Transcript Document

Electric Current and
Resistance
English/ Italian glossary
Current
corrente
Circuit
circuito
Charge
carica
Potential
potenziale
Voltage
Voltaggio = differenza di potenziale
Battery
batteria
Switch
Interruttore
Net
rete
Wire
Filo (conduttore)
Copper
Rame
Ammeter/Voltmeter
Amperometro/voltmetro
Drift
deriva
Plate
piastra
Positive/negative terminal
Polo positivo/negativo
electron
elettrone
Electric field
Campo elettrico
Resistor
resistore
Resistance
resistenza
Series/parallel
Serie/parallelo
Which of these connections could work to
light the bulb?
The Central Concept: Closed
Circuit
circuit diagram
Scientists usually draw electric circuits using symbols;
cell
lamp
switch
wires
Electric Circuit
Diagram of Electric Circuit
Remember: Electric Potential EnergyTwo Unlike Charges
Higher Potential
Energy
+
Lower Potential
Energy
-
•To cause movement of a charge,
there must be a potential difference.
While the switch is open:
• Free electrons (conducting electrons) are
always moving in random motion.
• The random speeds are at an order of
106 m/s.
• There is no net movement of charge across a
cross section of a wire.
What occurs in a wire when the
circuit switch is closed?
What occurs in a wire when the
circuit switch is closed?
• An electric field is established
instantaneously (at almost the speed of
light, 3x108 m/s).
• Free electrons, while still randomly moving,
immediately begin drifting due to the
electric field, resulting in a net flow of
charge.
• Average drift velocity is about 0.01cm/s.
Closing the switch establishes a potential difference
(voltage) and an electric field in the circuit.
• Electrons
flow in a
net
direction
away from
the (-)
terminal.
Low
Potential
High
Potential
Question:
• If the drift velocity is about 0.01cm/s, why
do the lights turn on instantaneously when
the circuit switch is closed?
Conventional Current
• By tradition,
direction in
which
“positive
charges”
would flow.
• Direction is
opposite of
electron
flow.
Question:
What is required in order to have an
electric current flow in a circuit?
Answers:
1. A voltage source.
2. The circuit must be closed.
Battery (Chemical Cell):
• A device that converts chemical energy to
electricity.
• A battery provides a potential energy
difference (voltage source).
Electric
Current:
• The flow of
electric
charges.
Electric Current, I
I = Dq
Dt
• Rate
• Unit: Coulomb / sec = Ampere
• Andre Ampere (1775-1836)
(A)
Conventional current has the
direction that the (+) charges
would have in the circuit.
TWO TYPES OF CURRENT
• Direct Current • Alternating
Current
• DC
• Provided by
• AC
batteries
• Provided by power
companies
MEASUREMENT DEVICES
:1) Ammeter
• Measures electric current.
• Must be placed in series.
2) Voltmeter
• Measures the
voltage between
two points in an
electric circuit.
• Must be
connected in
parallel.
Example:
• What charge flows through a cross
sectional area of a wire in 10min, if the
ammeter measures a current of 5mA?
• Answer: 3C
RESISTANCE
It is known from experiment that the
current flowing in a conductor is directly
proportional to the potential difference
across it.
The constant of proportionality, R, is
called the RESISTANCE
R = DV / I
(resistance equals the ratio of voltage to current)
Unit: Ohm (Ω)
1 Ω = 1 V/A
Ohm’s Law
I=V/R
I = Current (Amperes) (amps)
V = Voltage (Volts)
R = Resistance (ohms)
I
Georg Simon Ohm (1787-1854)
Gradient 
I
1

V R
V
A device that obeys Ohm’s Law is called a ohmic resistor
(its resistance does not depend on the voltage)
The current through an ohmic
conductor is:
• directly proportional to the voltage
across it (over a limited range of V)
(more voltage more current)
• inversely proportional to the
resistance of the conductor
(the greater the resistance  the less the current)
But what is resistance?
It is a measure of how much a conductor
impedes the flow of current
At the molecular level, electrons undergo
frequent collisions with the ions of materials.
The higher the number of collisions, the
higher the resistance of the material is.
 It’s a sort of friction, an opposition to the flow of
current
Resistor
• An object that
has a given
resistance.
RESISTORS
Circuit symbol
(or the “zig-zag symbol)
R
Colour codes are used to identify resistance value
The Resistor
Colour Code
Colour
Number
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Grey
8
White
9
The four colour code bands are at
one end of the component.
Counting from the end, the first
three (or sometimes four or five)
bands give the resistance value and
the last the tolerance
TOLERANCES
BROWN
1%
RED
2%
GOLD
5%
SILVER
10%
NONE
20%
Example:
• Calculate the current through a 3 Ω
resistor when a voltage of 12V is
applied across it.
• Answer: 4 A
Example:
• A 6 Ω resistor has a power source of 20V
across it. What will happen to the
resistance if the voltage doubles?
Answer:
resistance doesn’t change!
