Download Ch 18: Electric currents

Ch 18: Electric
currents
Charges in motion
How is this different from
static?
• Recall that a buildup of charges on an object is
called Static electricity. This buildup will
continue until an opportunity for discharge
arrives. THEN we SEE the discharge as a spark
(light lightning)
• In 1752 Benjamin Franklin’s famous “kite
experiment” showed that lightning is an
electric discharge- a giant spark.
Steady now…
• The transition from static electricity to flow of
electric charge was sparked by the invention
of the electric battery by Alessandro Volta
(1745-1827) in 1800.
• The steady electric current flowing
from this source transformed
our civilization.
Electric Battery
• The discovery of the battery came about as
a
result of an argument between Luigi Galvani and
Volta. In the 1780s Galvani connected 2 different
metals to a frog’s leg muscle and a static electricity
machine.
• Volta proved that the electricity was not due to the
animal cells, but rather due to two different metals
using the frog’s leg as an electrolyte. The source of
the electricity was in the different metals.
Alessandro Volta’s Pile (Battery)
• Volta found certain
combinations of metals
produced greater effects
than others. He listed an
“electrochemical series”
and found carbon could be
used in place of one metal.
• He put a piece of cloth
soaked in a salt solution
between 2 metals and
piled a “battery “ of such
couplings on top of each
other. This “pile” or
“battery” produced much
more potential difference.
Volta leads the
way
• Scientists eventually
realized the battery
produces electricity by
transforming chemical
energy into electrical
energy.
• Simplest batteries contain
2 plates (different metals)
called electrodes,
immersed in a solution
called the electrolyte. This
is called an electric cell.
• Several cells connected
together is called a
How does the battery
cell work?
• The electrodes “dissolve” in the acidic
electrolyte. Zn leaves behind 2 electrons and
enters the solution as “positive”. The zinc
electrode then acquires a “negative charge”.
• As the solution becomes more positive, it pulls
electrons off the carbon electrode, making it
acquire a “positive charge”.
• Opposite charges develop a potential difference
between the terminals and this is maintained until
a conductor is connected between them. (See pg
529)
How long will charge flow?
• After some time, one of the electrodes is used up
and the cell becomes “dead”.
• The voltage between the battery terminals
depends on what materials are used and their
ability to be dissolved or give up electrons.
• Connecting batteries so the positive terminal of
one touches the negative terminal of the other is in
“series” and their voltages add up.
Electric
Current
• An electric circuit is a continuous conducting path
between the terminals of a battery.
• A battery symbol is represented by
• Longer line = positive terminal, shorter = negative
terminal.
• A flow of charge through the battery and wires of a
complete path is called electric current.
Charge it up
• Electric Current in a wire is the net amount of
charge that passes through a wire per unit of
time at any point.
Q
• Average current, I is defined as I
t where
Q is the charge passing through the conductor
in any time interval t.
• Electric current is measured in
coulombs/second or amperes (abbrev amps or
A).
Conservation of Charge
• Charge doesn’t disappear when it flows
through a circuit.
• For any single circuit, the current at any instant
is the same at one point as it is at any other
point. This is the Conservation of Electric
charge.
• Current is the flow of charge through a circuit.
Example 18-1
• A steady current of 2.5A flows in a wire for 4.0
min. (a) How much charge passed through
any point in the circuit? (b) How many
electrons would this be?
18-1 Solution
• (a) Since the current was 2.5A or 2.5 C/s, then
in 4.0 mins (=240 seconds) the total charge
that flowed was Q I t
• ΔQ = (2.5 C/s) (240s) = 600 C
• (b) The charge on one electron is 1.60x10-19 C
so 600 C would consist of
600C
1.6 x10 19 C / electron
3.8 x1021 electrons
See Conceptual Ex 18-2
• What’s wrong with each scheme in trying to
light a light bulb with a flashlight battery and a
single wire? You try it…
• How many ways can this be done? Choose a
partner and figure it out.
Conduction, duction what’s
your function?
• Conductors contain many free electrons.
• When a potential difference (voltage) is established
across a circuit (complete closed conducting path), it is
electrons that actually flow in the wire.
• Conventions of electric current many years ago decided
conventional current is the direction positive charge will
move. (From + to -) but is equal to the negative charge
flowing from – to +.
Ohm’s Law: Resistance and Resistors
• Georg Simon Ohm (1787-1854) was the first to establish
experimentally that current, I, is directly proportional to
the potential difference, V, applied to the ends of a wire.
• One source of potential difference is a battery.
Current flowin’
• Compare current in a wire to the flow of water in a
river or pipe. In order to get current to “flow” a
difference in potential between the ends must
exist. (ie tip the pipe, gravity pulls water downhill.)
• How much current flows in a wire depends on the
voltage, but also on the resistance. More
resistance, like junk in a river, means less current.
Ohm’s Law: I
V
R
Ohm’s Law establishes a
relationship between
current, voltage, and
resistance in a circuit.
Current, I, is equal to
Voltage / Resistance.
Resistance is measured in
ohms.
Current is measured in
amps.
Potential difference is
measured in volts.
Example 18-3 Bulb Resistance
• A small flashlight bulb draws 300mA from its
1.5 V battery. (a) What is the resistance of the
bulb? (b) If the voltage dropped to 1.2 V, how
would the current change?
18-3 Solution
• (a) We use Ohm’s law and find R=V / I
• R = 1.5 V / 0.30 A = 5.0 Ω
• (b) If the resistance stayed constant, the
current would be approximately I = V / R
• I = 1.2 V / 5.0 Ω = 0.24 A
More on Resistance
• All electronic devices from wires to heaters to
stereo amplifiers to lights offer resistance to
the flow of current.
