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1. • Charge and current
2.1
• Potential difference, e.m.f. and power
2.2
• Current-potential difference relationships
2.3
• Resistance and resistivity
2.4
• Electric circuits
2.5
1

2. Electric Electric
I=nAve
charge current
Definition by Understanding
Definition
its formula formula
Different units,
Units Drift velocity
conversion
Number of
Metals,
elementary
semiconductors
charges
and insulators
flowing?
2. DC Electricity 2

3. Electric charge is a fundamental conserved
property of electrons and protons that gives rise
to electrical forces
Charge on protons is called positive and that on
electrons is called negative
All matter is made of atoms that contain protons
and electrons. Charges from the same number of
electrons and protons are canceled out
Different number of protons and electrons make a
body to be positively or negatively charged
2.1. Charge and current 3

4. 2.1. Charge and current 4

5. 2.1 Charge and current 5

6. Rate of flow of
charge
I=ΔQ/Δt • Quanity of charge
flowing past a given
point per unit time
2.1. Charge and current 6

7. 1nA=10-9A
SI current
unit=Ampère=A
1μA=10-6A Flow of a charge of 1A=1C/1s
1C through a given
point in 1 second
1mA=10-3A
2.1. Charge and current 7

8. Current
passing
Time through
flowing
e
Number of e
2.1. Charge and current 8

9. 2.1. Charge and current 9

10.  This velocity is not that of the electromagnetic
wave travelling but that of the carriers in the
material where the current is passing through. It is
normally very slow.
 Two samples of the same material but different
cross sectional areas in series will have the same
current passing through, so the one with the
smaller area will have a higher drift velocity to
compensate.
 Two sample with the same section but from
different material in series will have the same
product “nxv”. The higher number of carriers the
slower drift velocity.
2.1. Charge and current 10

11. • n≈1028m-3 or higher
• Increasing T, n remains constant, but atoms
Conductors vibrate stronger and so passing current
through is harder. Resistance increases.
• n≈1019m-3
• Increasing T (or adding impurities), n
Semiconductors increases very much and so current is
easier to flow. Resistance decreases.
• n≈0
Insulators • No current passes through them. (in normal
conditions)
2.1. Charge and current 11

12. Introduction Power
Potential Electrical
energies power
Electrical
potential Relationships
energy
Potential
difference
and e.m.f.
DC Electricity 12

13. Potential energy: Capability of a body to
do workt due to its position inside a
field.
Gravitational Electrical potential
potential energy: that energy: that which a
which a mass has just charge has just for
for being near a big being near a big
mass that creates a charge that creates
gravitational field. an electric field.
(Earth) (mgΔh) (Cell) (qEΔd)
2.2.Potential difference, electromotive force and power 13

14. Dividing the • Potentialdifference
energy of a (p.d.)
charge by • Electromotive force
its charge:
(e.m.f.)
Volt (V) • SI Unit
J=CV
• Relationship
between units
2.2.Potential difference, electromotive force and power 14

15. Potential difference
Electrical Other forms
energy of energy
Electromotive force
2.2.Potential difference, electromotive force and power 15

16. E=QV
• From
mechanics
• P=VQ/Δt
• Work≡Energy • Electrical • Q/Δt=I
Energy
P=W/Δt P=VI
2.2.Potential difference, electromotive force and power 16

17. P=VI E=QV P=E/Δt I=Q/Δt
2.2.Potential difference, electromotive force and power 17

18. P=VI
Q/Δt=I V=E/Q
P=VQ/Δt P=EI/Q
E=VQ I/Q=1/Δt
P=E/Δt
2.2.Potential difference, electromotive force and power 18

19. E=QV
IΔt=Q V=P/I
E=VIΔt E=QP/I
P=VI Q/I=Δt
E=PΔt
2.2.Potential difference, electromotive force and power 19

20. V=E/Q
PΔt=E Q=IΔt
V=PΔt/Q V=E/(IΔt)
1/I=Δt/Q E=PΔt
V=P/I
2.2.Potential difference, electromotive force and power 20

21. Q=IΔt
E/P=Δt I=P/V
Q=IE/P Q=PΔt/V
1/V=I/P PΔt=E
Q=E/V
2.2.Potential difference, electromotive force and power 21

22. I=Q/Δt
P/E=1/Δt Q=E/V
I=PQ/E I=E/(VΔt)
1/V=Q/E E/Δt=P
I=P/V
2.2.Potential difference, electromotive force and power 22

23. Δt=Q/I
V/P=1/I Q=E/V
Δt=QV/P Δt=E/(VI)
E=QV VI=P
Δt=E/P
2.2.Potential difference, electromotive force and power 23

