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Electric Current
Unit 3
Batteries
• A battery is a device that produces
electricity by transforming chemical
energy into electrical energy.
• There are many types of batteries, but
all operate on the same principle.
• We will examine the process behind a
simple, wet-cell battery.
Batteries
• A simple battery consists of
two rods of dissimilar metals,
called electrodes, immersed
in a solution called an
electrolyte.
• One electrode may be
constructed out of carbon.
• The part of the electrode not in
contact with the electrolyte is
called the terminal.
Batteries
• The sulfuric acid tends to
dissolve the zinc electrode.
• Zinc atoms break off from the
electrode and enter into
solution with the acid.
• Each zinc atom that dissolves
leaves behind two electrons
on the electrode.
Batteries
• As this process continues, the
zinc electrode becomes
negatively charged.
• As the acid gains more
positive zinc ions, electrons
are pulled off of the carbon
electrode, leaving it with a net
positive charge.
• This charge difference leads to
a potential difference
between the two terminals.
Batteries
• If the terminals are not connected,
only a little zinc is dissolved and the
potential difference is held constant.
• If the terminals are connected (say,
with a wire), charge can flow and
more zinc must be dissolved to
maintain the potential difference.
• This continues until the zinc
electrode is completely dissolved.
• The battery is then “dead.”
Batteries
• The potential difference a battery can
maintain depends on the materials the
electrodes are made of.
• If two batteries are connected such that the
positive terminal of one is connected to the
negative terminal of the other, the batteries
are connected in series.
• The voltages of two batteries connected in
series add.
Electric Current
Electric Current
• The purpose of a battery
is to create a potential
difference (voltage).
• Voltages cause charges to
move.
• When charges are
moving, we say there is
an electric current.
Electric Current
• More precisely, electric current is
defined as the amount of charge that
passes through the full cross section of
wire in a small amount of time.
• Mathematically, this is
Electric Current
Amount of
charge
Time interval
Electric Current
• Current is measured in coulombs per second
(C/s).
• This unit is known as the ampere (A).
• Ampere is often abbreviated as just amp.
• Often, we will have currents much smaller
than an ampere, usually on the order of a
milliampere (mA) or a microampere (A).
Electric Current
• WARNING: Electric current can only flow
when there is a continuous conducting path.
• This is called a complete circuit.
• If there is a break in the circuit, we call it a
open circuit.
• If a circuit is complete, but has no load, it is
called a short circuit.
Electric Current: An Analogy
Conclusion: Batteries do not
create charge, lightbulbs do not
destroy charge.
Example: Current
A steady current of 2.5 A exists in a wire for 4 minutes.
a) How much total charge passed through a point in
the circuit in this time?
b) How many electrons would this be?
Conventional Current
• When electric current
was defined, it was
assumed that positive
charges were what was
moving through the wire.
• As a result, electric
current was defined to
flow from the positive
terminal to the negative
terminal.
Conventional Current
• However, we know that
electrons are the mobile
charges in the circuit.
• As a result, charge actually
flows from the negative
terminal to the positive
terminal.
• We still use the original
definition of current, called
the conventional current.
Homework
• Read sections 18-1 and 18-2.
• Do problems 1-3 all on page 515.
Resistance
Ohm’s “Law”
Current and Voltage
• We have learned that a voltage is needed to
produce a current in a wire.
• It was discovered early on that the amount of
current flowing through the wire is
proportional to the voltage.
• So a 6 V battery produces twice the current of
a 3 V through the same piece of wire.
Water Analogy Revisited
Resistance
• The current flowing through a wire depends
not only on the size of the wire, but also on
the resistance it offers to the flow of electrons.
• The greater the resistance, the less current
for a given voltage.
• This relationship can be described
mathematically:
V
R=
I
Resistance
V
R=
I
• R is called the resistance of the
material.
• Notice that R and I are inversely
related. As R increases, I decreases.
Ohm’s “Law”
• The equation for resistance is often
written as
V = IR
• This is known as Ohm’s law.
• This is not a fundamental law of nature.
• It is only true for a certain class of
materials (usually metals), where R is a
constant and does not depend on
voltage.
