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Chapter 14
Chapter 14
–
–
Electric Current
Electric Current
14.1
14.1 Conduction of Conduction of electricityelectricity
Consider a simple closed circuit consists
Consider a simple closed circuit consists of wires, a battery and a of wires, a battery and a light bulb as shown inlight bulb as shown in Figure A Figure A..
Figure A Figure A From the Figure A,
From the Figure A,
Direction of electric field,Direction of electric field,
or current,or current,
:: PositivePositivetoto negativenegativeterminalterminal Direction of electron,Direction of electron,
flows:flows: NegativeNegativetoto positivepositiveterminalterminal TheThe electron accelerateselectron accelerates bec becausause of e of thethe electric forceelectric force acted on it.acted on it.
It is defined as theIt is defined as the total nett charge,total nett charge,
flowing through the flowing through theflowing through the flowing through the area perarea perunit time, unit time,
..
SI unit for SI unit for
1 ampere of current is defined as
1 ampere of current is defined as one coulomb of charge passing through the surface area inone coulomb of charge passing through the surface area in
one second
one second.. 14.2
14.2 Current densityCurrent density It is defined as
It is defined as the current flowing through a conductor per unit cross-sectional areathe current flowing through a conductor per unit cross-sectional area..
It is a
It is a vector quantityvector quantity Unit =
Unit =
The direction ofFrom, From,
((
))
Electrical conductivity,Electrical conductivity,
is the measure of a material’s ability to conduct electric current.is the measure of a material’s ability to conduct electric current.
SI unit for
SI unit for
isis
14.314.3 Drift velocityDrift velocity The drift velocity is the
The drift velocity is the average velocityaverage velocitythat a particle, such as an electron, attains due to anthat a particle, such as an electron, attains due to an
electric field
electric field.. When the
When the electric field is applied to the metalelectric field is applied to the metal, the, the freely moving electron experience anfreely moving electron experience an
electric force
electric force and tend toand tend to driftdrift withwith constant average velocityconstant average velocity (called drift velocity)(called drift velocity) towardstowards
a direction opposite to the direction of the field
a direction opposite to the direction of the field as shown inas shown in Figu Figure Bre B..
Figure B Figure B **1
**1 TheThe magnitudemagnitude of theof the drift velocitydrift velocity isis smallersmaller than thethan the random velocitiesrandom velocities of theof the freefree
electrons
electrons.. **2
**2 TheThe electric currentelectric current is flowing in theis flowing in the opposite directionopposite direction of theof the electron flowselectron flows..
Drift velocity of charges,
Drift velocity of charges,
LL == length of metal rodlength of metal rod AA ==crosscross-sec-sectional tional areaarea
J
J ==current densitycurrent density
ee == electronelectron
E
E == EElelectctriric filc fileedd
ê
ê Set,Set,
number of free electrons per volume in metal rod.number of free electrons per volume in metal rod.
the number of free electron,the number of free electron,
is given by:is given by:
ê
ê TheThe total chargetotal charge
of the free electrons that pasof the free electrons that pass through thes through the areaarea
along the rod isalong the rod is
ê
ê Time,Time,
required for electron move along the rod isrequired for electron move along the rod is
ê ê Then,Then,
:: number of free electron per unit volumenumber of free electron per unit volume [[DENSITY of free electronDENSITY of free electron]]
:: charge of the electroncharge of the electron14.4
14.4 Resistivity and Ohm’s lawResistivity and Ohm’s law
ê
ê Resistance, R Resistance, R Ratio of the
Ratio of the potential dipotential differencfferencee across an electrical component to theacross an electrical component to the currentcurrentpassingpassing through it.
through it.
# It is a measure of the
# It is a measure of the component’s opposition to the flow of the electric chargecomponent’s opposition to the flow of the electric charge.. # Scalar quantity with unit →
# Scalar quantity with unit →
oor r
ê
ê Resistivity,Resistivity,
The resistance of a unit
The resistance of a unit cross-sectional area per unit length of the materialcross-sectional area per unit length of the material..
# It is a measure of
# It is a measure of material’s ability to oppose the flow of an electric currentmaterial’s ability to oppose the flow of an electric current.. # Scalar quantity with unit →
# Scalar quantity with unit →
# Known as# Known as specific resistancespecific resistance
# #
Q
Q
t
t
ê
ê Conductivity,Conductivity,
TheThe reciprocal of the resistivity of reciprocal of the resistivity of a materiala material..
