13
Physics http://www.sigmaprc.in Current electricity Current electricity
Physics http://www.sigmaprc.in
Current electricity
Current electricity
Physics http://www.sigmaprc.in
Current electricity
Electric current
Drift speed
Mobility
Current density
relations
Resistance
Parameters
Physics http://www.sigmaprc.in
Current electricity
Electric current
It is the rate of flow of charge.
Average current is given by
Instantaneous value of current is given by
SI unit of current is ampere ( A )
Current in an electric circuit is indicated by arrows on the connecting wires of the circuit
QI
t
0
dlim i.e.
dt
Q QI I
t t
Physics http://www.sigmaprc.in
Current electricity
Resistance
It is the opposition to the flow of free charges in a material
It arises due to continuous and numerous collisions that the free charges undergo with other charges ( both mobile and fixed ) during their motion
Resistance depends on
(a) nature of material
(b) dimensions of the body such as length and area of cross-section
(c) temperature of the body
SI unit of resistance is ohm ( W )
In an electric circuit resistor is denoted by the symbol
A variable resistor is denoted by an arrow across the resistor
Physics http://www.sigmaprc.in
Current electricity
Ohm’s law
V I
Ohm’s law : 1828Electron discovery : 1897Almost 70 years later !!!
At constant temperature, potential difference acrossthe ends of a conductor is directly proportional to thecurrent through it.
V = R I
Ohm’s law is an empirical law
Ohm’s law is not obeyed by all materials
Materials that obey Ohm’s law are called ohmicconductors
Materials that do not obey Ohm’s law are callednon-ohmic conductors
Physics http://www.sigmaprc.in
Current electricity
Ohm’s lawV-I graph of ohmic conductors is a straight line
Physics http://www.sigmaprc.in
Current electricity
Drift speed ( vd ) It is the average speed of charge carriers ( such as electrons ) under the influence ofelectric field and continuous collisions that they undergo in the conductor.
In a conductor, on an average, each atom contributes one free electron ( which isfree to move in the conductor ). Movement of these free electrons leads to electriccurrent.
Force on the charge ( e ) due toelectric field of intensity E is
From Newton’s law we get
F = eE
F = ma
eEa =
mUsing the relation v = u + at for theaverage of the motion of electrons weget
v = + a td 0Average time interval between twosuccessive collisions that the freecharges undergo is called relaxationtime. Denoting that as t we get
eEv =
mtd
i
ii
iii
iv
More motivation – more velocity
Physics http://www.sigmaprc.in
Current electricity
Mobility ( m )
It is the drift speed per unit electric field intensity
Drift speed of a particle is given by the relation
Mobility is therefore given by
eEv =
mtd
Mobility is determined by the nature of the free charge ( i.e. its mass m andcharge e ) and the nature of material and temperature ( that determines t )
e=
mm t
SI unit of mobility is C s kg-1
Physics http://www.sigmaprc.in
Current electricity
Current density ( j )
It is the current through a unit area ( considered normal to the current )
In terms of current density , electric current is given by
Ij =
A
I = j • A
SI unit of current density is Am-2
Physics http://www.sigmaprc.in
Current electricity
Relation between I and vd
Consider a conductor of area of crosssection A carrying constant current I in it.
Let Q be the total charge crossing apoint in the conductor in a interval oftime t.
QI =
t
N eI =
t
n eI =
t
vol
n A v t eI =
t
d
I = n A e vd
Considering average distance coveredthe charges, due to their drift speed, ina interval of time t we get
Let n be the free charge density ( i.e.number of free charges per unitvolume ).
Physics http://www.sigmaprc.in
Current electricity
Relation between I and V
I = n A v ed
Current in a conductor is given bythe relation
Using the relation of vd we get
eEI = n A e
mt
Using the relation between electricpotential difference and field
e VI = n A e
m lt
e n AI = V
ml
t
2
V = R I
mlV = I
e n At
2
m lR =
e n At2
lR =
A
Separating the terms that do notdepend on dimensions of the body weget
Resistance is directly proportional tolength
Resistance is inversely proportionalto area of cross-section
Physics http://www.sigmaprc.in
Current electricity
Temperature dependence of resistance
o ( 1 )R = R T
Resistance of a body changes withtemperature as
is called temperature coefficient of resistance
Physics http://www.sigmaprc.in
Current electricity
Colour code of resistors
