Batteries, conductors and resistors
Lecture 3
1
How do we generate electric fields –
where does the energy come from?
The e.m.f. generator uses some
physical principle to create an
excess of electrons at one terminal
and a deficit at the other. This
requires energy
conductor
+ terminal
(electron
deficit)
e.m.f.
generator
+
electric field
energy
Electrical conductors transfer the
potential difference to the device
(more later …!)
potential
difference
- terminal
(electron
excess)
When electrons move in the
device electrons flow from the
negative terminal to the positive
terminal.
Energy has been transferred
from the e.m.f. generator to the
K.E. of electrons
Lecture 3
2
1
How can we generate e.m.f.? : 1
• Dynamo, generator
– Rotary energy from a petrol engine,
turbine etc. moves a conductor in a
magnetic field
– Mains power – we can use a
POWER SUPPLY to create the
e.m.f. we need
• Solar cells
– Ultraviolet photons from the sun create electrons directly in
silicon
• Thermo-electric generator
– Temperature difference between junctions of different metals
generates electron excess Lecture 3
3
How can we generate e.m.f.? : 2
• Fuel cell
– Recombining H2 and O2 to make water releases
extra electrons (energy is needed to separate H2 and
O2 in the first place)
• Chemical battery
– Chemical reactions transfer electrons
Lecture 3
4
2
Batteries
• Store a fixed amount of charge (in the form of chemical
energy)
– So they run down
• Cannot supply an unlimited current (more later)
A battery with a stored charge Q can supply a current I for how long?
Lecture 3
5
The ideal battery: 1 Voltage source
• We will see that (for physicists!) it does not matter
exactly how the e.m.f. is generated
• We will represent our e.m.f. generator as an ideal
battery
– E.m.f. is constant independent of the current supplied
– Capable of supplying any current indefinitely
Circuit symbol
Lecture 3
6
3
The ideal battery: 2 Current source
• A device which provides a constant current
INDEPENDENT OF THE VOLTAGE
REQUIRED TO DO THIS
Circuit symbol
Lecture 3
7
Things you can’t do with ideal sources
V1
V2
I1
Connect voltage sources in
PARALLEL
I2
Connect current sources in
SERIES
Lecture 3
8
4
Electrons in conductors:1
Two states of the outer electrons
1. Valence electrons
These are responsible for holding
the metal together – very tightly
bound to the atoms
2. Conduction electrons
“Left over” from chemical bonds
Loosely bound to atoms and can
drift through the lattice
Lecture 3
9
Electrons in metals:2
• Drifting electrons have
many collisions.
• Electrons do not accelerate
but reach a constant
average “drift” velocity
proportional to the applied
field
Electron
velocity
Free
electron
Electron
in metal
v = μE
where μ is the electron mobility
in the metal (units m2 V-1 s-1)
Average
velocity
time
Mobility depends on the chemical and physical form of the
material and on temperature
Lecture 3
10
5
Resistance
Now we can calculate the current that passes through a block
of material if you apply a potential difference across it
Area A
v
Electrons / second:
dn
n=
dt
dn
n=
dt
E
ne A μ E
ne A μV
l
Charge / sec (= current)
l
V
i = ne μ e ⋅
A
⋅V
l
This is OHM’S LAW: Current is proportional to applied voltage
Lecture 3
11
Georg Simon Ohm
(1789 – 1854)
Discovered Ohm’s law in 1829
(experimentally) at the University of
Cologne.
The Prussian Minister of Science thundered
that
“… any professor who preaches such heresy
is unworthy to teach science!”.
Ohm resigned his professorship, went into
exile and eventually settled in Bavaria
Lecture 3
12
6
Resistance and Resistivity
i = ne μ e ⋅
A
⋅V
l
V
w here
R
ρl
and
R=
A
1
ρ =
ne e μ
i=
R is a property of the
conductor called
RESISTANCE
[Symbol in equations r, R.
