chapter 24: electric current
DESCRIPTION
Chapter 24: Electric Current. Definition of current. A current is any motion of charge from one region to another. Suppose a group of charges move perpendicular to surface of area A. The current is the rate that charge flows through this area:. Current. Units: 1 A = 1 ampere = 1 C/s. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 24: Electric Current
Current Definition of current
A current is any motion of charge from one region to another.
• Suppose a group of charges move perpendicular to surface of area A.
• The current is the rate that charge flows through this area:
dt
dQdt
dQI
interval time theduring
flows that charge ofamount ;
Units: 1 A = 1 ampere = 1 C/s
Current Microscopic view of current
Current Microscopic view of current (cont’d)
Current Microscopic view of current (cont’d)
• In time t the electrons move a distance tx d • There are n particles per unit volume that carry charge q
• The amount of charge that passes the area A in time t is
)( tnAqQ d • The current I is defined by:
Anqt
Q
dt
dQI d
t
0
lim
• The current density J is defined by:
dnqA
IJ Current per unit area
Units: A/m2
dnqJ
Vector current density
Resistivity
Ohm’s law• The current density J in a conductor depends on the electric field E and on the properties of the material.• This dependence is in general complex but for some material, especially metals, J is proportional to E.
E
J Ohm’s law
mm/AV)(V/m)/(A/m Units,y resistivit : 2
V/A ohm
vity1/resisitityconductivi
Substance Substancem) m)
silver
copper
goldsteel
81047.1 81072.1 81044.2
81020
graphite
siliconglass
teflon
5105.3
1410 1010 1310
2300
EJ
Resistivity
Conductors, semiconductors and insulators• Good electrical conductors such as metals are in general good heat conductors as well.
• Poor electrical conductors such as plastic materials are in general poor thermal conductors as well.
In a metal the free electrons that carry charge in electrical conduction alsoprovide the principal mechanism for heat conduction.
• Semiconductors have resistivity intermediate between those of metals and those of insulators.
• A material that obeys Ohm’s law reasonably well is called an ohmic conductor or a linear conductor.
Resistivity
Resistivity and temperature• The resistivity of a metallic conductor nearly always increases with increasing temperature.
)](1[)( 00 TTT reference temp. (often 0 oC)
temperature coefficient of resistivity
Material oC)-1
aluminum
brass
graphitecopper
0039.0
0020.00005.000393.0
iron
leadmanganin
silver
0050.0
00000.0
0038.0
0043.0
Material oC)-1
Resistivity
Resistivity vs. temperature• The resistivity of graphite decreases with the temperature, since at higher temperature more electrons become loose out of the atoms and more mobile.
• This behavior of graphite above is also true for semiconductors.
• Some materials, including several metallic alloys and oxides, has a property called superconductivity. Superconductivity is a phenomenon where the resistivity at first decreases smoothly as the temperature decreases, and then at a certain critical temperature Tc the resistivity suddenly drops to zero.
T
T
TTc
metal semiconductor superconductor
Resistance Resistance
• For a conductor with resistivity , the current density J at a point where the electric field is E : JE
• When Ohm’s law is obeyed, is constant and independent of the magnitude of the electric field.
• Consider a wire with uniform cross-sectional area A and length L, and let V be the potential difference between the higher-potential and lower-potential ends of the conductor so that V is positive.
E
JI
AL
ELVJAI ,
JE
IA
LV
A
I
L
VE
I
VR
resistance1 V/A=1
• As the current flows through the potential difference, electric potential is lost; this energy is transferred to the ions of the conducting material during collisions.
Resistance
Resistance (cont’d)• As the resistivity of a material varies with temperature, the resistance of a specific conductor also varies with temperature. For temperature ranges that are not too great, this variation is approximately a linear relation:
)](1[)( 00 TTRTR • A circuit device made to have a specific value of resistance is called a resistor.
V
V
resistor that obeysOhm’s law
semiconductordiode
Resistance
Example: Calculating resistance
b
a
• Consider a hollow cylinder of length L and inner and outer radii a and b, made of a material with . The potential difference between the inner and outer surface is set up so that current flows radially through cylinder.
r
A flowscurrent which thefrom circle
dashed aby drepresentecylinder a of area : 2 rLA
• Now imagine a cylindrical shell of radius r, length L, and thickness dr.
shell thisof resistance : 2 rL
drdR
b
a a
b
Lr
dr
LdRR ln
22
Electromotive Force (emf) and Circuit
Complete circuit and steady current• For a conductor to have a steady current, it must be part of a path that forms a closed loop or complete circuit.
1E
JI
1E
JI
1E
JI
---
--
--
-
+
+
+ +
+
+
++
2E
2E
current causesconductor inside
produced field Electric 1E
current reducing
and field opposing
producing ends,at up build
tocharge causesCurrent
2E
.completely stopscurrent
and 0 field total
: as magnitude same the
has short time very aAfter
1
2
totalE
E
E
Electromotive Force (emf) and Circuit
Maintaining a steady current and electromotive force• When a charge q goes around a complete circuit and returns to its starting point, the potential energy must be the same as at the beginning.• But the charge loses part of its potential energy due to resistance in a conductor.
