ELECTRIC CURRENT

When two conductors at different potential are connected by a metal wire, charges begin to flow from higher to lower potential. This flow of charge constitutes a current. Current flows as long as there is potential difference.

This current, however, is short lived. To maintain the flow of charge, some electrical energy should be included and that is supplied by cell or battery where a chemical reaction transforms the chemical energy into electrical energy.

ELECTRICAL RESISTANCE

The charge flowing through an electric circuit per second is called current. It is denoted by 'i'.

Where, Q is the total charge, n is the no. of electrons and e=1.6 x10^-19

Electric current is a scalar quantity since it does not follow the vector rule of addition or subtraction.

Current density: If a current is distributed over a surface of a conductor, it is called current density, it is denoted by j and j=i/A where A is the area of cross-section. This is a vector quantity and a unique property of a point inside surface.

FLOW OF CHARGE:

Flow of charge inside the conductors can be explained by free electron theory. Electrons bound to the nucleus do not take part in conduction; however, the ones farther apart can be easily removed by applying force. These outer electrons, then move freely inside the conductors. Electrical conductivity of any substance depends on no. of free electrons. The more it is, greater is the conductivity. Metals have large no. of free electrons present in them.

Free electrons in the metal are often considered as molecules inside of the gas that undergo random collisions. Now, when the two ends of a conductor is maintained at certain potential, an electric field is created that drives the electrons in a direction opposite to that of field. However, the velocity of electrons does not increase continuously due to collisions between them. So, when we connect a battery, the energy inside of it gives them a uniform velocity with which they move. This uniform velocity is termed as drift velocity.

RELATION BETWEEN ELECTRIC CURRENT AND DRIFT VELOCITY

Total current i=Q/t

Now, to calculate Q, we need to consider a cross section of the wire A, the electron density is n -the no. of free electrons per unit volume is. Total charge Q=neAv_d , V_d is the drift velocity. Hence in 't' seconds, Q=neAv_dt.

Current (i)=neAv_d.

Current density j= neAV_d/A, j=neV_d.

J is in a direction opposite to that of flow of electrons.

Resistance:

The ratio of the potential difference to that of the current is termed as resistance.

Conductance is just the reciprocal of resistance.

OHM'S LAW:

According to this law, if there is no change in the state of the conductor, then the ratio of the potential difference to that of current is called resistance.

RESISTANCE IN TERMS OF v_d, t and n

Current from free electron theory is:

When potential difference V is applied across its length l, then

This is ohm's law.

Specific resistance

The ratio of the intensity of electric field at any point inside the conductor and the current density (j) at that point is called specific resistance.

From the expression, it is clear that R is proportional to length of the conductor and inversely proportional to its cross section.

The ration of resistivity is conductivity.

SPECIFIC CONDUCTANCE:

The reciprocal of specific resistance is called specific conductance. It is

EFFECT OF TEMPERATURE:

When the temperature of metallic wire is raised, its electric resistance increases.

Where, a is the temperature coefficient of resistance.

LIMITATIONS OF OHM'S LAW:

Ohm's law does not hold for all electric circuits. For diode rectifiers, thermistors, transistors-ohm's law does not hold good. Hence, they are also termed as non linear circuits.