Units OHMS, symbol Ω]
Resistance depends on the
shape of the conductor
(cross section area, A,
length, l) and the properties
of the material, ρ
ρ is the RESISTIVITY of
the material [units
OHM.METRE, Ω m]
V
Ohms law again: volts = amps x ohms
I
Lecture 3
R
13
Calculating resistance
Material
Resistivity
(ohm.m)
Silver
1.59 x 10-8
Copper
1.68 x 10-8
Aluminium
2.69 x 10-8
Iron
9.71 x 10-8
Platinum
10.6 x 10-8
Nichrome*
Carbon (graphite)
Glass
Rubber
Quartz
1.0 x 10-7
3 – 60 x 10-5
1 – 10000 x 109
1 – 100 x
1013
7.5 x
1017
A
R=
ρl
l
A
Example: resistance of 1 m. of 1mm
diameter Pt wire:
A = π r 2 = π (0.5 × 10−3 ) 2 = 7.85 × 10−7 m 2
R=
ρl
A
=
10.6 × 10−8 × 1.0
= 0.135 Ω
7.85 × 10−7
*Nichrome – an alloy of Ni, Fe and Cr
used for making resistor wire
Lecture 3
14
7
Resistors
R
Components designed to have a well defined
value of resistance are called RESISTORS
These can be made of carbon,
metal film or metal wire
R
Circuit symbols
The values of small resistors are often indicated by
coloured rings (the colour code).
http://www.dannyg.com/examples/res2/resistor.htm
has a nice graphical calculator
Lecture 3
15
Connectors, wires
•We will assume that all the components we use are
connected together by ideal conductors of ZERO
resistance (so we can ignore them – not always true in
real life!)
• Real connectors are usually
copper wire (low resistivity,
comparatively cheap) or
copper foil printed in a
pattern onto an insulating
sheet (printed circuit board,
PCB)
Lecture 3
16
8
Energy in resistors
Each time an electron in a conductor collides
with another electron in the material, it loses
kinetic energy.
This energy is eventually transferred to the
lattice – HEAT!
I
The power dissipated in a resistor is equal to
the energy drawn from the power source:
W = VI watts
watts = volts x amps
V
Conservation of energy: In any circuit the power dissipated
in the resistors is ALWAYS equal to the power drawn from the
Lecture 3
batteries
17
Summary of formulae so far …
Q = It (for constant current)
V = IR; I = V / R; R = V / I (Ohm's law)
P = IV
(Power in a resistor)
P = I 2R
P =V2 / R
Lecture 3
18
9
Measuring devices
I
A
An AMMETER is inserted into a
circuit to measure current. Ideal
ammeter has ZERO RESISTANCE
(introduces no voltage drop)
V
V
A VOLTMETER is used to measure the
potential difference across a component.
An ideal voltmeter has INFINITE
RESISTANCE (draws no current)
Lecture 3
19
I-V curves
V
V
I
A
X
We can learn a lot about a component by plotting its I-V curve
I
ideal
resistor
(low R)
ideal
resistor
(high R)
I-V curve is LINEAR (only two
points required)
I
REAL resistor:
R increases
when resistor
gets hot
V
V
Lecture 3
NON-linear I-V curve – several
points required
20
10
I-V curves - active and passive
I
2
1
VI< 0
VI > 0
V
VI > 0
VI< 0
3
4
In quadrants 1 and 3:
• VI > 0
• Current flowing in the same
direction as applied voltage
• Energy is dissipated in the
component
• Passive (e.g. resistor)
In quadrants 2 and 4:
• VI < 0
• Current flowing against the
applied voltage
• Energy is supplied by the
component
• Active (e.g. battery or current
source)
Lecture 3
21
I-V curves - Sources
I
V
I
V
Voltage source (battery)
• Voltage is constant independent of current
• When current has the same sign as
voltage, battery is absorbing energy
Current source
• Current is constant independent
of voltage
• When voltage has the same sign
as current, source is absorbing
energy
Lecture 3
22
11