24. Introduction I-V graphs
Resistance Ohmic materials
Tungsten
Ohm’s law
filament lamps
Semiconductors
diodes
DC Electricity 24

25. Resistance
It can be
The resistance defined as the
of an electrical quotient
component is a between the R=V/I
measure of its potential Unit “Ohm” (Ω)
opposition to an difference Ω=VA-1
electric current across it and
flowing in it the current
through it
2.3. I-V Relationships 25

26. Under certain conditions, current
is proportional to the potential
difference
V/I is constant, so R is constant
Components that obey Ohm’s law
are called “ohmic components”
Ohm’s law≠Resistance
2.3. I-V Relationships 26

27.  I-V graphs show how current behaves when
voltage varies.
 Knowing that “V=IR” we can realise that
“I/V=1/R”
 The “gradient”(slope) for a point in these graphs
shows the value for “1/R” at its certain
conditions.
 The bigger the gradient the lower resistance.
 The smaller the gradient the higher resistance.
2.3. I-V Relationships 27

28. Ohmic
components:
Resistors Tungsten Semiconductors
Conductors filament lamps diodes
(under certain
conditions)
2.3. I-V Relationships 28

29. Conductors. (In normal conditions)
• Constant slope means constant
resistance.
2.3. I-V Relationships 29

30. Conductors.
• For values of V close to zero, normal
conditions. So, (almost)constant slope and
(almost)constant resistance.
• For values of V far from zero, T increases
and resistance increases (as we saw from
I=nAve). Then slope gets smaller
2.3. I-V Relationships 30

31. Semiconductors. (under special configuration)
• For negative values of V, no current is
allowed to pass through, so I=0.
• For positive values of V, (as semiconductor
has impurities) n⇈ and so resistance
decreases. Hence the gradient increases
2.3. I-V Relationships 31

32. 2.3. I-V Relationships 32

33. Resistance Resistivity
Material
Resistor
property
Power
dissipated Units
by a resistor
DC Electricity 33

34. • Every electrical
component, no matter its
function, has a certain
resistance. (R=V/I)
• Those components that
have no other purpose than
make current harder to
pass through it are called
“resistors”.
Resistors are
usually
symbolised by…
2.4. Resistance and resistivity 34

35. P=VI
I=V/R V=IR
P=V2/R P=I2R
I2=V2/R2
Every component in a circuit will dissipate power (energy per unit
time)
This power can be shown in these 3 different ways
For a resistor, the more power it dissipates the higher temperature
it gets
2.4. Resistance and resistivity 35

36. Two wires of the
same material
Wire1 (Resistance=R1)
Wire1 has length l and a cross
section area A
Wire2 (Resistance=R2)
Wire2 has length l2>l and
cross section area A
R2>R1 R∝l The longer the resistor, the
higher resistance
2.4. Resistance and resistivity 36

37. Two wires of the
same material
Wire1 (Resistance=R1)
Wire1 has length l and a cross
section area A
Wire2 (Resistance=R2)
Wire2 has length l and cross
section area A2>A
The wider the resistor,
R2<R1 R∝1/A the lower resistance
2.4. Resistance and resistivity 37

38. Two wires of
different materials
Wire1 (Resistance=R1)
Wire1 has length l and a cross
section area A
Wire2 (Resistance=R2)
Wire2 has length l and cross
section area A
R depends
R2≠R1
on material
2.4. Resistance and resistivity 38

39. R=(constant)x(l/A)
This constant is a property of the
material and is called resistivity (ρ)
ρ=RA/l so units for resistivity ρ≡Ωm
Resistivity is different for each material (bigger for insulators,
smaller for conductors)
Resistivity in a material changes depending on conditions
2.4. Resistance and resistivity 39

40. Increasing temperature, terms in I=nAve are affected as follows:
Conductor Semiconductor
n constant n⇈ Exponential increase of charge carriers
A constant A constant
Because of the lattice vibrations v ↓ v↓ Because of the lattice vibrations
e constant e constant
I∝v I↓ I↑ I∝nv
So R↑ So R↓
In a conductor, resistivity increases if temperature increases
Conductors have a positive temperature coefficient
In a semiconductor, resistivity decreases if temperature increases
Semiconductors have a negative temperature coefficient (NTC)
NTC resistors are called thermistors. Symbolised by
2.4. Resistance and resistivity 40

41. Conductor Resistor
R
Thermistor
R
Positive Temperature Coefficient Negative Temperature Coefficient
(PTC) (NTC)
The great dependence with temperature of thermistors makes
them very useful as temperature sensors
2.4. Resistance and resistivity 41

