Electric Current (i)

 Electric current (i):

We know that electric potential of a body is defined as the degree of electrification and it determines the direction of flow of charge. Consider two bodies 'A' and 'B' charged to potentials 'V1' and 'V2', respectively, such that V1 > V2. If they are not connected to each other [Fig. 1(i)], no charge flows and hence their potentials remain constant. If they are connected by means of good conductor R [Fig. 1(ii)], positive charge flows from higher potential to the lower potential or negative charge, i.e., electrons move from lower potential to higher potential till the potentials become equal. This is an instantaneous process. Within a fraction of a second the charge adjusts itself. There is no movement of charge after the potentials have been equalised. Now connect 'A' and 'B' to the two terminals of a source 'S' of e.m.f. having it's two terminals at potential difference 'V1 - V2' [Fig. 1(iii)]. Source 'S' helps in maintaining the difference of potentials between 'A' and 'B'. As a result of this, the charge keeps moving through the conductor R. In other words, a current 'i' keeps on flowing through the conductor.

Fig. 1. Flow of charge due to potential difference. 

 Current strength, in a conductor, is defined as the rate of flow of charge across any cross-section of the conductor. 

If a charge 'q' flows across any cross-section in 't' second, current i is given by           

                       i = q/t                 ..... (1) 

Electric current flowing through a conductor is associated with magnitude as well as direction. In spite of this, the electric current is considered to be a scalar quantity. Whenever we have to find the resultant current through a wire we have to take the algebraic sum of all the individual currents. Since the rule is valid only for scalar quantities, we take current to be a scalar quantity. 

Relation (1) holds good if the flow of charge is uniform with time. In case of non-uniform flow, let '∆q' be the small amount of charge flowing across any cross-section of the conductor in a small interval of time '∆t', then current 'i' is given by

                i = ∆q/∆t

If the time interval is choosen to be very small, i.e., ∆t →0

               i = Lt   ∆q/∆t = dq/dt                                                        ∆t→0

Electric current is time derivative of charge. 

Unit of current in S.I. is coulomb/sec or ampere. 

Type of electric currents:

1) steady current. A current is said to be steady if it's magnitude is constant and direction is always the same. Fig. 2(i) shows the current-time graph for d.c. or steady current. 

Fig. 2. Various types of electric currents. 

2) Variable current. A variable current, in general, is defined as the current which changes in magnitude with time while its direction may or may not change. Fig. 2(ii) shows a current whose magnitude changes within 1 A and 3 A, while its direction is always same (positive). Such a current is called variable direct current. Fig. 2(iii) shows a current whose magnitude changes between +1 A and -1 A, while its directions gets reversed after equal intervals of time. This current is called alternating current (a.c.). 

Conventional Current:

By convention the direction of flow of current is taken to be the direction of flow of positive charge. 

The current in that sense is called conventional current. The direction of conventional current is from A to B if positive charge flows from A to B. A negative charge moving from A to B is equivalent to a current flowing from B to A [in Fig. 3].

Fig. 3. Convention regarding direction of current. 

Units of Electric Current:

1) C.G.S. electro-static unit (e.s.u.). The current flowing through a conductor is said to be one e.s.u. if a charge of 1 e.s.u. flows across any of its cross-section in one second. 

 ∴  1 e.s.u. of current = 1 e.s.u of charge/1sec    

The e.s.u. of current is also called statampere. 

2) C.G.S. electro-magnetic unit (e.m.u). The current flowing through a conductor is said to be one e.m.u. if a charge of 1 e.m.u. flows across any of its cross-section in one second. 

∴ 1 e.s.u. of current = 1 e.m.u. of charge/1sec

The e.m.u. of current is also called abampere. 

3) S.I. unit (ampere). The current flowing through a conductor is said to be one ampere if a charge of 1 coulomb flows across any of its cross-section in one second

  ∴     1 ampere = 1 coulomb/1 second

Relation between ampere and statampere (e.s.u):

We know that, 

     1 coulomb = 3 × 10⁹ e.s.u. of charge

∴   1 ampere = 1 coulomb/1 second

                    = 3 × 10⁹ e.s.u. of charge/1 second

1A = 3 × 10⁹ e.s.u. of current or statampere

Relation between ampere and abampere:

We know that, 

      1 coulomb = 1/10 e.m.u. of charge, 

      1 ampere = 1 coulomb/1 second

1A = 1/10 e.m.u. of charge/1 second

      = 1/10 e.m.u. of current or ampere. 

Important notes:

1. A current taken to be along the direction of motion of electrons is called electronic current. 
2. A current taken to be opposite to the direction of motion of electrons is called conventional current. In physics, we often deal with conventional currents.