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CURRENT ELECTRICITY
Electric Current : The time rate of flow of
change through any cross section is called current
-
.




9T is denoted i. current is a scalar quantity unit is ampere (A)
by .
gt's so I •




"°
I =
% where q is net amount of change passing through any cross-sectional
area .
and q =
q, -

q if flow is uniform .




t -
,



also i =
Lim AI if flow is non -
uniform . or i =
DI
Dt→o ☐t dt

Note: → if the moving charges are + ve
,
the current is in the direction of motion .




if the moving charges are -
ve , the current is opposite to the direction of motion .




CURRENT CARRIERS
• Solid : In solid conductors like metals current carriers are free electrons .




•
Liquids : In liquids current carriers are positive and negative ions .




• Gases : In gases current carriers are positive ions and free electrons .



• Semiconductor : In semiconductors current carriers are holes and free electrons .




OHM 'S LAH
The current flowing through
µgµJ
the conductor is directly
portion potential it's two ends i
µ
→
al to the difference across
pyoit the physical
.




, condition of Conductor ( length , temperature , mechanical
strain) remain same .
v -



i. e v. ✗ i or 11 =
iR Toten Hal difference
where R is constant of proportionality called as Resistance of the conductor .



S1 unit of Resistance is 0hm ( R ) .



ya
13=1
i. Resistance =
slope of v -
i graph .
Slope of the line

Note: → The devices or substances which don't obey tano =
Y =
R
Ohm's law e. g gases , crystal rectifiers , thermionic i
'




valve , transistors etc are called non ohmic or non -
-
go > i
linear conductor .
and which obey 0hm's law called as

Ohmic conductor .


eiq All metals .




RESISTANCE
• The property of substance by virtue of which it opposes the flow of current through
a
it is known as the resistance The resistance of a conductor is directly proportional .

,
to the
length of the conductor and inversely proportional to the cross-sectional area of
conductor .
R ✗ l -

d)
✗ I -
(2) .




A.
f- Proportionality
134¥ R =P
,§ constant called as

NOTE :→P depend upon the material of Resistivity of conductor .




Conductor .




Question : → show that one ampere is equivalent to a flow of 6.25×1010
elementary charges per second .




Solution : → Given i= 1A 1.6×10-19 c i I
t= Is
neg
,
e= = =



Number of t
ite
electrons n=
6.25 101°
y.iq#a--
= ✗ Answer
:

, Thermal velocity : Free electrons in a metal move randomly with a very high speed
.




of the order of 105m Is ( when no external electric field is applied) This speed is called
.
•




thermal velocity
of free electrons As there is a large number of free electrons moving in random.




directions , the number of electrons crossing an area IS from one side very nearly equals the number crossing
from the other side in
any given time interval
.




i. e
average thermal velocity Ñaug= 0



Drift velocity
when a potential difference is applied across the ends of a conductor ,
the free electrons
in it move with an average velocity opposite to the direction of electric field , which is
called drift
velocity of free electrons . ← f- length of conductor →

Drift velocity
+ -
is
very small , it is of the 4
A
Order of 10 m/s .




For a conductor n= no .
of é per unit volume of the
Conductor .




A =
Area of cross -
section V -
-
Potential diff .
across

E- Electric field inside conductor conductor .
Potential
Fig p .

.


The
magnitude of electric field setup is E =


T
V

• if is the mass of an electron , the
m

acceleration of each electron is a= -
eÉ [ -


ve shows that the direction of force
_m
The
average drift velocity is given by is opposite to that of electric field applied ) .




E- tea, + at
Here
Ñag=O Fig .
shows movement


$0 I = It Ñd= -
CÉI of electron from to A to B
'



Tm on application of electric
f- I ( Average relaxation time .


field .




In
magnitude Vd =
eE_
M
I And movement from A to B

without electric field .




Relation between current & Drift velocity
we know that
i =
9- & 9 =
Nite
t q from
nlae fig P
=
.




and
i i 1.6×10"C
half
1- =L Now ✗ Vd An eye e- number density
= =
n= .




µ,


•
Deduction of OHM 'S Law from idea of Drift velocity .




know that I ① Put value of Vd in eg ①
eImT
we = An eye -

and Vd =
we


get i=AnÉ-EF and E= 11
T
from fig P.




so
i=AnÉmY- .
.
>
,f
Constant


Cwstant) MI
R=¥×¥?ne÷!
iml_ nd i. e R=
¥
✗ =
or
= =
R
Anette Andi Anett

f- m_ ,
called as
Resistivity
net and depend upon material of conductor .