Atomic Energy Education Society, Mumbai

Class XII Chapter-3 Module -1 CURRENT By Girish Kumar PGT (Physics) AECS Narora Current Electricity Topics Covered in Module - 1 1) 2) Conventional current 3) Electric current in conductors 4) Drift current 5) Relationship between Current and drift velocity 6) Current 7) Mobility of electric current 8) Relationship between electric current and mobility for semiconductors Electric Current: The electric current is defined as the charge flowing through any section of the conductor in one .

I = q / t (if the rate of flow of charge is steady) I = dq / dt (if the rate of flow of charge varies with time)

b a c Different types of current: I a) Steady current which does not vary with time b) & c) Varying current whose d magnitude varies with time 0 t d) Alternating current whose magnitude varies continuously and direction changes periodically + - Conventional Current: + + + + - + - Conventional current is the current whose I direction is along the direction of the of + - positive charge under the action of . - + - - - Conventional current due to motion of is in - + the direction opposite to that of motion of electrons. - I + - +

SI unit of electric Current is Ampere (A) 1A = 1 /1 second

Thus, electric current through a conductor is 1A, if one coulomb of flows through any cross-section in 1 second.

Current is a scalar quantity although it has direction associated with it. The reason because of laws of ordinary algebra are used to add electric currents in wires and laws of vector algebra are not applicable to the addition of electric currents. Electric Current in conductors:

A conductor contains a large number of loosely bound electrons which we call free electrons or conduction electrons. The remaining material is a collection of relatively heavy ions which we call lattices or fixed ions. When no electric field is applied, the electrons will be moving due to thermal motion during which they collide with fixed ions. An electrons colliding with an ions emerges with same speed as before the collision. However, the direction of it's velocity after collision is completely random. On average, the number of electrons travelling in any direction will be equal to the number of electrons travelling in opposite direction. So, there will be no net electric Current. When an electric field is applied, each electrons experiences an acceleration of (eE/m) opposite to field direction but the acceleration is momentary because electrons losses the gained velocity due to collisions with vibrating or ions or other free electrons. The average velocity of the electrons gained against electric field is then called drift velocity. Drift Velocity and Current: Drift velocity is defined as the velocity with which the free electrons get drifted towards the positive terminal under the effect of the applied electric field. vd - drift velocity, a – acceleration, Ꚍ – relaxation time, E – electric field, e – electronic charge, m – of , n – of electrons, l – of the conductor and A – Area of cross section The electrons travel in a straight line between successive collisions. An average time between two successive collisions is called relaxation time(Ꚍ) and it is covered with a drift velocity(vd ). Force on each each electron in the presence of electric field, E F = -eE Thus , acceleration of the electrons a = -eE/m Average velocity (drift velocity) in terms of relaxation time v = u+at v = 0+(-eE/m)Ꚍ Hence, drift velocity in time, Ꚍ vd = - (eE / m) Ꚍ If V is potential along l (length of conductor), the electric field, E = V/l So, vd = - (eV / ml) Ꚍ Relationship between Current and Drift Velocity

Let total number of free electrons in a conductor of length l, cross-section area A, having n free electrons per unit is N = n x volume of conductor N = n x Al Time t in which an electron moves from one end to another, all N free electrons pass through cross-section

T = l/vd

Electric Current through conductor is given by I = q/t I = Ne/t

I = (nAle) / l/vd

I = nAevd

Current is directly proportional to drift velocity. : Current density at a point, within a conductor, is the current through a unit area of the conductor, around that point, provided the area is perpendicular to the direction of flow of current at that point.

J = I / A = nevd

In vector form, I = J . A

I = JAcosθ

J = ne {(eE/m)Ꚍ} J = ( ne2 E /m) Ꚍ J = σ E where σ is conductivity of medium

σ = (ne2 /m)/Ꚍ Mobility of Electric charge:

Mobility of charge carriers is defined as magnitude of drift velocity per unit electric field. µ = | vd |/E

In semiconductor, the charge carriers are holes and electrons.

Mobility of electrons, µe = eEꚌe/meE = eꚌe/me Mobility of holes, µh = eꚌh/mh SI unit of mobility is m2 /Vs

Relationship between electric current and mobility for a conductor

I = neAvd Vd = µeE I = neAµeE Relationship between Electric current and mobility for a semiconductor

Total current, I = Ie + Ih

I = neAµeE + peAµhE

I = eAE(µeE + pµh) where n = no. of electrons p = no of holes Conductivity of a Semiconductor According to Ohm’s law, I = V/R = El/ ρl/A I = EA/ρ

EA/ρ = eAE(µeE + pµh)

1/ ρ = e(µeE + pµh)

Conductivity, σ= 1/ ρ = e(µeE + pµh)