, where
v is the drift velocity of electrons
I is the current flowing through the conductor
n is the density of the charge-carrier
q is the charge on carrier
A is the area of the cross-section