Ohm’s Law
• Materials that obey Ohm’s Law are
called ohmic materials. Materials that
do not are called nonohmic.
• Resistance is measured in V/A.
• This unit is called an ohm ()
Example
A small flashlight is powered by a 1.5 V battery. If the
lightbulb draws 300 mA of current, what is the resistance of
the bulb?
Suppose the battery begins to run low and the voltage drops
to 1.2 V. What would be the new current in the circuit?
Resistors
• Any component of an electric circuit has
a resistance to the flow of current.
• Wires generally have very low
resistances, while items such as
lightbulbs and heaters have much
higher resistances.
Resistors
• We have already seen that the current
through a circuit depends on the
resistance.
• In electronics, resistors with known
values of resistance are used to control
the amount of current in the circuit.
Resistors
• Resistors can be found that range from
less than an ohm to millions of ohms.
• On a circuit diagram, a resistor is
represented with the symbol
Conceptual Example
A current I enters a resistor R as shown.
a) Is the potential higher at point A or point B?
b) Is the current greater at point A or point B?
Resistors
• In a circuit, the electric potential on one
side of the resistor is greater than on
the other.
• This makes sense, as energy is needed
to push the current past the resistance.
• We say there is a voltage drop across
the resistor.
Some Clarifications
• A battery maintains a constant voltage
between its two terminals. It is a
voltage source.
• Voltage is applied across a wire or
circuit element. Voltage increases
across a battery, and drops across a
resistor.
Some Clarifications
• Electric current passes through a wire
or circuit element.
• The amount of current that flows
depends on the resistance of the
device.
• Resistance is a property of the device.
It does not depend on I or V.
Some Clarifications
• Conventional current flows from high potential
(+) to low potential (-).
• Electrons actually flow in the opposite
direction of the conventional current.
• Current and charge do not increase,
decreased, or get used up. The amount of
charge that goes into one end of the circuit
comes out the other.
Homework
• Read 18-3.
• Do problems 5, 7, and 9 on pages 515516.
Resistivity
Resistivity
• We learned yesterday that resistance is
a property of the material.
• Scientists quickly asked what aspects of
the material determine its resistance to
electric current.
Resistivity
• Through experiments, scientists determined
that resistance was directly proportional to
the length of the resistor.
• They also determined that it was inversely
proportional to the cross-sectional area of
the resistor.
L
A
Resistivity
• Mathematically, this is described in the
relationship
L
R=r
A
• The constant  (rho) is known as the
resistivity of the material.
• Resistivity is measured in units of m, and
its value depends on the material.
Resistivity
• We generally look up resistivity in a table.
• Lower values indicate lower resistances.
Example: Speaker Wires
You are setting up your speakers for your stereo system.
In order to get the optimal sound, you want the wires
(made of copper) to each have a resistance of no more
than 0.10 .
a) If each wire must be 20 m long, what diameter
of wire should be used?
b) If the current in the wire is 4.0 A, what is the
potential drop across the wire?
Temperature and Resistivity
• Resistance is also dependent on
temperature.
• At higher temperatures, the atoms are
moving more rapidly and in a less
orderly fashion.
• This results in a greater interference
with the current.
Temperature and Resistivity
• Therefore, resistivity increases as
temperature increases in most
materials.
• The main exception to this rule is
semiconductors.
Problems
• Do problems 12, 13, 14, and 16 on
page 516.
• We will whiteboard these problems at
the end of class.
Whiteboarding Groups
Group
1
2
3
4
5
6
7
Members
Drew, Abbey, Aidan
Sarah, John, Angi
Rachel, Ellen, Connor
Miggy, Bailey, Armen
Anthony, Brie, Robert
Krystiana, Jacob
Piper, Jeremiah, Kaleb
Problem
5
7
9
12
13
14
16
Homeowork
• Do problem 21 on page 516.
• This is the only problem I am assigning
tonight. I expect you to put a full 30
minutes of effort into this problem.
Power
Power
• In physics, power is defined as the rate
at which work is done.
• An alternative definition is the rate at
which energy is transferred.
Power
• If power is not being delivered at a constant
rate, we need calculus to find it.
• However, we can define average power.
energy delivered
P=
time
• In DC circuits, power is delivered a constant
rate, so average power is also the power at
any instant.