• In many circuits, resistors are used to control
the amount of current.
• Two main types of resistors are wire wound
resistors and composition resistors (which
have color codes marking levels of resistance.)
Your turn to Practice
• Please do ch. 18 Review pg 551 #s 1-10
Resistivity
• Resistance of a wire is directly proportional to its
length, L and inversely proportional to its crosssectional area, A. (A thicker wire has less
resistance because there is more room for
electrons to pass and a longer wire has greater
resistance because there are more obstacles to
electron flow.
• The third factor is a proportionality constant, ρ,
called resistivity, and depends on material type.
• Low R = good conductor.
R
L
A
Ex 18-4 Speaker Wires
• Suppose you want to connect your stereo to
remote speakers. (a) If each wire must be 20m
long, what diameter of copper wire should you
use to keep the resistance less than 0.10Ω per
wire? (b) If the current to each speaker is
4.0A, what is the voltage drop across each
wire?
18-4 Solution
• (a) We solve for the area A and use table 18-1
A
L
R
(1.68 x10 8 * m)(20m)
(0.10 )
3.4 x10 6 m 2
• The cross-sectional area of a wire is related to
its diameter by A=πd2/4. The diameter must
4A
then be at least
d
2.1x10 3 m 2.1mm
• (b) From Ohm’s Law, V=IR = (4.0A)(0.10Ω)=
0.40 V
Resistivity
• The resistivity of a material depends on
temperature in that resistance of metals
increases with temperature. At higher speeds,
atoms are moving faster and interfere with
each other more with the flow of electrons.
• There is a temperature coefficient of
resistivity, α, that is given in Table 18-1 for
various materials.
Electric Power
• Electric energy can be transformed into other
forms of energy such as thermal energy or
light because the current is large and many
collisions occur in tiny wire filaments or
heating elements. (Low resistances of up to a
few hundred ohms)
• During collisions KE of atoms increases and
thus temperature increases.
Electric Power
• Power is the rate at which energy is
transformed. P = (QV)/t.
• Recall charge flowing per second is current
I=Q/t so it follows that Power = I * V
• SI unit of Power is the same for any kind, watt.
(1W=1J/s)
• P=IV = I(IR) = I2R = (V/R)*V = V2/R
• Remember “PIVVIR” : P=I*V, V=I*R
Ex 18-7 Headlights
• Calculate the resistance of a 40 W automobile
headlight designed for 12 V.
• SOLN: R = V2/P
• R = (12V)2 / (40W) = 3.6Ω
• This is the resistance when the bulb is burning
brightly at 40 W. When the bulb is cold, the
resistance is lower and since the current is high,
most bulbs burn out when first turned on.
Electric Energy
• Our electric bill costs us money based on the
electric energy we use, not just power.
• Since Power is the rate energy is transformed,
electric energy is just Power * time the power
is used.
• E=P*t (kilowatt*hours) 1kWh=1000W*3600s
=3.6x106 J.
Ex 18-8 Electric Heater
• An electric heater draws 15.0A on a 120 V line.
How much power does it use and how much
does it cost per month (30days) if it operates
3.0 h per day and the electric company charges
10.5 cents per kWh?
• Solution: P=IV = (15.0A)(120V)= 1800 W
• To operate per month (3h/d)(30d)=90hrs so it
would cost (1.80kWh)(90h)($0.105)=$17.
Ex 18-9 Lightning Bolt
• A typical lightning bolt can
transfer 109 J of energy
across a potential difference
of perhaps 5 x 107 V during a
time interval of 0.2s. Use
this information to estimate
the total amount of charge
transferred, the current,
and the average power over
the 0.2s.
18-9 Soln
9
• Energy =QV so Q
10 J
5 x10 7 V
20 C
• The current over the 0.2s is about I
Q
t
20C
0.2s
100 A
• The average power delivered is Pavg = energy/time
P
10 9 J
0.2 s
5 x10 9 W
5GW
• Which can also be found by P=IV=100A(5x107 V)=5GW
Power in Household Circuits
• If current in wires gets too large, the wires get hot
(produce thermal energy at a rate of I2 R). Wires in
walls of a building can get so hot & start a fire.
• Buildings should be designed to handle any
expected load & prevent “overloading”. (Carrying
more current than is safe)
• Fuses and circuit breakers are devices used to help
prevent overloading. This occurs when too many
devices draw current in that area OR when wires are
faulty.
Household Power
• Household circuits are designed so every
device connected receives the standard
voltage (120V in the US).
• These circuits are typically arranged “parallel”
(more later).
• Total current in a circuit that “blows” should
be checked!
• Never replace a properly rated fuse with a
higher one!
Open circuits
• A blown fuse or breaker will “open” a circuit
so there is no longer a complete conducting
path and current will not flow.
Alternating Current
• When a battery is connected to a circuit, current
flows steadily in one direction. This is called direct
current, DC.
• Electric generators (power plants) produce
alternating current, AC.
• AC reverses directions many times each second and
is sinusoidal (creates sine wave) Current supplied to
homes and businesses around the world is ac.
AC
• AC voltage oscillates between –V0 and +V0 where V0
is referred to as peak voltage.
• As a function of time, the voltage can be found by
V=V0 sin2πft.
• The frequency, f, is the number of complete cycles
per second and in the US and Canada is 60 Hz.
Some countries use 50Hz.
Your turn to Practice
• Complete the wksh for series circuits given in
class.
• Please do Ch 18 Review pg 551 #s 11, 12, & 13
• Please do Ch 18 Review pg 552 #s 23, 24, & 27