# Scalar quantity with unit →
# Scalar quantity with unit →
ê
ê Ohm’s LawOhm’s Law
States that the
States that the potential difference across a potential difference across a metallic conductormetallic conductor isis proportionalproportional to theto the current
current flowing through it if its temperature is flowing through it if its temperature is constant.constant.
It can be stated in other form, It can be stated in other form,
is maintainedis maintained across the conductor sets up by anacross the conductor sets up by an electric field,electric field,
and this fieldand this field produce a current,produce a current,
that isthat is proportionaproportional to l to the potential differencethe potential difference..
If the field is assumed to If the field is assumed to be uniform,be uniform,
From ohm’s
From ohm’s law,law,
… where… where
andand
(( ))
or
or
and
and
Graphs of
Graphs of potential difference,potential difference,
againstagainst current,current,
for various materials.for various materials.METAL SEMICONDUCTOR
METAL SEMICONDUCTOR
CARBON ELECTROLYTE
CARBON ELECTROLYTE
14.5
14.5 Dependence of resistivity on temperatureDependence of resistivity on temperature Metal
Metal
o
o Temperature (Temperature ( T T)) ==
,, Number of electrons per unit volume (Number of electrons per unit volume (nn))== UNCHANGEDUNCHANGED.. oo Metal atomsMetal atomsin the crystal lattice vibrate within the crystal latticevibrate withgreatergreater amplitudeamplitudeand cause theand cause the number of number of
collisions between the free electrons and metal atoms
collisions between the free electrons and metal atoms increasesincreases. Hence the. Hence the resistanceresistance in thein the metal
metal increasesincreases.. Superconductor Superconductor
o
o Temperature (Temperature ( T T)) ==
TheThe resistanceresistance decreasesdecreasesto 0.to 0.ê
ê Temperature coefficient of resistivity,Temperature coefficient of resistivity,
Fractional increase in resistivity of aFractional increase in resistivity of a conductor per unit rise in conductor per unit rise in temperattemperatureure
Since,
Since,
The resistivity of a conductor varies approximatel
The resistivity of a conductor varies approximately linearly with temperaturey linearly with temperature # Unit for # Unit for
→→
oror
Thus, Thus,
Graphs ofGraphs of resistance,resistance,
againstagainst temperature,temperature,
for various materials.for various materials.METAL SEMICONDUCTOR
METAL SEMICONDUCTOR
SUPERCONDUCTOR CARBON
Problems Problems
1.
1. Resistivity of a wire depends onResistivity of a wire depends on
2.
2. A silver wire carries a current of A silver wire carries a current of
..Determine Determine
a)
a) The numbers of electrons per second pass through the wire.The numbers of electrons per second pass through the wire. b)
b) The amount of charge flows through a cross-sectional area of the wire in 55 s.The amount of charge flows through a cross-sectional area of the wire in 55 s. (Given charge of electron,
(Given charge of electron,
9
9
))3.
3. A high voltage transmission line with a diameter of A high voltage transmission line with a diameter of
and a length of and a length of
carries acarries asteady current of
steady current of
. If the conductor is copper wire with a free charge density of . If the conductor is copper wire with a free charge density of
8
8
electronselectrons
, calculate the time taken by one electron to travel the full length of the line., calculate the time taken by one electron to travel the full length of the line. ((
9
9
))4.
4. When a potential difference of 240 V is applied across a wire that isWhen a potential difference of 240 V is applied across a wire that is
long and has along and has a
radius, the current density isradius, the current density is
99
.. CalculateCalculate a)
a) The resistivity of the wire.The resistivity of the wire. b)
b) The conductivity of the wire.The conductivity of the wire.
5.
5. A copper wire carries a current of A copper wire carries a current of
. The cross section. The cross sectionof the wire is a square of side
of the wire is a square of side
and its length isand its length is
.. The density ofthe free electron in the wire isThe density ofthe free electron in the wire is
8
8
. Determine. Determine a)a) The current densityThe current density b)
b) The drift velocity of the electronsThe drift velocity of the electrons c)
c) The electric field intensity between both end of the wireThe electric field intensity between both end of the wire d)
d) The potential difference across the wireThe potential difference across the wire e)
e) The resistance of the wireThe resistance of the wire
(Given the resistivity of copper is
(Given the resistivity of copper is
8
8
and charge of electron,and charge of electron,
9
9
A. A. LengthLength B. B. MaterialMaterial C.C. Cross-section areaCross-section area D. D. ElectronsElectrons Answers: Answers: 1. 1. BB 2 2.. aa))