Power
• In an electric circuit, we have charges
moving through a potential difference
across a wire.
• We learned in Unit 2 that these charges
have potential energy given by
U = qV
Power
• Since the charge is continually moving,
it makes more sense to talk about
power rather than energy.
• We often want to know how much
energy is being delivered to a device in
a circuit by the moving charges.
Power
• Recall the definition of power:
energy delivered
P=
time
• For one charge, the energy delivered is
QV. However, we have many charges
flowing, so the energy is
Power
• So, the power delivered in a time t is
• But notice that Q/t is the current
through the wire (I). So, the power
delivered by the circuit is
P = IV
Power
• We can also combine this formula with
Ohm’s Law.
P = IV
V = IR
• With this, we can get two other expressions
for power
P=I R
2
V
P=
R
2
A Quick Warning
P=I R
2
V
P=
R
2
• These alternate equations are only true
for the power delivered to a resistor.
• However, P=IV is true for any part of the
circuit.
Power
• The unit of power is a J/s.
• This is known as a watt (W).
• However, you usually pay for electricity in
terms of energy. This is power times time.
• Energy companies usually measure energy in
kilowatt-hours (kWh).
1 kWh = 3.6 ´10 J
6
Example
A typical headlight bulb in a car draws 40 W of power. If the
light draws its power directly from a 12 V car battery,
a) Calculate the current flowing through the bulb.
b) Calculate the resistance of the bulb.
Example
An electric heater draws a current of 15 A from a standard
120 V wall socket.
a) How much power is delivered to the heater?
b) If the heater is operated 3 hours a day for a 30 day
month, how much does it cost to operate the heater?
Assume electricity costs 9.2 ¢/kWh.
Homework
• Read 18-5.
• Do problems 27-33 odd on pages 516517.
Homework
• Do problems 26-32 even on pages 516517.
Household Electricity
Lightbulbs, Fuses, and Circuit
Breakers
Lightbulbs
• A lightbulb is a device that converts
electrical energy into light (and heat).
• There are two types of lightbulbs.
– Incandescent
– Fluorescent
Incandescent Bulbs
• In an incandescent
bulb a current is
passed through a
filament encased in
an evacuated glass
bulb.
• The filament quickly
becomes hot and
begins to glow.
Incandescent Bulbs
• Since the filament is
glowing, it gives off
light.
• It also gives off a
great deal of heat.
• In order to make the
filament glow
sufficiently brightly, a
fair amount of power
is needed.
Fluorescent Bulbs
• Fluorescent bulbs operate
on a different principle than
an incandescent.
• A fluorescent bulb is filled
with a gas (usually Argon).
• When the bulb is connected
to a battery, some of the
gas molecules become
ionized.
Fluorescent Bulbs
• Current is able to flow
throughout the tube.
• As electrons flow, the
sometimes strike other gas
molecules.
• This collision excites at
least one electron in the
molecule to a higher
energy level.
Fluorescent Bulbs
• As the excited electron
returns to its original
energy level, it releases its
excess energy as a
photon.
• The color of the light
depends on the how much
the electron was excited.
• Fluorescent bulbs have a
coating to control the color
of light emitted.
Fuses and Circuit Breakers
Fuses
• Although wires generally have very low
resistance, their resistance does cause
some electrical energy to be lost as
heat.
• The rate of heating is equal to the
power delivered through the wire.
P=I R
2
Fuses
• If the current is very
large, the wire can
heat up to the point
of becoming a fire
hazard.
• A fuse is a piece of
metal placed in the
circuit.
Fuses
• The metal in the fuse
melts when the
temperature in the
circuit gets too high.
• When the fuse melts,
the circuit is broken,
thereby preventing a
fire.
Circuit Breakers
• A circuit breaker operates on a similar principle.
• When the temperature gets too hot, the
bimetallic strip bends and the circuit is broken.
Circuit Breakers
• Circuit breakers are generally preferable because
they can be reset without being replaced.
• When a fuse has been blown, it must be replaced
with a new fuse in order for the circuit to function.
Homework
• Read 18-6.
• Do problems 35, 37, and 39 on page
517. Check your answers with the back
of the book.