42. Circuit
Cells Applications
components
Using
Components Internal
voltmeters and
table resistance
ammeters
Conservation
of energy and Resistors
Solar cells
charge in configurations
circuits
Potential
divider
DC Electricity 42

43. Cell, battery
(longer=positive)
Resistor
(Conductor)
Diode
In every
(semiconductor) component will be
Variable resistor a potential
(can vary from 0 to R)
difference fall
Thermistor when current
(NTC)
passes through it
Filament Lamp
(dissipates much heat)
Ammeter
(R≈0)
Voltmeter
(R≈∞)
2.5. Electric circuits 43

44. Cell
Component 1 Component 2 Component 3
Energy Energy Energy
Electrical
dissipated dissipated dissipated
energy
by by by
converted in
component component component
the cell
1 2 3
This means, in terms of energy per unit charge:
ε= Vi= Iri
Electromotive force of the cell=sum of potential difference in every component
2.5. Electric circuits 44

45.  For every point in a circuit, the current “in”
must be the same as the current “out”
Ii→ A Io→ For every single wire, the
For point A Ii=Io current passing through it
will be constant
I2→
I1→ I1→ For point A I1=I2+I3
A B
I3→ For point B I2+I3=I1
VA-VB is the same for both wires
2.5. Electric circuits 45

46.  An ideal cell would give all the electric
energy converted without dissipate any at all
 This is, in fact, not possible. Real cells loose
energy by themselves
 The real value of the potential difference
given by a cell is shown as: V=ε-Ir
 Where ε is the electromotive force given by
the cell, I is the current passing through it
and r is known as internal resistance
2.5. Electric circuits 46

47. V=ε-Ir
Connecting the cell directly to a voltmeter will
give a reading of ε because the high resistance
of the voltmeter will make I≈0 and then V≈ε
Connecting the cell in series with a resistor
will give a reading different to ε due to the
presence of a current flowing through the
internal resistance. A reading≠0
2.5. Electric circuits 47

48. Repeating the readings for several different resistances (a variable
resistance can be used to do this) will allow us to get a V-I graph
that will look like:
ε
V
I
As the straight line must obey the equation V=ε-Ir, the y
intercept will show ε and the gradient will show -r
2.5. Electric circuits 48

49.  Efficiency (E) of a component is defined as
the quotient between the energy given by it
and the energy needed to give it
 For a cell we can express this as E=V/ε
 But we saw before that V decreases in a cell
when current increases
 Efficiency of a cell decreases when current
increases
 To get a good efficiency of a cell we must
take care about “r” of the cell being very
lower than the resistance in the circuit (so
the effect of “r” will be very small)
2.5. Electric circuits 49

50.  These are a special kind of cells, also called
photovoltaic, made of a semiconductor
material
 They work following the photoelectric effect
 e.m.f. of these cells are constant (as normal
cells)
 Internal resistance in solar cells is only
constant for low intensities
 For larger intensities, internal resistance
increases significally
2.5. Electric circuits 50

51. In order to measure the current passing through a component an
ammeter has to be connected in series with it
To measure the voltage fall in a component we should connect a
voltmeter in parallel with it
•As resistance of the ammeter is very
close to zero, does not affect the
current passing through and does
not dissipate energy
•As resistance in the voltmeter is
very large (≈∞), it does not affect
current passing through the resistor
as it is in parallel with an infinite
resistance
Readings in A and V in this
configuration will show the
current and voltage of the
resistor
2.5. Electric circuits 51

52. Resistors in series:
is equivalent to
R1 R2 R=R1+R2
Resistors in parallel:
R1
is equivalent to
R=R1xR2/(R1+R2)
R2
For combinations of more than 2 resistors, just join two of them
in a equivalent one and go on step by step
2.5. Electric circuits 52

53. From conservation of energy in circuits we know that referring
to the next configuration:
VA-B VB-C VC-D V
If we connect wires A and B (or any other pair)
to another circuit, in fact, we are performing a
new cell with a lower potential difference
Different values for the resistors will arrange
different voltage values (always lower than V)
An “ideal” potential divider will allow us to take any possible
voltage value between 0 and V
This kind of potential divider can be done with a variable resistor
2.5. Electric circuits 53

54. There are two
kinds of variable
resistors
Rheostats:
Potentiometers:
Resistor can be
Three-terminal
changed but it has
variable resistor
only two terminals
2.5. Electric circuits 54

55. This is the
configuration for a
potentiometer that allow
to obtain all the possible
V voltage values by a
potential divider
Connecting any
component to VOUT we
can vary the voltage on
0≤VOUT≤V it in all the range
2.5. Electric circuits 55