• There needs to be something in the circuit that increases the potential energy.
• This something to increase the potential energy is called electromotive force (emf).
• Emf makes current flow from lower to higher potential. A device that produces emf is called a source of emf.
Units: 1 V = 1 J/C
+-
current flow
EeF
nF
E
E
source of emf
ab
If a positive charge q is moved from b to a inside the source, the non-electrostatic force Fn does a positive amount of work Wn=qVab on the charge.This replacement is opposite to the electrostatic force Fe, so the potential energy associated with the charge increases by qVab. For an ideal source of emf Fe=Fn
in magnitude but opposite in direction.Wn=qqVab , so Vab= =IR for an ideal source.
Electromotive Force (emf) and Circuit
Internal resistance• Real sources in a circuit do not behave ideally; the potential difference across a real source in a circuit is not equal to the emf.
Vab= – Ir (terminal voltage, source with internal resistance r)
• So it is only true that Vab=E only when I=0. Furthermore,
–Ir = IR or I = / (R + r)
Electromotive Force (emf) and Circuit
Real battery
br
+
I
a
dR
c
−
Battery
outV I rI I
R R R r
• Real battery has internal resistance, r.
• Terminal voltage, ΔVoutput = (Va −Vb) = − I r.
•
a b
c d
Electromotive Force (emf) and Circuit
Potential in an ideal resistor circuit
ba
b
c d
dab c
Electromotive Force (emf) and Circuit
Potential in a resistor circuit in realistic situation
b
r
+
I
ad
R
c
-
Battery
V
ab
c d
r
+
-
R
I r
IR
0
a b
ba
Energy and Power in Electric Circuit
Electric power
Electrical circuit elements convert electrical energy into1) heat energy( as in a resistor) or 2) light (as in a light emitting diode) or3) work (as in an electric motor). It is useful to know the electrical power being supplied. Consider the following simple circuit.
dUe is electrical potential energy lost as dQ traverses the resistor and falls in V by ΔV.
Electric power = rate of supply from Ue.
abe dQVVdQdU
abV
abV(watts) W 1 J/s 1 C/s) J/C)(1 (1 :Units
power Electric2
2
R
VRIIVV
dt
dQP ab
abab
R
Energy and Power in Electric Circuit
Power output of a source• Consider a source of emf with the internal resistance r, connected by ideal conductors to an external circuit.• The rate of the energy delivered to the external circuit is given by:
IVP ab• For a source described by an emf and an internal resistance r
IrVab
rIIIVP ab2
+
a + b -
-
II
battery
(source)
headlight(external circuit)
rate of conversion ofnonelectrical energyto electrical energy inthe source
rate of electricalenergy dissipationin the internalresistance of thesource
net electricalpower outputof the source
Energy and Power in Electric Circuit
Power input of a source• Consider a source of emf with the internal resistance r, connected by ideal conductors to an external circuit.
alternatorlarge emf
+
a + b -
-
II
battery
small emf
+v
Fn
rIIIVPIrV abab2
rate of conversion ofelectrical energy intononeletrical energy inthe battery
rate of dissipationof energy in theinternal resistancein the battery
total electrical power inputto the battery
Electromotive Force (emf) and Circuit Examples:
V
A
voltmeteram
met
erabcd VV
4V,12,2 Rr
V. 8 ) A)(2 (2 - V 12
V. 8) A)(4 2(
.
A. 2 2 4
V 12
IrV
IRV
VVrR
I
ab
cd
cdab
W.16) 4(A) 2(by given also isIt
W.16A) V)(2 (8by given also isoutput power The
W.16 isoutput power electrical The
W.8) 2(A) 2( isbattery in theenergy ofn dissipatio of rate The
W.24A) V)(2 (12 isbattery in the conversionenergy of rate The
22
2
22
IR
IV
rII
Ir
I
bc
ba
A V: measures pot- ential difference
: measures current through it
Electric Conduction
Drude’s model
Electric Conduction
Drude’s model (cont’d)
Electric Conduction
Drude’s model (cont’d)
80 3 2
20 m(11 10 m) 11
[0.5(0.5 10 m)]
lR
A
Calculate the resistance of a coil of platinum wire with diameter 0.5 mm and length 20 m at 20 C given =11×10−8 m. Also determine the
resistance at 1000 C, given that for platinum =3.93×10−3 /°C.
To find the resistance at 1000 C: 0 01 T T
lR
A 0 01R R T T But so we have :
Where we have assumed l and A are independent of temperature - could cause an error of about 1% in the resistance change.
3 1(1000 C) (11 )[1 (3.93 10 C )(1000 C 20 C)] = 53R
Exercise 1
The hair dryer is taken to the UK where it is turned on with a 240 V source. What happens?
1000 W8.33A
120V
PI
V
120V14.4
8.33A
VV IR R
I
A 1000 W hair dryer manufactured in the USA operates on a 120 V source. Determine the resistance of the hair dryer, and the current it draws.
2 2( ) (240V)4000 W
14.4
VP
R
This is four times the hair dryer’s power rating – BANG and SMOKE!
Exercise 2