Factors that affect resistance:
• Type of material
• Size and shape
• Temperature
Resistance
R=ρ L
A
(a.k.a. Ohm’s 2nd law)
L: length of the wire
A: cross-sectional area
ρ: resistivity (inherent to material)
Unit: Wm
RESISTIVITIES FOR CERTAIN MATERIALS AT 20°C
(measured in Wm)
Silver
Copper
Aluminium
Tungsten
Constantan
1.6 × 10-8
1.7 × 10-8
2.8 × 10-8
5.6 × 10-8
(alloy of copper and nickel)
49 × 10-8
Nichrome
100 × 10-8
(3 - 60) × 10-5
0.1 – 60
(1 - 500) × 10-3
1012
(alloy of nickel, iron & chromium)
Graphite
Silicon
Germanium
Pyrex glass
(semiconductor)
(insulator)
What is the best material?
The table of resistivity values shows
that, although silver has a low resistivity,
it is expensive to use in electrical
circuits.
Copper is the preferred metal although
aluminum is commonly used in
electricity transmission cables because
of its lower density.
Example:
Determine the resistance of a piece of copper wire
that is 10.0 m long and 1.2 mm in diameter.
Solution
The resistance, R, is given by the formula
R = ρL / A, where A = πr2.
This means that
R = (1.7 × 10-8 Ωm) (10.0 m) / π(6.0 × 10-4)2 m2 =
0.150 Ω.
The resistance of the copper wire is 0.15 Ω.
Question:
• What happens to the resistance when the
length is doubled and the area is
quadrupled?
Answer: It changes by 1/2
Temperature Dependence of Resistance
The resistance of a material increases with temperature
because of the thermal agitation of the atoms it contains,
and this impedes the movement of electrons that make up
the current.
Resistance increases because resistivity increases, as
shown in this formula:
rt = r20[1 + a(t -20°)]
where r20 equals the resistivity at 20 °C, rt is the resistivity at some
temperature, t °C, above the reference temperature, and a is the
temperature coefficient for the material being used.
SUPERCONDUCTIVITY
One interesting phenomenon of the effect of temperature
on resistance is superconductivity.
In 1911, H. Kammerlingh Onnes found that mercury loses
all its resistance abruptly at a critical temperature of 4.1 K.
When a material attains zero resistance at some critical
temperature, it is called a superconductor.
The possibility of having a material that has an induced
electric current that lasts forever has become a topic for
research physicists.
Just think of the energy saving if the perfect superconductor
is found that can give zero resistance at room temperature.
POWER DISSIPATION IN
RESISTORS
Electric power is the rate at which energy is
supplied to or used by a device.
It is measured in J/ s called watts (W).
When a steady current is flowing through a load
such as a resistor, it dissipates energy in it.
This energy is equal to the potential energy lost
by the charge as it moves through the potential
difference that exists between the terminals
of the load.
Some possible power ratings for
household appliances
If a vacuum cleaner has a power rating of 1500 W,
it means it is converting electrical energy to
mechanical, sound and heat energy at the rate of
1500 J/s.
A 60 W light globe converts electrical energy to
light and heat energy at the rate of 60 J/s .
Electric power
Basic definition of power: P = W/ t
Work / time
We know that W = q V and q = I t
P = q V/t = I t V/ t  P = V I
(V is the voltage)
And applying Ohm’s law: P= R I2 = V2 / R
UNIT OF ELECTRIC ENERGY
The commercial unit of electrical energy is
the kilowatthour (kW h).
It is the energy consumed when 1 kW of
power is used for one hour.
The consumer has to pay a certain cost per
kilowatt-hour.
--------------------------
Question: How many Joules in a kWh?
1 kWh = 1000 W x 3600 s = 3600000 J
= 3.6 x 106 J
HEATING EFFECT OF A CURRENT
(Effetto Joule)
It was investigated in 1841 by James Joule.
He was able to demonstrate that by supplying
electrical energy to a high resistance coil of wire this
energy could be converted to thermal energy.
V × I × t = m× c × ΔT
electric energy  heat = infrared radiation
Example
An electrical appliance is rated as 2.5 kW, 240 V.
(a) Determine the current needed for it to operate.
(b) Calculate the energy it would consume in 2.0 hours.
Solution:
(a)Given that P = 2.5 × 103 and V = 240 V, we use the
formula, P = IV  I = P/W = …10.4
So I = 1.0 × 101 A.
(b) Next, we use the formula W = VIt, so that
W =(240 V) x(10.4 A)x 7.2 103 s = = 1.8 × 107 J
The energy consumed is 1.8 × 107J.
Exercises
1) The element of an electric jug has a resistance
of 60 Ω and draws a current of 3.0 A. Determine by
how much the temperature of 5.0 kg of water will
rise if it is on for 6 minutes.
2) Calculate the cost to heat 200 kg of water from
12°C to its boiling point if power costs 14 cents
per kilowatt-hour.